FunctionIC

function

C++ Type:FunctionName

Controllable:No

Description:The initial condition function.

block

C++ Type:std::vector<SubdomainName>

Controllable:No

Description:The list of blocks (ids or names) that this object will be applied

boundary

C++ Type:std::vector<BoundaryName>

Controllable:No

Description:The list of boundaries (ids or names) from the mesh where this boundary condition applies

(test/tests/ics/function_ic/parsed_function.i)

#
# Test the automatically generated gradients in ParsedFunction and the gradient pass-through in FunctionIC
# OLD MOOSE behavior was for parsed_function to behave the same as parsed_zerograd_function
# NEW MOOSE behavior is for parsed_function to behave the same as parsed_grad_function
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 3.141
  ymin = 0
  ymax = 3.141
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Functions]
  [./parsed_function]
    type = ParsedFunction
    value = 'sin(x)-cos(y/2)'
  [../]
  [./parsed_grad_function]
    type =ParsedGradFunction
    value = 'sin(x)-cos(y/2)'
    grad_x = 'cos(x)'
    grad_y = 'sin(y/2)/2'
  [../]
  [./parsed_zerograd_function]
    type = ParsedGradFunction
    value = 'sin(x)-cos(y/2)'
    grad_x = '0'
    grad_y = '0'
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = 'u'
    function = parsed_function
  [../]
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[]

[Outputs]
  file_base = parsed
  [./OverSampling]
    type = Exodus
    refinements = 3
  [../]
[]

(test/tests/functions/image_function/crop.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  uniform_refine = 2
  xmin = 0.5
  ymin = 0.5
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    file_suffix = png
    origin = '0 0 0'
    dimensions = '1 1 0'
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/tensor_mechanics/test/tests/interface_stress/multi.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 10
  nz = 10
  xmax = 1
  ymax = 1
  zmax = 1
  xmin = -1
  ymin = -1
  zmin = -1
[]

[GlobalParams]
  order = CONSTANT
  family = MONOMIAL
  rank_two_tensor = extra_stress
[]

[Functions]
  [./sphere1]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2); if(r>1,0,1-3*r^2+2*r^3)'
  [../]
  [./sphere2]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2); 0.5-0.5*if(r>1,0,1-3*r^2+2*r^3)'
  [../]
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[AuxVariables]
  [./eta1]
    [./InitialCondition]
      type = FunctionIC
      function = sphere1
    [../]
    order = FIRST
    family = LAGRANGE
  [../]
  [./eta2]
    [./InitialCondition]
      type = FunctionIC
      function = sphere2
    [../]
    order = FIRST
    family = LAGRANGE
  [../]
  [./s00]
  [../]
  [./s01]
  [../]
  [./s02]
  [../]
  [./s10]
  [../]
  [./s11]
  [../]
  [./s12]
  [../]
  [./s20]
  [../]
  [./s21]
  [../]
  [./s22]
  [../]
[]

[AuxKernels]
  [./s00]
    type = RankTwoAux
    variable = s00
    index_i = 0
    index_j = 0
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    index_i = 0
    index_j = 1
  [../]
  [./s02]
    type = RankTwoAux
    variable = s02
    index_i = 0
    index_j = 2
  [../]
  [./s10]
    type = RankTwoAux
    variable = s10
    index_i = 1
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    index_i = 1
    index_j = 1
  [../]
  [./s12]
    type = RankTwoAux
    variable = s12
    index_i = 1
    index_j = 2
  [../]
  [./s20]
    type = RankTwoAux
    variable = s20
    index_i = 2
    index_j = 0
  [../]
  [./s21]
    type = RankTwoAux
    variable = s21
    index_i = 2
    index_j = 1
  [../]
  [./s22]
    type = RankTwoAux
    variable = s22
    index_i = 2
    index_j = 2
  [../]
[]

[Materials]
  [./interface]
    type = ComputeInterfaceStress
    v = 'eta1 eta2'
    stress   = '1.0 2.0'
    op_range = '1.0 0.5'
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  file_base = test_out
  execute_on = timestep_end
  hide = 'dummy eta1 eta2'
[]

(test/tests/misc/check_error/function_conflict.i)

# A function name that could be interpreted as a ParsedFunction

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Functions]
  [./x]
    type = ConstantFunction
  [../]
[]

[Variables]
  [./var]
  [../]
[]

[ICs]
  [./dummy]
    type = FunctionIC
    variable = var
    function = x
  [../]
[]


[Kernels]
  [./diff]
    type = Diffusion
    variable = var
  [../]
[]

[Executioner]
  type = Steady
[]

(test/tests/multiapps/grid-sequencing/vi-fine-alone.i)

l=10
nx=80
num_steps=2

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [bounds][]
[]

[Bounds]
  [./u_upper_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = upper
    bound_value = ${l}
  [../]
  [./u_lower_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = lower
    bound_value = 0
  [../]
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options = '-snes_vi_monitor'
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type -snes_type'
  petsc_options_value = '0                           30          asm      16                    basic                 vinewtonrsls'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  active = 'upper_violations lower_violations'
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

(tutorials/tutorial03_verification/app/test/tests/step04_mms/2d_mms_spatial.i)

[ICs]
  active = 'mms'
  [mms]
    type = FunctionIC
    variable = T
    function = mms_exact
  []
[]

[BCs]
  active = 'mms'
  [mms]
    type = FunctionDirichletBC
    variable = T
    boundary = 'left right top bottom'
    function = mms_exact
  []
[]

[Kernels]
  [mms]
    type = HeatSource
    variable = T
    function = mms_force
  []
[]

[Functions]
  [mms_force]
    type = ParsedFunction
    value = 'cp*rho*sin(x*pi)*sin(5*y*pi) + 26*pi^2*k*t*sin(x*pi)*sin(5*y*pi) - shortwave*exp(y*kappa)*sin((1/2)*x*pi)*sin((1/3600)*pi*t/hours)'
    vars = 'rho cp   k     kappa shortwave hours'
    vals = '150 2000 0.01  40    650       9'
  []
  [mms_exact]
    type = ParsedFunction
    value = 't*sin(pi*x)*sin(5*pi*y)'
  []
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    variable = T
    function = mms_exact
  []
  [h]
    type = AverageElementSize
  []
[]

(test/tests/fvkernels/mms/advective-outflow/limited-advection.i)

a=1.1

[Mesh]
  [./gen_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0.1
    xmax = 1.1
    nx = 2
  [../]
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = exact
  []
[]

[Variables]
  [./u]
    two_term_boundary_expansion = true
    type = MooseVariableFVReal
  [../]
[]

[FVKernels]
  [./advection_u]
    type = FVLimitedAdvection
    variable = u
    velocity = '${a} 0 0'
    boundaries_to_force = 'right'
    limiter = 'vanLeer'
  [../]
  [body_u]
    type = FVBodyForce
    variable = u
    function = 'forcing'
  []
[]

[FVBCs]
  [left_u]
    type = FVFunctionNeumannBC
    boundary = 'left'
    function = 'advection'
    variable = u
  []
[]

[Functions]
  [exact]
    type = ParsedFunction
    value = 'cos(x)'
  []
  [advection]
    type = ParsedFunction
    value = '${a} * cos(x)'
  []
  [forcing]
    type = ParsedFunction
    value = '-${a} * sin(x)'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_abs_tol = 1e-13
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/phase_field/test/tests/MultiPhase/asymmetriccrosstermbarrierfunction.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 200
  xmin = 0
  xmax = 9
[]

[Functions]
  [./func1]
    type = ParsedFunction
    value = 'il:=x-7; ir:=2-x; if(x<1, 1,
                               if(x<2, 0.5-0.5*cos(ir*pi),
                               if(x<7, 0,
                               if(x<8, 0.5-0.5*cos(il*pi),
                               1))))'
  [../]
  [./func2]
    type = ParsedFunction
    value = 'il:=x-1; ir:=5-x; if(x<1, 0,
                               if(x<2, 0.5-0.5*cos(il*pi),
                               if(x<4, 1,
                               if(x<5, 0.5-0.5*cos(ir*pi),
                               0))))'
  [../]
  [./func3]
    type = ParsedFunction
    value = 'il:=x-4; ir:=8-x; if(x<4, 0,
                               if(x<5, 0.5-0.5*cos(il*pi),
                               if(x<7, 1,
                               if(x<8, 0.5-0.5*cos(ir*pi),
                               0))))'
  [../]
[]

[AuxVariables]
  [./eta1]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = func1
    [../]
  [../]
  [./eta2]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = func2
    [../]
  [../]
  [./eta3]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = func3
    [../]
  [../]
[]

[Materials]
  [./symmetriccrosstermbarrier_low]
    type = AsymmetricCrossTermBarrierFunctionMaterial
    etas     = 'eta1 eta2 eta3'
    hi_names = 'h1   h2   h3'
    W_ij = '0   1   2.2
            1   0   3.1
            2.2 3.1 0'
    function_name = gsl
    g_order = LOW
    outputs = exodus
  [../]
  [./asymmetriccrosstermbarrier_low]
    type = AsymmetricCrossTermBarrierFunctionMaterial
    etas     = 'eta1 eta2 eta3'
    hi_names = 'h1   h2   h3'
    W_ij = ' 0    1.2 5.2
             0.8  0   2.1
            -0.8 4.1  0'
    function_name = gal
    g_order = LOW
    outputs = exodus
  [../]

  [./asymmetriccrosstermbarrie_simple]
    type = AsymmetricCrossTermBarrierFunctionMaterial
    etas     = 'eta1 eta2 eta3'
    hi_names = 'h1   h2   h3'
    W_ij = '0   1.2   3.2
            0.8   0   2.1
            1.2 4.1 0'
    function_name = gas
    g_order = SIMPLE
    outputs = exodus
  [../]

  [./switch1]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
  [../]
  [./switch2]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
  [../]
  [./switch3]
    type = SwitchingFunctionMaterial
    function_name = h3
    eta = eta3
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  num_steps = 1
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

[Outputs]
  exodus = true
  execute_on = final
[]

(modules/porous_flow/test/tests/numerical_diffusion/fully_saturated_action.i)

# Using the fully-saturated action, which does mass lumping but no upwinding
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[PorousFlowFullySaturated]
  porepressure = porepressure
  coupling_type = Hydro
  gravity = '0 0 0'
  fp = the_simple_fluid
  mass_fraction_vars = tracer
  stabilization = none
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-1
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/richards/test/tests/uo_egs/seff1.i)

# Outputs a effective saturation relationship into an exodus file
# and into a CSV file.
# In the exodus file, the Seff will be a function of "x", and
# this "x" is actually porepressure
# In the CSV file you will find the Seff at the "x" point
# specified by you below.
#
# You may specify:
#  - the "type" of Seff in the UserObjects block
#  - the parameters of this Seff function in the UserObjects block
#  - the "x" point (which is porepressure) that you want to extract
#       the Seff at, if you want a value at a particular point
#  - the range of "x" values (which is porepressure values) may be
#       changed in the Mesh block, below


[UserObjects]
  [./seff]
    type = RichardsSeff1VG
    al = 1E-6
    m = 0.8
  [../]
[]

[Postprocessors]
  [./point_val]
    type = PointValue
    execute_on = timestep_begin
    # note this point must lie inside the mesh below
    point = '-1 0 0'
    variable = seff
  [../]
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  # the following specify the range of porepressure
  xmin = -3E6
  xmax = 1E5
[]

############################
# You should not need to change any of the stuff below
############################


[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = x
  [../]
[]

[AuxVariables]
  [./seff]
  [../]
[]

[AuxKernels]
  [./seff_AuxK]
    type = RichardsSeffAux
    variable = seff
    seff_UO = seff
    execute_on = timestep_begin
    pressure_vars = u
  [../]
[]

[Kernels]
  [./dummy]
    type = Diffusion
    variable = u
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 0
[]

[Outputs]
  file_base = seff1
  [./csv]
    type = CSV
  [../]
  [./exodus]
    type = Exodus
    hide = u
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/free-flow-hllc.i)

[GlobalParams]
  fp = fp
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = 1.1
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Variables]
  [rho]
    type = MooseVariableFVReal
  []
  [rho_u]
    type = MooseVariableFVReal
  []
  [rho_et]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [rho]
    type = FunctionIC
    variable = rho
    function = 'exact_rho'
  []
  [rho_u]
    type = FunctionIC
    variable = rho_u
    function = 'exact_rho_u'
  []
  [rho_et]
    type = FunctionIC
    variable = rho_et
    function = 'exact_rho_et'
  []
[]

[FVKernels]
  [mass_advection]
    type = CNSFVMassHLLC
    variable = rho
  []
  [mass_fn]
    type = FVBodyForce
    variable = rho
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = CNSFVMomentumHLLC
    variable = rho_u
    momentum_component = x
  []
  [momentum_fn]
    type = FVBodyForce
    variable = rho_u
    function = 'forcing_rho_u'
  []

  [fluid_energy_advection]
    type = CNSFVFluidEnergyHLLC
    variable = rho_et
  []
  [energy_fn]
    type = FVBodyForce
    variable = rho_et
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_in]
    variable = rho
    type = CNSFVHLLCSpecifiedMassFluxAndTemperatureMassBC
    boundary = left
    temperature = 'exact_T'
    rhou = 'exact_rho_u'
  []
  [momentum_in]
    variable = rho_u
    type = CNSFVHLLCSpecifiedMassFluxAndTemperatureMomentumBC
    boundary = left
    temperature = 'exact_T'
    rhou = 'exact_rho_u'
    momentum_component = 'x'
  []
  [energy_in]
    variable = rho_et
    type = CNSFVHLLCSpecifiedMassFluxAndTemperatureFluidEnergyBC
    boundary = left
    temperature = 'exact_T'
    rhou = 'exact_rho_u'
  []

  [mass_out]
    variable = rho
    type = CNSFVHLLCSpecifiedPressureMassBC
    boundary = right
    pressure = 'exact_p'
  []
  [momentum_out]
    variable = rho_u
    type = CNSFVHLLCSpecifiedPressureMomentumBC
    boundary = right
    pressure = 'exact_p'
    momentum_component = 'x'
  []
  [energy_out]
    variable = rho_et
    type = CNSFVHLLCSpecifiedPressureFluidEnergyBC
    boundary = right
    pressure = 'exact_p'
  []
[]

[Materials]
  [var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = rho_u
    rho_et = rho_et
  []
[]

[Functions]
  [exact_rho]
    type = ParsedFunction
    value = '3.48788261470924*cos(x)'
  []
  [forcing_rho]
    type = ParsedFunction
    value = '-3.83667087618017*sin(1.1*x)'
  []
  [exact_rho_u]
    type = ParsedFunction
    value = '3.48788261470924*cos(1.1*x)'
  []
  [forcing_rho_u]
    type = ParsedFunction
    value = '-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) + 3.48788261470924*sin(x)*cos(1.1*x)^2/cos(x)^2 - 7.67334175236034*sin(1.1*x)*cos(1.1*x)/cos(x)'
  []
  [exact_rho_et]
    type = ParsedFunction
    value = '26.7439413073546*cos(1.2*x)'
  []
  [forcing_rho_et]
    type = ParsedFunction
    value = '1.0*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(x)*cos(1.1*x)/cos(x)^2 - 1.1*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(1.1*x)/cos(x) + 1.0*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) - 32.0927295688256*sin(1.2*x))*cos(1.1*x)/cos(x)'
  []
  [exact_T]
    type = ParsedFunction
    value = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
  []
  [exact_p]
    type = ParsedFunction
    value = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
  []
[]

[Executioner]
  solve_type = NEWTON
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = none
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho]
    type = ElementL2Error
    variable = rho
    function = exact_rho
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_u]
    variable = rho_u
    function = exact_rho_u
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_et]
    variable = rho_et
    function = exact_rho_et
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/fluid_properties/test/tests/brine/brine_tabulated.i)

# Test BrineFluidProperties calculations of density, viscosity and thermal
# conductivity with a TabulatedFluidProperties water.
#
# Experimental density values from Pitzer et al, "Thermodynamic properties
# of aqueous sodium chloride solution", Journal of Physical and Chemical
# Reference Data, 13, 1-102 (1984)
#
# Experimental viscosity values from Phillips et al, "Viscosity of NaCl and
# other solutions up to 350C and 50MPa pressures", LBL-11586 (1980)
#
# Thermal conductivity values from Ozbek and Phillips, "Thermal conductivity of
# aqueous NaCl solutions from 20C to 330C", LBL-9086 (1980)
#
#  --------------------------------------------------------------
#  Pressure (Mpa)                |   20      |    20     |   40
#  Temperature (C)               |   50      |   200     |  200
#  NaCl molality (mol/kg)        |    2      |     2     |    5
#  NaCl mass fraction (kg/kg)    |  0.1047   |  0.1047   |  0.2261
#  --------------------------------------------------------------
#  Expected values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1068.52  |  959.27   |  1065.58
#  Viscosity (1e-6Pa.s)          |  679.8    |  180.0    |  263.1
#  Thermal conductivity (W/m/K)  |  0.630    |  0.649    |  0.633
#  --------------------------------------------------------------
#  Calculated values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1067.18  |  958.68   |  1065.46
#  Viscosity (1e-6 Pa.s)         |  681.1    |  181.98    |  266.1
#  Thermal conductivity (W/m/K)  |  0.637    |   0.662    |  0.658
#  --------------------------------------------------------------
#
# All results are within expected accuracy

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 1
  xmax = 3
  # This test uses ElementalVariableValue postprocessors on specific
  # elements, so element numbering needs to stay unchanged
  allow_renumbering = false
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./pressure]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./temperature]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./xnacl]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./density]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./enthalpy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./internal_energy]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Functions]
  [./pic]
    type = ParsedFunction
    value = 'if(x<2,20e6, 40e6)'
  [../]
  [./tic]
    type = ParsedFunction
    value = 'if(x<1, 323.15, 473.15)'
  [../]
  [./xic]
    type = ParsedFunction
    value = 'if(x<2,0.1047, 0.2261)'
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    function = pic
    variable = pressure
  [../]
  [./t_ic]
    type = FunctionIC
    function = tic
    variable = temperature
  [../]
  [./x_ic]
    type = FunctionIC
    function = xic
    variable = xnacl
  [../]
[]

[AuxKernels]
  [./density]
    type = MaterialRealAux
     variable = density
     property = density
  [../]
  [./enthalpy]
    type = MaterialRealAux
     variable = enthalpy
     property = enthalpy
  [../]
  [./internal_energy]
    type = MaterialRealAux
     variable = internal_energy
     property = e
  [../]
[]

[Modules]
  [./FluidProperties]
    [./water]
      type = Water97FluidProperties
    [../]
    [./water_tab]
      type = TabulatedFluidProperties
      fp = water
      save_file = false
    [../]
    [./brine]
      type = BrineFluidProperties
      water_fp = water_tab
    [../]
  [../]
[]

[Materials]
  [./fp_mat]
    type = MultiComponentFluidPropertiesMaterialPT
    pressure = pressure
    temperature = temperature
    xmass = xnacl
    fp = brine
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Postprocessors]
  [./density0]
    type = ElementalVariableValue
    variable = density
    elementid = 0
  [../]
  [./density1]
    type = ElementalVariableValue
    variable = density
    elementid = 1
  [../]
  [./density2]
    type = ElementalVariableValue
    variable = density
    elementid = 2
  [../]
  [./enthalpy0]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 0
  [../]
  [./enthalpy1]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 1
  [../]
  [./enthalpy2]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 2
  [../]
  [./e0]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 0
  [../]
  [./e1]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 1
  [../]
  [./e2]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 2
  [../]
[]

[Outputs]
  csv = true
  file_base = brine_out
[]

(modules/porous_flow/test/tests/flux_limited_TVD_pflow/pffltvd_2D_angle.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, mploying PorousFlow Kernels and UserObjects, with superbee flux-limiter
# 2D version with velocity = (0.1, 0.2, 0)
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  xmin = 0
  xmax = 1
  ny = 10
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x - 2 * y'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1 | x > 0.3 | y < 0.1 | y > 0.3, 0, 1)'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_boundary_porepressure]
    type = FunctionDirichletBC
    variable = porepressure
    function = '1 - x - 2 * y'
    boundary = 'left right top bottom'
  []
  [no_tracer_at_boundary]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = 'left right top bottom'
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 0.3
  dt = 0.1
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'initial final'
  []
[]

(test/tests/ics/lagrange_ic/3d_second_order.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 5
  ny = 5
  nz = 5
  elem_type = HEX27
[]

[Variables]
  [./u]
    order = SECOND
  [../]
[]

[Functions]
  [./afunc]
    type = ParsedFunction
    value = x^2
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./func_ic]
    function = afunc
    variable = u
    type = FunctionIC
  [../]
[]

(modules/porous_flow/examples/lava_lamp/2phase_convection.i)

# Two phase density-driven convection of dissolved CO2 in brine
#
# Initially, the model has a gas phase at the top with a saturation of 0.29
# (which corresponds to an initial value of zi = 0.2).
# Diffusion of the dissolved CO2
# component from the saturated liquid to the unsaturated liquid below reduces the
# amount of CO2 in the gas phase. As the density of the CO2-saturated brine is greater
# than the unsaturated brine, a gravitational instability arises and density-driven
# convection of CO2-rich fingers descend into the unsaturated brine.
#
# The instability is seeded by a random perturbation to the porosity field.
# Mesh adaptivity is used to refine the mesh as the fingers form.
#
# Note: this model is computationally expensive, so should be run with multiple cores,
# preferably on a cluster.

[GlobalParams]
  PorousFlowDictator = 'dictator'
  gravity = '0 -9.81 0'
[]

[Adaptivity]
  max_h_level = 2
  marker = marker
  initial_marker = initial
  initial_steps = 2
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = zi
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      refine = 0.8
    []
    [initial]
      type = BoxMarker
      bottom_left = '0 1.95 0'
      top_right = '2 2 0'
      inside = REFINE
      outside = DO_NOTHING
    []
  []
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  ymax = 2
  xmax = 2
  ny = 40
  nx = 40
  bias_y = 0.95
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pgas
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pgas
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    fluid_component = 0
    variable = pgas
    disp_long = '0 0'
    disp_trans = '0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = zi
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = zi
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = zi
    disp_long = '0 0'
    disp_trans = '0 0'
  []
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.01
  []
  [saturation_gas]
    order = FIRST
    family = MONOMIAL
  []
  [xco2l]
    order = FIRST
    family = MONOMIAL
  []
  [density_liquid]
    order = FIRST
    family = MONOMIAL
  []
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = 'timestep_end'
  []
  [xco2l]
    type = PorousFlowPropertyAux
    variable = xco2l
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = 'timestep_end'
  []
  [density_liquid]
    type = PorousFlowPropertyAux
    variable = density_liquid
    property = density
    phase = 0
    execute_on = 'timestep_end'
  []
[]

[Variables]
  [pgas]
  []
  [zi]
    scaling = 1e4
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    function = 10e6-9.81*1000*y
    variable = pgas
  []
  [zi]
    type = BoundingBoxIC
    variable = zi
    x1 = 0
    x2 = 2
    y1 = 1.95
    y2 = 2
    inside = 0.2
    outside = 0
  []
  [porosity]
    type = RandomIC
    variable = porosity
    min = 0.25
    max = 0.275
    seed = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2sw]
      type = CO2FluidProperties
    []
    [co2]
      type = TabulatedFluidProperties
      fp = co2sw
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = '45'
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = 'pgas'
    z = 'zi'
    temperature_unit = Celsius
    xnacl = 'xnacl'
    capillary_pressure = pc
    fluid_state = fs
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = porosity
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0 0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    phase = 0
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [diffusivity]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '2e-9 2e-9 2e-9 2e-9'
    tortuosity = '1 1'
  []
[]

[Preconditioning]
  active = basic
  [mumps_is_best_for_parallel_jobs]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e6
  nl_max_its = 25
  l_max_its = 100
  dtmax = 1e4
  nl_abs_tol = 1e-6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 10
    growth_factor = 2
    cutback_factor = 0.5
  []
[]

[Functions]
  [flux]
    type = ParsedFunction
    vals = 'delta_xco2 dt'
    vars = 'dx dt'
    value = 'dx/dt'
  []
[]

[Postprocessors]
  [total_co2_in_gas]
    type = PorousFlowFluidMass
    phase = 1
    fluid_component = 1
  []
  [total_co2_in_liquid]
    type = PorousFlowFluidMass
    phase = 0
    fluid_component = 1
  []
  [numdofs]
    type = NumDOFs
  []
  [delta_xco2]
    type = ChangeOverTimePostprocessor
    postprocessor = total_co2_in_liquid
  []
  [dt]
    type = TimestepSize
  []
  [flux]
    type = FunctionValuePostprocessor
    function = flux
  []
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  exodus = true
  csv = true
[]

(test/tests/functions/solution_function/solution_function_scale_mult.i)

# checking scale_multiplier
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  nx = 3
  ymin = -1
  ymax = 1
  ny = 3
[]

[UserObjects]
  [./solution_uo]
    type = SolutionUserObject
    mesh = square_with_u_equals_x.e
    timestep = 1
    system_variables = u
    scale_multiplier = '2 2 0'
    transformation_order = scale_multiplier
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = solution_fcn
  [../]
[]

[Functions]
  [./solution_fcn]
    type = SolutionFunction
    from_variable = u
    solution = solution_uo
  [../]
[]

[Kernels]
  [./diff]
    type = TimeDerivative
    variable = u
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  l_max_its = 800
  nl_rel_tol = 1e-10
  num_steps = 1
  end_time = 1
  dt = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = solution_function_scale_mult
  exodus = true
[]

(modules/richards/test/tests/dirac/bh_fu_04.i)

# unsaturated
# production
# fullyupwind
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1E-2 1E-1 1 1E1 1E2 1E3'
    x = '0 1E-1 1 1E1 1E2 1E3'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = -1E6
    point_file = bh02.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = 1
    fully_upwind = true
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 0
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]

[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1E3
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  file_base = bh_fu_04
  exodus = false
  execute_on = timestep_end
  csv = true
[]

(modules/richards/test/tests/theis/th_lumped_22.i)

# two-phase, fully-saturated
# production
# lumped
[Mesh]
  type = FileMesh
  file = th02_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1 2 4 20'
    x = '0 1 10 100'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]

  [./total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]


[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_pressure
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsLumpedMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsLumpedMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsPolyLineSink
    pressures = '-1E9 1E9'
    fluxes = '200 200'
    point_file = th01.points
    SumQuantityUO = total_outflow_mass
    variable = pwater
  [../]
[]


[Postprocessors]
  [./flow_report]
    type = RichardsPlotQuantity
    uo = total_outflow_mass
  [../]
  [./p50]
    type = PointValue
    variable = pwater
    point = '50 0 0'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E5
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    mat_porosity = 0.1
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    viscosity = '1E-3 1E-5'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]



[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt -snes_linesearch_monitor'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               2E-7 1E-10 20 1E-10 1E-100'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 100
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = th_lumped_22
  exodus = true
  csv = true
[]

(test/tests/time_integrators/explicit-euler/ee-2d-linear-adapt.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = (x+y)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*(x+y)
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    lumping = true
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[BCs]
  active = 'all'

  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
    implicit = true
  [../]
[]

[Adaptivity]
  steps = 1
  marker = box
  max_h_level = 2
  [./Markers]
    [./box]
      bottom_left = '-0.4 -0.4 0'
      inside = refine
      top_right = '0.4 0.4 0'
      outside = do_nothing
      type = BoxMarker
    [../]
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'explicit-euler'

  start_time = 0.0
  num_steps = 4
  dt = 0.005
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/porous_flow/test/tests/poroperm/poro_hm.i)

# Test that porosity is correctly calculated.
# Porosity = biot + (phi0 - biot) * exp(-vol_strain + (biot_prime - 1) / solid_bulk * (porepressure - ref_pressure))
# The parameters used are:
# biot = 0.7
# biot_prime = 0.75
# phi0 = 0.5
# vol_strain = 0.5
# solid_bulk = 0.3
# porepressure = 2
# ref_pressure = 3
# which yield porosity = 0.420877515
[Mesh]
  type = GeneratedMesh
  dim = 3
[]

[GlobalParams]
  PorousFlowDictator = dictator
  displacements = 'disp_x disp_y disp_z'
  biot_coefficient = 0.7
[]

[Variables]
  [porepressure]
    initial_condition = 2
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[ICs]
  [disp_x]
    type = FunctionIC
    function = '0.5 * x'
    variable = disp_x
  []
[]

[Kernels]
  [dummy_p]
    type = TimeDerivative
    variable = porepressure
  []
  [dummy_x]
    type = TimeDerivative
    variable = disp_x
  []
  [dummy_y]
    type = TimeDerivative
    variable = disp_y
  []
  [dummy_z]
    type = TimeDerivative
    variable = disp_z
  []
[]

[AuxVariables]
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [porosity]
    type = PorousFlowPropertyAux
    property = porosity
    variable = porosity
  []
[]

[Postprocessors]
  [porosity]
    type = PointValue
    variable = porosity
    point = '0 0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 3
  []
  [eff_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [total_strain]
    type = ComputeSmallStrain
  []
  [vol_strain]
    type = PorousFlowVolumetricStrain
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [porosity]
    type = PorousFlowPorosity
    fluid = true
    mechanical = true
    ensure_positive = false
    porosity_zero = 0.5
    solid_bulk = 0.3
    reference_porepressure = 3
    biot_coefficient_prime = 0.75
  []
[]

[Executioner]
  solve_type = Newton
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
[]

(test/tests/bcs/mat_neumann_bc/ad_mat_neumann.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 10
  ymax = 10
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./phi]
  [../]
[]

[ICs]
  [./phi_IC]
    type = FunctionIC
    variable = phi
    function = ic_func_phi
  [../]
[]

[Functions]
  [./ic_func_phi]
    type = ParsedFunction
    value = '0.5 * (1 - tanh((x - 5) / 0.8))'
  [../]
[]

[BCs]
  [./top]
    type = ADMatNeumannBC
    variable = u
    boundary = top
    value = 2
    boundary_material = hm
  [../]
[]

[Kernels]
  [./dudt]
    type = ADTimeDerivative
    variable = u
  [../]
  [./diff]
    type = ADDiffusion
    variable = u
  [../]
[]

[Materials]
  [./hm]
    type = ADParsedMaterial
    f_name = hm
    args = 'phi'
    function = '3*phi^2 - 2*phi^3'
    outputs = exodus
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  end_time = 10
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/GrandPotentialPFM/SinteringIdeal.i)

#input file to test the GrandPotentialSinteringMaterial using the ideal energy profile

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 17
  ny = 10
  xmin = 0
  xmax = 660
  ymin = 0
  ymax = 380
[]

[GlobalParams]
  op_num = 2
  var_name_base = gr
  int_width = 40
[]

[Variables]
  [./w]
    [./InitialCondition]
      type = FunctionIC
      variable = w
      function = f_w
    [../]
  [../]
  [./phi]
  [../]
  [./PolycrystalVariables]
  [../]
[]

[AuxVariables]
  [./T]
    order = CONSTANT
    family = MONOMIAL
    [./InitialCondition]
      type = FunctionIC
      variable = T
      function = f_T
    [../]
  [../]
[]

[ICs]
  [./phi_IC]
    type = SpecifiedSmoothCircleIC
    variable = phi
    x_positions = '190 470'
    y_positions = '190 190'
    z_positions = '  0   0'
    radii = '150 150'
    invalue = 0
    outvalue = 1
  [../]
  [./gr0_IC]
    type = SmoothCircleIC
    variable = gr0
    x1 = 190
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
  [./gr1_IC]
    type = SmoothCircleIC
    variable = gr1
    x1 = 470
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
[]

[Functions]
  [./f_T]
    type = ConstantFunction
    value = 1600
  [../]
  [./f_w]
    type = ParsedFunction
    value = '1.515e-7 * x'
  [../]
[]

[Materials]
  # Free energy coefficients for parabolic curve
  [./kv]
    type = ParsedMaterial
    f_name = kv
    args = 'T'
    constant_names = 'a b'
    constant_expressions = '-0.025 1571.6'
    function = 'a*T + b'
  [../]
  # Diffusivity and mobilities
  [./chiD]
    type = GrandPotentialTensorMaterial
    f_name = chiD
    solid_mobility = L
    void_mobility = Lv
    chi = chi
    surface_energy = 19.7
    c = phi
    T = T
    D0 = 2.0e11
    GBmob0 = 1.4759e9
    Q = 2.77
    Em = 2.40
    bulkindex = 1
    gbindex = 20
    surfindex = 100
  [../]
  # Equilibrium vacancy concentration
  [./cs_eq]
    type = DerivativeParsedMaterial
    f_name = cs_eq
    args = 'gr0 gr1 T'
    constant_names = 'Ef Egb kB'
    constant_expressions = '2.69 2.1 8.617343e-5'
    function = 'bnds:=gr0^2 + gr1^2; cb:=exp(-Ef/kB/T); cgb:=exp(-(Ef-Egb)/kB/T);
                cb + 4.0*(cgb-cb)*(1.0 - bnds)^2'
  [../]
  # Everything else
  [./sintering]
    type = GrandPotentialSinteringMaterial
    chemical_potential = w
    void_op = phi
    Temperature = T
    surface_energy = 19.7
    grainboundary_energy = 9.86
    void_energy_coefficient = kv
    equilibrium_vacancy_concentration = cs_eq
    solid_energy_model = IDEAL
    outputs = exodus
  [../]

  # Concentration is only meant for output
  [./c]
    type = ParsedMaterial
    f_name = c
    material_property_names = 'hs rhos hv rhov'
    constant_names = 'Va'
    constant_expressions = '0.04092'
    function = 'Va*(hs*rhos + hv*rhov)'
    outputs = exodus
  [../]
[]

[Kernels]
  [./dt_gr0]
    type = TimeDerivative
    variable = gr0
  [../]
  [./dt_gr1]
    type = TimeDerivative
    variable = gr1
  [../]
  [./dt_phi]
    type = TimeDerivative
    variable = phi
  [../]
  [./dt_w]
    type = TimeDerivative
    variable = w
  [../]
[]

[AuxKernels]
  [./T_aux]
    type = FunctionAux
    variable = T
    function = f_T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = JFNK
  dt = 1
  num_steps = 2
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/phase_field_kernels/ADAllenCahnVariableL.i)

#
# Test the forward automatic differentiation Allen-Cahn Bulk kernel with a
# spatially varying mobility
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 12
  ymax = 12
  elem_type = QUAD4
[]

[AuxVariables]
  [./chi]
    [./InitialCondition]
      type = FunctionIC
      function = 'x/24+0.5'
    [../]
  [../]
[]

[Variables]
  [./eta]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = 0.0
      y1 = 0.0
      radius = 6.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 3.0
    [../]
  [../]
[]

[Kernels]
  [./detadt]
    type = ADTimeDerivative
    variable = eta
  [../]

  [./ACBulk]
    type = ADAllenCahn
    variable = eta
    f_name = F
  [../]

  [./ACInterface]
    type = ADACInterface
    variable = eta
    kappa_name = 1
    variable_L = true
    args = chi
  [../]
[]

[Materials]
  [./L]
    type = ADTestDerivativeFunction
    function = F2
    f_name = L
    op = 'eta chi'
  [../]

  [./free_energy]
    type = ADTestDerivativeFunction
    function = F1
    f_name = F
    op = 'eta'
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'
  solve_type = 'NEWTON'
  num_steps = 2
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/sinks/s05.i)

# checking the multiplying_fcn of RichardsPiecewiseLinearSinkFlux.
# This test is constructed so it should produce exactly the same answer as s02.i
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1 # same deal with PETScs constant state
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 2
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-lfout-rfout-mf)/2/(mi+mf))
    vars = 'mi mf lfout rfout'
    vals = 'mass_init mass_fin left_flux_out right_flux_out'
  [../]
[]

[Postprocessors]
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]
  [./mass_fin]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]
  [./left_flux_out]
    type = RichardsHalfGaussianSinkFlux
    boundary = left
    variable = pressure
    centre = 1
    max = 4
    multiplying_fcn = 0.5
    sd = 1
  [../]
  [./right_flux_out]
    type = RichardsHalfGaussianSinkFlux
    boundary = right
    variable = pressure
    centre = 1
    max = 1
    multiplying_fcn = 2
    sd = 1
  [../]
  [./p0]
    type = PointValue
    point = '0 0 0'
    variable = pressure
  [../]
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]

[BCs]
  [./left_flux]
    type = RichardsHalfGaussianSink
    boundary = left
    variable = pressure
    centre = 1
    max = 2
    sd = 1
  [../]
  [./right_flux]
    type = RichardsHalfGaussianSink
    boundary = right
    variable = pressure
    centre = 1
    max = 2
    sd = 1
  [../]
[]

[Kernels]
  active = 'richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 4E-3
  end_time = 0.4
[]

[Outputs]
  file_base = s05
  csv = true
  execute_on = timestep_end
[]

(modules/phase_field/test/tests/ExpressionBuilderCoupledVectorTest/testCoupledVector.i)

[Mesh]
  type = GeneratedMesh
  dim = 2 # Problem dimension
  nx = 10
  ny = 10
[]

[GlobalParams]
  op_num = 2 # Number of grains
  var_name_base = gr # Base name of grains
[]

[AuxVariables]
  [./gr0]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
  [./gr1]
    [./InitialCondition]
      type = FunctionIC
      function = y
    [../]
  [../]
[]

[Materials]
  [./Tester]
    type = EBCoupledVarTest
    outputs = exodus
  [../]
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[../]

[Outputs]
  exodus = true
  execute_on = 'INITIAL TIMESTEP_END'
[]

(test/tests/transfers/multiapp_projection_transfer/high_order_master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 4
  ny = 4
[]

[Functions]
  [./test_function]
    type = ParsedFunction
    value = '2.5*x^2 + 0.75*y^2 + 0.15*x*y'
  [../]
[]

[AuxVariables]
  [./from_sub]
    family = monomial
    order = first
  [../]
  [./test_var]
    family = monomial
    order = first
    [./InitialCondition]
      type = FunctionIC
      function = test_function
    [../]
  [../]
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

[MultiApps]
  [./sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    execute_on = initial
    positions = '0.0 0.0 0.0'
    input_files = high_order_sub.i
  [../]
[]

[Transfers]
  [./from]
    type = MultiAppProjectionTransfer
    execute_on = same_as_multiapp
    from_multi_app = sub
    source_variable = test_var
    variable = from_sub
  [../]
  [./to]
    type = MultiAppProjectionTransfer
    execute_on = same_as_multiapp
    to_multi_app = sub
    source_variable = test_var
    variable = from_master
  [../]
[]

(test/tests/kernels/conservative_advection/full_upwinding_2D.i)

# 2D test of advection with full upwinding
# Note there are no overshoots or undershoots
# but there is numerical diffusion.
# The center of the blob advects with the correct velocity
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 40
  ny = 40
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_blob]
    type = FunctionIC
    variable = u
    function = 'if(x<0.2,if(y<0.2,1,0),0)'
  [../]
[]

[Kernels]
  [./udot]
    type = MassLumpedTimeDerivative
    variable = u
  [../]
  [./advection]
    type = ConservativeAdvection
    variable = u
    upwinding_type = full
    velocity = '2 1 0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = LINEAR
  dt = 0.01
  end_time = 0.1
  l_tol = 1E-14
[]

[Outputs]
  exodus = true
[]

(test/tests/fvkernels/mms/advective-outflow/kt-limited-advection.i)

a=1.1
c=343
max_abs_eig=${fparse c + a}

[Mesh]
  [./gen_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0.1
    xmax = 1.1
    nx = 2
  [../]
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = exact
  []
[]

[Variables]
  [./u]
    two_term_boundary_expansion = true
    type = MooseVariableFVReal
  [../]
[]

[FVKernels]
  [./advection_u]
    type = FVKTLimitedAdvection
    variable = u
    velocity = '${a} 0 0'
    limiter = 'vanLeer'
    max_abs_eig = ${max_abs_eig}
    add_artificial_diff = true
  [../]
  [body_u]
    type = FVBodyForce
    variable = u
    function = 'forcing'
  []
[]

[FVBCs]
  [left_u]
    type = FVFunctionNeumannBC
    boundary = 'left'
    function = 'advection'
    variable = u
  []
  [diri_left]
    type = FVFunctionDirichletBC
    boundary = 'left'
    function = 'exact'
    variable = u
  []
  [right]
    type = FVConstantScalarOutflowBC
    variable = u
    velocity = '${a} 0 0'
    boundary = 'right'
  []
[]

[Functions]
  [exact]
    type = ParsedFunction
    value = 'cos(x)'
  []
  [advection]
    type = ParsedFunction
    value = '${a} * cos(x)'
  []
  [forcing]
    type = ParsedFunction
    value = '-${a} * sin(x)'
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-snes_linesearch_minlambda'
  petsc_options_value = '1e-3'
  nl_abs_tol = 1e-9
[]

[Outputs]
  file_base = 'kt-limited-advection_out'
  [csv]
    type = CSV
    execute_on = 'final'
  []
  [exo]
    type = Exodus
    execute_on = 'final'
  []
[]

[Postprocessors]
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/phase_field/examples/kim-kim-suzuki/kks_example_dirichlet.i)

#
# KKS simple example in the split form
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  elem_type = QUAD4
  nx = 50
  ny = 2
  nz = 0
  xmin = 0
  xmax = 20
  ymin = 0
  ymax = 0.4
  zmin = 0
  zmax = 0
[]

[AuxVariables]
  [./Fglobal]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Variables]
  # order parameter
  [./eta]
    order = FIRST
    family = LAGRANGE
  [../]

  # hydrogen concentration
  [./c]
    order = FIRST
    family = LAGRANGE
  [../]

  # chemical potential
  [./w]
    order = FIRST
    family = LAGRANGE
  [../]

  # Liquid phase solute concentration
  [./cl]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  [../]
  # Solid phase solute concentration
  [./cs]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.9
  [../]
[]

[Functions]
  [./ic_func_eta]
    type = ParsedFunction
    value = 0.5*(1.0-tanh((x)/sqrt(2.0)))
  [../]
  [./ic_func_c]
    type = ParsedFunction
    value = '0.9*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.1*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
  [../]
[]

[ICs]
  [./eta]
    variable = eta
    type = FunctionIC
    function = ic_func_eta
  [../]
  [./c]
    variable = c
    type = FunctionIC
    function = ic_func_c
  [../]
[]

[BCs]
  [./left_c]
    type = DirichletBC
    variable = 'c'
    boundary = 'left'
    value = 0.5
  [../]
  [./left_eta]
    type = DirichletBC
    variable = 'eta'
    boundary = 'left'
    value = 0.5
  [../]
[]

[Materials]
  # Free energy of the liquid
  [./fl]
    type = DerivativeParsedMaterial
    f_name = fl
    args = 'cl'
    function = '(0.1-cl)^2'
  [../]

  # Free energy of the solid
  [./fs]
    type = DerivativeParsedMaterial
    f_name = fs
    args = 'cs'
    function = '(0.9-cs)^2'
  [../]

  # h(eta)
  [./h_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta
  [../]

  # g(eta)
  [./g_eta]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'M   L   eps_sq'
    prop_values = '0.7 0.7 1.0  '
  [../]
[]

[Kernels]
  # enforce c = (1-h(eta))*cl + h(eta)*cs
  [./PhaseConc]
    type = KKSPhaseConcentration
    ca       = cl
    variable = cs
    c        = c
    eta      = eta
  [../]

  # enforce pointwise equality of chemical potentials
  [./ChemPotSolute]
    type = KKSPhaseChemicalPotential
    variable = cl
    cb       = cs
    fa_name  = fl
    fb_name  = fs
  [../]

  #
  # Cahn-Hilliard Equation
  #
  [./CHBulk]
    type = KKSSplitCHCRes
    variable = c
    ca       = cl
    fa_name  = fl
    w        = w
  [../]

  [./dcdt]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
  [./ckernel]
    type = SplitCHWRes
    mob_name = M
    variable = w
  [../]

  #
  # Allen-Cahn Equation
  #
  [./ACBulkF]
    type = KKSACBulkF
    variable = eta
    fa_name  = fl
    fb_name  = fs
    w        = 1.0
    args = 'cl cs'
  [../]
  [./ACBulkC]
    type = KKSACBulkC
    variable = eta
    ca       = cl
    cb       = cs
    fa_name  = fl
  [../]
  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = eps_sq
  [../]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[AuxKernels]
  [./GlobalFreeEnergy]
    variable = Fglobal
    type = KKSGlobalFreeEnergy
    fa_name = fl
    fb_name = fs
    w = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      ilu          nonzero'

  l_max_its = 100
  nl_max_its = 100
  nl_abs_tol = 1e-10

  end_time = 800
  dt = 4.0
[]

#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
  [./full]
    type = SMP
    full = true
  [../]
[]

[Postprocessors]
  [./dofs]
    type = NumDOFs
  [../]
  [./integral]
    type = ElementL2Error
    variable = eta
    function = ic_func_eta
  [../]
[]

[Outputs]
  exodus = true
  console = true
  gnuplot = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d/hllc-mms.i)

[GlobalParams]
  fp = fp
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = 1
    nx = 2
  []
[]

[Variables]
  [rho]
    type = MooseVariableFVReal
  []
  [rho_u]
    type = MooseVariableFVReal
  []
  [rho_et]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [rho]
    type = FunctionIC
    variable = rho
    function = 'cos(1.1*x)'
  []
  [rho_u]
    type = FunctionIC
    variable = rho_u
    function = '2*sin(1.1*x)'
  []
  [rho_et]
    type = FunctionIC
    variable = rho_et
    function = '3*cos(1.1*x)'
  []
[]

[FVKernels]
  [mass_advection]
    type = CNSFVMassHLLC
    variable = rho
  []
  [fake_diffusivity]
    type = FVDiffusion
    variable = rho
    coeff = 1
  []
  [mass_fn]
    type = FVBodyForce
    variable = rho
    function = 'forcing_rho'
  []
  [momentum_advection]
    type = CNSFVMomentumHLLC
    variable = rho_u
    momentum_component = x
  []
  [viscosity]
    type = FVDiffusion
    variable = rho_u
    coeff = 1
  []
  [momentum_fn]
    type = FVBodyForce
    variable = rho_u
    function = 'forcing_rho_u'
  []
  [fluid_energy_advection]
    type = CNSFVFluidEnergyHLLC
    variable = rho_et
  []
  [fake_conduction]
    type = FVDiffusion
    variable = rho_et
    coeff = 1
  []
  [energy_fn]
    type = FVBodyForce
    variable = rho_et
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [rho]
    type = FVFunctionDirichletBC
    boundary = 'left right'
    variable = rho
    function = 'exact_rho'
  []
  [rho_u]
    type = FVFunctionDirichletBC
    boundary = 'left right'
    variable = rho_u
    function = 'exact_rho_u'
  []
  [rho_et]
    type = FVFunctionDirichletBC
    boundary = 'left right'
    variable = rho_et
    function = 'exact_rho_et'
  []
[]

[Materials]
  [var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = rho_u
    rho_et = rho_et
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = TestConservedVarFluidProperties
    []
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  value = 'cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  value = '3*cos(x)'
[]
[exact_rho_u]
  type = ParsedFunction
  value = '2*sin(x)'
[]
[forcing_rho_u]
  type = ParsedFunction
  value = '4*sin(x)^3/cos(x)^2 + 9*sin(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  value = '3*cos(x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  value = '11*cos(x)'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho]
    type = ElementL2Error
    variable = rho
    function = exact_rho
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_u]
    variable = rho_u
    function = exact_rho_u
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_et]
    variable = rho_et
    function = exact_rho_et
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/porous_flow/test/tests/heat_advection/heat_advection_1d_KT.i)

# 1phase, heat advecting with a moving fluid
# Using the Kuzmin-Turek stabilization scheme
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 50
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [temp]
    initial_condition = 200
  []
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1-x'
  []
[]

[BCs]
  [pp0]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 1
  []
  [pp1]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 0
  []
  [spit_heat]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  []
  [suck_heat]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 200
  []
[]

[Kernels]
  [mass_dot]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [fluid_advection]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = pp
    advective_flux_calculator = fluid_advective_flux
  []
  [energy_dot]
    type = PorousFlowEnergyTimeDerivative
    variable = temp
  []
  [heat_advection]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = temp
    advective_flux_calculator = heat_advective_flux
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.6
    alpha = 1.3
  []
  [fluid_advective_flux]
    type = PorousFlowAdvectiveFluxCalculatorSaturated
    flux_limiter_type = superbee
  []
  [heat_advective_flux]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedHeat
    flux_limiter_type = superbee
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 100
      density0 = 1000
      viscosity = 4.4
      thermal_expansion = 0
      cv = 2
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 1.0
    density = 125
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 2 0 0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [PS]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres bjacobi 1E-15 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.01
  end_time = 0.6
[]

[VectorPostprocessors]
  [T]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 51
    sort_by = x
    variable = temp
  []
[]

[Outputs]
  file_base = heat_advection_1d_KT
  [csv]
    type = CSV
    sync_times = '0.1 0.6'
    sync_only = true
  []
[]

(test/tests/bcs/coupled_var_neumann/on_off.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[AuxVariables]
  [./coupled_bc_var]
  [../]

  [./active]
    initial_condition = 1
  [../]
[]

[AuxKernels]
  [./active_right]
    type = ConstantAux
    variable = active
    value = 0.5
    boundary = 1
  [../]
[]

[ICs]
  [./coupled_bc_var]
    type = FunctionIC
    variable = coupled_bc_var
    function = set_coupled_bc_var
  [../]
[]

[Functions]
  [./set_coupled_bc_var]
    type = ParsedFunction
    value = 'y - 0.5'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = CoupledVarNeumannBC
    variable = u
    boundary = 1
    v = coupled_bc_var
    scale_factor = active
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(test/tests/ics/array_function_ic/array_function_ic_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 8
[]

[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Variables]
  [u]
    components = 2
  []
  [u0]
  []
  [u1]
  []
[]

[AuxVariables]
  [v]
    components = 2
  []
[]

[Functions]
  [sinx]
    type = ParsedFunction
    value = sin(x)
  []
  [siny]
    type = ParsedFunction
    value = sin(y)
  []
[]

[ICs]
  [uic]
    type = ArrayFunctionIC
    variable = u
    function = 'sinx siny'
  []
  [u0ic]
    type = FunctionIC
    variable = u0
    function = sinx
  []
  [u1ic]
    type = FunctionIC
    variable = u1
    function = siny
  []
  [vic]
    type = ArrayFunctionIC
    variable = v
    function = 'sinx siny'
  []
[]

[Postprocessors]
  [uint0]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 0
  []
  [uint1]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 1
  []
  [u0int]
    type = ElementIntegralVariablePostprocessor
    variable = u0
  []
  [u1int]
    type = ElementIntegralVariablePostprocessor
    variable = u1
  []
  [vint0]
    type = ElementIntegralArrayVariablePostprocessor
    variable = v
    component = 0
  []
  [vint1]
    type = ElementIntegralArrayVariablePostprocessor
    variable = v
    component = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/automatic_differentiation/admatreaction.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[Variables]
  [./u]
    [./InitialCondition]
      type = FunctionIC
      function = cos(x*2*pi)
    [../]
  [../]
  [./v]
    [./InitialCondition]
      type = FunctionIC
      function = sin(x*2*pi)
    [../]
  [../]
[]

[Kernels]
  [./dudt]
    type = ADTimeDerivative
    variable = u
  [../]
  [./dvdt]
    type = ADTimeDerivative
    variable = v
  [../]
  [./u]
    type = ADMatReaction
    variable = u
    #v = v
  [../]
  [./v]
    type = ADMatReaction
    variable = v
  [../]
[]

[Materials]
  [./L]
    type = ADTestDerivativeFunction
    function = F3
    f_name = L
    op = 'u v'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.1
  num_steps = 5
[]

[Outputs]
  exodus = true
[]

(modules/xfem/test/tests/moving_interface/phase_transition_3d.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 11
    ny = 1
    nz = 1
    xmin = 0.0
    xmax = 20.0
    ymin = 0.0
    ymax = 5.0
    zmin = 0.0
    zmax = 5.0
    elem_type = HEX8
  []
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [velocity]
    type = XFEMPhaseTransitionMovingInterfaceVelocity
    diffusivity_at_positive_level_set = 5
    diffusivity_at_negative_level_set = 1
    equilibrium_concentration_jump = 1
    value_at_interface_uo = value_uo
  []
  [value_uo]
    type = NodeValueAtXFEMInterface
    variable = 'u'
    interface_mesh_cut_userobject = 'cut_mesh'
    execute_on = TIMESTEP_END
    level_set_var = ls
  []
  [cut_mesh]
    type = InterfaceMeshCut3DUserObject
    mesh_file = flat_interface_2d.e
    interface_velocity_uo = velocity
    heal_always = true
  []
[]

[Variables]
  [u]
  []
[]

[ICs]
  [ic_u]
    type = FunctionIC
    variable = u
    function = 'if(x<5.01, 2, 1)'
  []
[]

[AuxVariables]
  [ls]
    order = FIRST
    family = LAGRANGE
  []
[]

[Constraints]
  [u_constraint]
    type = XFEMEqualValueAtInterface
    geometric_cut_userobject = 'cut_mesh'
    use_displaced_mesh = false
    variable = u
    value = 2
    alpha = 1e6
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = diffusion_coefficient
  []
  [time]
    type = TimeDerivative
    variable = u
  []
[]

[AuxKernels]
  [ls]
    type = MeshCutLevelSetAux
    mesh_cut_user_object = cut_mesh
    variable = ls
    execute_on = 'TIMESTEP_BEGIN'
  []
[]

[Materials]
  [diffusivity_A]
    type = GenericConstantMaterial
    prop_names = A_diffusion_coefficient
    prop_values = 5
  []
  [diffusivity_B]
    type = GenericConstantMaterial
    prop_names = B_diffusion_coefficient
    prop_values = 1
  []
  [diff_combined]
    type = LevelSetBiMaterialReal
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = diffusion_coefficient
  []
[]

[BCs]
  # Define boundary conditions
  [left_u]
    type = DirichletBC
    variable = u
    value = 2
    boundary = left
  []

  [right_u]
    type = NeumannBC
    variable = u
    boundary = right
    value = 0
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = 'none'

  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  start_time = 0.0
  dt = 1
  num_steps = 5
  max_xfem_update = 1
[]

[Outputs]
  execute_on = timestep_end
  exodus = true
  perf_graph = true
  csv = true
[]

(modules/combined/test/tests/surface_tension_KKS/surface_tension_KKS.i)

#
# KKS coupled with elasticity. Physical parameters for matrix and precipitate phases
# are gamma and gamma-prime phases, respectively, in the Ni-Al system.
# Parameterization is as described in L.K. Aagesen et al., Computational Materials
# Science, 140, 10-21 (2017), with isotropic elastic properties in both phases
# and without eigenstrain.
#

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 200
  xmax = 200
[]

[Problem]
  coord_type = RSPHERICAL
[]

[GlobalParams]
  displacements = 'disp_x'
[]

[Variables]
  # order parameter
  [./eta]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute concentration
  [./c]
    order = FIRST
    family = LAGRANGE
  [../]

  # chemical potential
  [./w]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute phase concentration (matrix)
  [./cm]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.13
  [../]
  # solute phase concentration (precipitate)
  [./cp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.235
  [../]
[]

[AuxVariables]
  [./energy_density]
    family = MONOMIAL
  [../]
  [./extra_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./extra_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./extra_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./eta_ic]
    variable = eta
    type = FunctionIC
    function = ic_func_eta
  [../]
  [./c_ic]
    variable = c
    type = FunctionIC
    function = ic_func_c
  [../]
[]

[Functions]
  [./ic_func_eta]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2);0.5*(1.0-tanh((r-r0)/delta_eta/sqrt(2.0)))'
    vars = 'delta_eta r0'
    vals = '6.431     100'
  [../]
  [./ic_func_c]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2);eta_an:=0.5*(1.0-tanh((r-r0)/delta/sqrt(2.0)));0.235*eta_an^3*(6*eta_an^2-15*eta_an+10)+0.13*(1-eta_an^3*(6*eta_an^2-15*eta_an+10))'
    vars = 'delta r0'
    vals = '6.431 100'
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    add_variables = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz'
  [../]
[]


[Kernels]

  # enforce c = (1-h(eta))*cm + h(eta)*cp
  [./PhaseConc]
    type = KKSPhaseConcentration
    ca       = cm
    variable = cp
    c        = c
    eta      = eta
  [../]

  # enforce pointwise equality of chemical potentials
  [./ChemPotVacancies]
    type = KKSPhaseChemicalPotential
    variable = cm
    cb       = cp
    fa_name  = f_total_matrix
    fb_name  = f_total_ppt
  [../]

  #
  # Cahn-Hilliard Equation
  #
  [./CHBulk]
    type = KKSSplitCHCRes
    variable = c
    ca       = cm
    fa_name  = f_total_matrix
    w        = w
  [../]

  [./dcdt]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
  [./ckernel]
    type = SplitCHWRes
    mob_name = M
    variable = w
  [../]

  #
  # Allen-Cahn Equation
  #
  [./ACBulkF]
    type = KKSACBulkF
    variable = eta
    fa_name  = f_total_matrix
    fb_name  = f_total_ppt
    w        = 0.0033
    args = 'cp cm'
  [../]
  [./ACBulkC]
    type = KKSACBulkC
    variable = eta
    ca       = cm
    cb       = cp
    fa_name  = f_total_matrix
  [../]
  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = kappa
  [../]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[AuxKernels]
  [./extra_xx]
    type = RankTwoAux
    rank_two_tensor = extra_stress
    index_i = 0
    index_j = 0
    variable = extra_xx
  [../]
  [./extra_yy]
    type = RankTwoAux
    rank_two_tensor = extra_stress
    index_i = 1
    index_j = 1
    variable = extra_yy
  [../]
  [./extra_zz]
    type = RankTwoAux
    rank_two_tensor = extra_stress
    index_i = 2
    index_j = 2
    variable = extra_zz
  [../]
  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = mechanical_strain
    index_i = 0
    index_j = 0
    variable = strain_xx
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = mechanical_strain
    index_i = 1
    index_j = 1
    variable = strain_yy
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = mechanical_strain
    index_i = 2
    index_j = 2
    variable = strain_zz
  [../]
[]

[Materials]
  # Chemical free energy of the matrix
  [./fm]
    type = DerivativeParsedMaterial
    f_name = fm
    args = 'cm'
    function = '6.55*(cm-0.13)^2'
  [../]
# Elastic energy of the matrix
  [./elastic_free_energy_m]
    type = ElasticEnergyMaterial
    base_name = matrix
    f_name = fe_m
    args = ' '
  [../]
# Total free energy of the matrix
  [./Total_energy_matrix]
    type = DerivativeSumMaterial
    f_name = f_total_matrix
    sum_materials = 'fm fe_m'
    args = 'cm'
  [../]

  # Free energy of the precipitate phase
  [./fp]
    type = DerivativeParsedMaterial
    f_name = fp
    args = 'cp'
    function = '6.55*(cp-0.235)^2'
  [../]

# Elastic energy of the precipitate
  [./elastic_free_energy_p]
    type = ElasticEnergyMaterial
    base_name = ppt
    f_name = fe_p
    args = ' '
  [../]

# Total free energy of the precipitate
  [./Total_energy_ppt]
    type = DerivativeSumMaterial
    f_name = f_total_ppt
    sum_materials = 'fp fe_p'
    args = 'cp'
  [../]

# Total elastic energy
  [./Total_elastic_energy]
    type = DerivativeTwoPhaseMaterial
    eta = eta
    f_name = f_el_mat
    fa_name = fe_m
    fb_name = fe_p
    outputs = exodus
    W = 0
  [../]

  # h(eta)
  [./h_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta
  [../]

  # g(eta)
  [./g_eta]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta
    outputs = exodus
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'M   L   kappa'
    prop_values = '0.7 0.7 0.1365'
  [../]

  #Mechanical properties
  [./Stiffness_matrix]
    type = ComputeElasticityTensor
    C_ijkl = '74.25 14.525'
    base_name = matrix
    fill_method = symmetric_isotropic
  [../]
  [./Stiffness_ppt]
    type = ComputeElasticityTensor
    C_ijkl = '74.25 14.525'
    base_name = ppt
    fill_method = symmetric_isotropic
  [../]
  [./strain_matrix]
    type = ComputeRSphericalSmallStrain
    base_name = matrix
  [../]
  [./strain_ppt]
    type = ComputeRSphericalSmallStrain
    base_name = ppt
  [../]
  [./stress_matrix]
    type = ComputeLinearElasticStress
    base_name = matrix
  [../]
  [./stress_ppt]
    type = ComputeLinearElasticStress
    base_name = ppt
  [../]
  [./global_stress]
    type = TwoPhaseStressMaterial
    base_A = matrix
    base_B = ppt
  [../]
  [./interface_stress]
    type = ComputeSurfaceTensionKKS
    v = eta
    kappa_name = kappa
    w = 0.0033
  [../]
[]

[BCs]
  [./left_r]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
[]

#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
  [./full]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -sub_pc_type   -sub_pc_factor_shift_type'
  petsc_options_value = 'asm       lu            nonzero'

  l_max_its = 30
  nl_max_its = 10
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-9
  nl_abs_tol = 1.0e-10

  num_steps = 2
  dt = 0.5
[]

[Outputs]
  exodus = true
  [./csv]
    type = CSV
    execute_on = 'final'
  [../]
[]

(test/tests/auxkernels/solution_aux/aux_nonlinear_solution_xdr.i)

[Mesh]
  # This test uses SolutionUserObject which doesn't work with DistributedMesh.
  type = GeneratedMesh
  parallel_type = replicated
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./u_aux]
  [../]
[]

[Functions]
  [./u_xdr_func]
    type = SolutionFunction
    solution = xdr_u
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[AuxKernels]
  [./aux_xdr_kernel]
    type = SolutionAux
    variable = u_aux
    solution = xdr_u_aux
    execute_on = initial
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 2
  [../]
[]

[UserObjects]
  [./xdr_u_aux]
    type = SolutionUserObject
    system = aux0
    mesh = aux_nonlinear_solution_xdr_0001_mesh.xdr
    es = aux_nonlinear_solution_xdr_0001.xdr
    execute_on = initial
  [../]
  [./xdr_u]
    type = SolutionUserObject
    system = nl0
    mesh = aux_nonlinear_solution_xdr_0001_mesh.xdr
    es = aux_nonlinear_solution_xdr_0001.xdr
    execute_on = initial
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_rel_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./u_func_ic]
    function = u_xdr_func
    variable = u
    type = FunctionIC
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/cartesian-version/2d-rc-no-slip-walls.i)

mu=1.1
rho=1.1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1
    xmax = 1
    ymin = -1
    ymax = 1
    nx = 2
    ny = 2
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  two_term_boundary_expansion = true
  advected_interp_method = 'average'
  velocity_interp_method = 'rc'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = u
    v = v
    pressure = pressure
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[ICs]
  [u]
    type = FunctionIC
    function = 'exact_u'
    variable = u
  []
  [v]
    type = FunctionIC
    function = 'exact_v'
    variable = v
  []
  [pressure]
    type = FunctionIC
    function = 'exact_p'
    variable = pressure
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = INSFVBodyForce
    variable = u
    functor = forcing_u
    momentum_component = 'x'
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = INSFVBodyForce
    variable = v
    functor = forcing_v
    momentum_component = 'y'
  []
[]

[FVBCs]
  [u_walls]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'left right'
    function = 'exact_u'
  []
  [v_walls]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'left right'
    function = 'exact_v'
  []
  [p]
    type = INSFVOutletPressureBC
    variable = pressure
    function = 'exact_p'
    boundary = 'top'
  []
  [inlet_u]
    type = INSFVInletVelocityBC
    variable = u
    function = 'exact_u'
    boundary = 'bottom'
  []
  [inlet_v]
    type = INSFVInletVelocityBC
    variable = v
    function = 'exact_v'
    boundary = 'bottom'
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    value = 'sin(x*pi)*cos(y*pi)'
  []
  [forcing_u]
    type = ADParsedFunction
    value = '2*pi^2*mu*sin(x*pi)*cos(y*pi) - 2*pi*rho*sin(x*pi)*sin(y*pi)*cos(1.3*x)*cos(y*pi) + 2*pi*rho*sin(x*pi)*cos(x*pi)*cos(y*pi)^2 + 1.5*cos(1.5*x)*cos(1.6*y)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    value = 'cos(1.3*x)*cos(y*pi)'
  []
  [forcing_v]
    type = ADParsedFunction
    value = '1.69*mu*cos(1.3*x)*cos(y*pi) + pi^2*mu*cos(1.3*x)*cos(y*pi) - 1.3*rho*sin(1.3*x)*sin(x*pi)*cos(y*pi)^2 - 2*pi*rho*sin(y*pi)*cos(1.3*x)^2*cos(y*pi) + pi*rho*cos(1.3*x)*cos(x*pi)*cos(y*pi)^2 - 1.6*sin(1.5*x)*sin(1.6*y)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin(1.5*x)*cos(1.6*y)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-pi*rho*sin(y*pi)*cos(1.3*x) + pi*rho*cos(x*pi)*cos(y*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       NONZERO               superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [p_avg]
    type = ElementAverageValue
    variable = pressure
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/vectorpostprocessors/variable_value_volume_histogram/volume_histogram.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 200
  xmin = -5
  xmax = 5
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x<2&x>-2'
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
[]

[BCs]
  [./all]
    type = DirichletBC
    variable = c
    boundary = 'left right'
    value = 0
  [../]
[]

[VectorPostprocessors]
  [./histo]
    type = VolumeHistogram
    variable = c
    min_value = 0
    max_value = 1.1
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 1
  solve_type = PJFNK
[]

[Outputs]
  execute_on = 'initial timestep_end'
  csv = true
[]

(modules/phase_field/test/tests/MultiPhase/thirdphasesuppressionmaterial.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  nz = 0
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  elem_type = QUAD4
[]

[AuxVariables]
  [./eta1]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      variable = eta1
      function = x
    [../]
  [../]
  [./eta2]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      variable = eta2
      function = 1-x
    [../]
  [../]
  [./eta3]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      variable = eta3
      function = y
    [../]
  [../]
[]

[BCs]
  [./Periodic]
    [./All]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Materials]
  [./suppressionbarrier]
    type = ThirdPhaseSuppressionMaterial
    etas = 'eta1 eta2 eta3'
    function_name = g
    outputs = exodus
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Problem]
  solve = false
[]

[Outputs]
  exodus = true
[]

(test/tests/restart/restart_subapp_not_master/two_step_solve_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./average]
    type = ElementAverageValue
    variable = u
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0.0
  end_time = 2.0
  dt = 1.0
[]

[Outputs]
  [./checkpoint]
    type = Checkpoint
    num_files = 3
  [../]
[]

(modules/richards/test/tests/theis/th_lumped_02.i)

# fully-saturated
# production
# lumped
[Mesh]
  type = FileMesh
  file = th02_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1 2 4 20'
    x = '0 1 10 100'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]

  [./total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsLumpedMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsPolyLineSink
    pressures = '-1E9 1E9'
    fluxes = '200 200'
    point_file = th01.points
    SumQuantityUO = total_outflow_mass
    variable = pressure
  [../]
[]


[Postprocessors]
  [./flow_report]
    type = RichardsPlotQuantity
    uo = total_outflow_mass
  [../]
  [./p50]
    type = PointValue
    variable = pressure
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E5
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-6 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 100
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  file_base = th_lumped_02
  csv = true
[]

(test/tests/functions/solution_function/solution_function_rot4.i)

# checking rotation of points by 45 deg about z axis in a SolutionUserObject for a 2D situation
[Mesh]
  # this is chosen so when i rotate through 45deg i get a length of "1" along the x or y direction
  type = GeneratedMesh
  dim = 2
  xmin = -0.70710678
  xmax = 0.70710678
  nx = 3
  ymin = -0.70710678
  ymax = 0.70710678
  ny = 3
[]

[UserObjects]
  [./solution_uo]
    type = SolutionUserObject
    mesh = square_with_u_equals_x.e
    timestep = 1
    system_variables = u
    rotation0_vector = '0 0 1'
    rotation0_angle = 45
    transformation_order = rotation0
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = solution_fcn
  [../]
[]

[Functions]
  [./solution_fcn]
    type = SolutionFunction
    from_variable = u
    solution = solution_uo
  [../]
[]

[Kernels]
  [./diff]
    type = TimeDerivative
    variable = u
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  l_max_its = 800
  nl_rel_tol = 1e-10
  num_steps = 1
  end_time = 1
  dt = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = solution_function_rot4
  exodus = true
[]

(modules/rdg/test/tests/advection_1d/rdgP0.i)

# This test demonstrates the advection of a tracer in 1D using the RDG module.
# There is no slope limiting.  Changing the SlopeLimiting scheme to minmod, mc,
# or superbee means that a linear reconstruction is performed, and the slope
# limited according to the scheme chosen.  Doing this produces RDG(P0P1) and
# substantially reduces numerical diffusion

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[Variables]
  [./tracer]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  [../]
[]

[UserObjects]
  [./lslope]
    type = AEFVSlopeLimitingOneD
    execute_on = 'linear'
    scheme = 'none' #none | minmod | mc | superbee
    u = tracer
  [../]

  [./internal_side_flux]
    type = AEFVUpwindInternalSideFlux
    execute_on = 'linear'
    velocity = 0.1
  [../]

  [./free_outflow_bc]
    type = AEFVFreeOutflowBoundaryFlux
    execute_on = 'linear'
    velocity = 0.1
  [../]
[]

[Kernels]
  [./dot]
    type = TimeDerivative
    variable = tracer
  [../]
[]
[DGKernels]
  [./concentration]
    type = AEFVKernel
    variable = tracer
    component = 'concentration'
    flux = internal_side_flux
    u = tracer
  [../]
[]

[BCs]
  [./concentration]
    type = AEFVBC
    boundary = 'left right'
    variable = tracer
    component = 'concentration'
    flux = free_outflow_bc
    u = tracer
  [../]
[]

[Materials]
  [./aefv]
    type = AEFVMaterial
    slope_limiting = lslope
    u = tracer
  [../]
[]


[VectorPostprocessors]
  [./tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 100
    sort_by = x
    variable = tracer
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  end_time = 6
  dt = 6E-1
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  #exodus = true
  csv = true
  execute_on = final
[]

(modules/richards/test/tests/buckley_leverett/bl01_adapt.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 15
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2.0E6
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-4
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]


[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]

[AuxKernels]
  active = 'calculate_seff'
  [./calculate_seff]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffVG
    pressure_vars = pressure
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[BCs]
  active = 'left'
  [./left]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 980000
  [../]
[]

[Kernels]
  active = 'richardsf richardst'

  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]


[Functions]
 active = 'initial_pressure'
  [./initial_pressure]
    type = ParsedFunction
    value = max((1000000-x/5*1000000)-20000,-20000)
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Adaptivity]
  marker = errorfrac
  max_h_level = 3
  [./Indicators]
    [./error]
      type = RichardsFluxJumpIndicator
      variable = pressure
    [../]
  [../]
  [./Markers]
    [./errorfrac]
      type = ErrorFractionMarker
      refine = 0.5
      coarsen = 0.3
      indicator = error
   [../]
  [../]
[]

[Preconditioning]
  active = 'andy'

  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 20'
  [../]

[]

[Executioner]
  type = Transient
  end_time = 50


  [./TimeStepper]
    type = FunctionControlledDT
    functions = ''
    maximums = ''
    minimums = ''
    dt = 0.3
    increment = 1.1
    decrement = 1.1
    maxDt = 0.3
    minDt = 1E-5
    adapt_log = false
    percent_change = 0.1
  [../]

[]

[Outputs]
  file_base = bl01_adapt
  interval = 10000
  exodus = true
[]

(modules/combined/test/tests/surface_tension_KKS/surface_tension_VDWgas.i)

# Test for ComputeExtraStressVDWGas
# Gas bubble with r = 15 nm in a solid matrix
# The gas pressure is counterbalanced by the surface tension of the solid-gas interface,
# which is included with ComputeSurfaceTensionKKS

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 300
  xmin = 0
  xmax = 30
[]

[Problem]
  coord_type = RSPHERICAL
[]

[GlobalParams]
  displacements = 'disp_x'
[]

[Variables]
  # order parameter
  [./eta]
    order = FIRST
    family = LAGRANGE
  [../]

  # gas concentration
  [./cg]
    order = FIRST
    family = LAGRANGE
  [../]

  # vacancy concentration
  [./cv]
    order = FIRST
    family = LAGRANGE
  [../]


  # gas chemical potential
  [./wg]
    order = FIRST
    family = LAGRANGE
  [../]

  # vacancy chemical potential
  [./wv]
    order = FIRST
    family = LAGRANGE
  [../]


  # Matrix phase gas concentration
  [./cgm]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1.01e-31
  [../]

  # Matrix phase vacancy concentration
  [./cvm]
    order = FIRST
    family = LAGRANGE
    initial_condition = 2.25e-11
  [../]

  # Bubble phase gas concentration
  [./cgb]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.2714
  [../]

  # Bubble phase vacancy concentration
  [./cvb]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.7286
  [../]
[]

[ICs]
  [./eta_ic]
    variable = eta
    type = FunctionIC
    function = ic_func_eta
  [../]
  [./cv_ic]
    variable = cv
    type = FunctionIC
    function = ic_func_cv
  [../]
  [./cg_ic]
    variable = cg
    type = FunctionIC
    function = ic_func_cg
  [../]
[]

[Functions]
  [./ic_func_eta]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2);0.5*(1.0-tanh((r-r0)/delta_eta/sqrt(2.0)))'
    vars = 'delta_eta r0'
    vals = '0.321     15'
  [../]
  [./ic_func_cv]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2);eta_an:=0.5*(1.0-tanh((r-r0)/delta/sqrt(2.0)));cvbubinit*eta_an^3*(6*eta_an^2-15*eta_an+10)+cvmatrixinit*(1-eta_an^3*(6*eta_an^2-15*eta_an+10))'
    vars = 'delta r0  cvbubinit cvmatrixinit'
    vals = '0.321 15  0.7286    2.25e-11'
  [../]
  [./ic_func_cg]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2);eta_an:=0.5*(1.0-tanh((r-r0)/delta/sqrt(2.0)));cgbubinit*eta_an^3*(6*eta_an^2-15*eta_an+10)+cgmatrixinit*(1-eta_an^3*(6*eta_an^2-15*eta_an+10))'
    vars = 'delta r0  cgbubinit cgmatrixinit'
    vals = '0.321 15  0.2714    1.01e-31'
  [../]
[]



[Modules/TensorMechanics/Master]
  [./all]
    add_variables = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz'
  [../]
[]

[Kernels]
  # enforce cg = (1-h(eta))*cgm + h(eta)*cgb
  [./PhaseConc_g]
    type = KKSPhaseConcentration
    ca       = cgm
    variable = cgb
    c        = cg
    eta      = eta
  [../]

  # enforce cv = (1-h(eta))*cvm + h(eta)*cvb
  [./PhaseConc_v]
    type = KKSPhaseConcentration
    ca       = cvm
    variable = cvb
    c        = cv
    eta      = eta
  [../]

  # enforce pointwise equality of chemical potentials
  [./ChemPotVacancies]
    type = KKSPhaseChemicalPotential
    variable = cvm
    cb       = cvb
    fa_name  = f_total_matrix
    fb_name  = f_total_bub
    args_a = 'cgm'
    args_b = 'cgb'
  [../]
  [./ChemPotGas]
    type = KKSPhaseChemicalPotential
    variable = cgm
    cb       = cgb
    fa_name  = f_total_matrix
    fb_name  = f_total_bub
    args_a = 'cvm'
    args_b = 'cvb'
  [../]

  #
  # Cahn-Hilliard Equations
  #
  [./CHBulk_g]
    type = KKSSplitCHCRes
    variable = cg
    ca       = cgm
    fa_name  = f_total_matrix
    w        = wg
    args_a   = 'cvm'
  [../]
  [./CHBulk_v]
    type = KKSSplitCHCRes
    variable = cv
    ca       = cvm
    fa_name  = f_total_matrix
    w        = wv
    args_a   = 'cgm'
  [../]

  [./dcgdt]
    type = CoupledTimeDerivative
    variable = wg
    v = cg
  [../]
  [./dcvdt]
    type = CoupledTimeDerivative
    variable = wv
    v = cv
  [../]

  [./wgkernel]
    type = SplitCHWRes
    mob_name = M
    variable = wg
  [../]
  [./wvkernel]
    type = SplitCHWRes
    mob_name = M
    variable = wv
  [../]

  #
  # Allen-Cahn Equation
  #
  [./ACBulkF]
    type = KKSACBulkF
    variable = eta
    fa_name  = f_total_matrix
    fb_name  = f_total_bub
    w        = 0.356
    args = 'cvm cvb cgm cgb'
  [../]
  [./ACBulkCv]
    type = KKSACBulkC
    variable = eta
    ca       = cvm
    cb       = cvb
    fa_name  = f_total_matrix
    args     = 'cgm'
  [../]
  [./ACBulkCg]
    type = KKSACBulkC
    variable = eta
    ca       = cgm
    cb       = cgb
    fa_name  = f_total_matrix
    args     = 'cvm'
  [../]
  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = kappa
  [../]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[Materials]
  # Chemical free energy of the matrix
  [./fm]
    type = DerivativeParsedMaterial
    f_name = fm
    args = 'cvm cgm'
    material_property_names = 'kvmatrix kgmatrix cvmatrixeq cgmatrixeq'
    function = '0.5*kvmatrix*(cvm-cvmatrixeq)^2 + 0.5*kgmatrix*(cgm-cgmatrixeq)^2'
  [../]
# Elastic energy of the matrix
  [./elastic_free_energy_m]
    type = ElasticEnergyMaterial
    base_name = matrix
    f_name = fe_m
    args = ' '
  [../]
# Total free energy of the matrix
  [./Total_energy_matrix]
    type = DerivativeSumMaterial
    f_name = f_total_matrix
    sum_materials = 'fm fe_m'
    args = 'cvm cgm'
  [../]

  # Free energy of the bubble phase
  [./fb]
    type = DerivativeParsedMaterial
    f_name = fb
    args = 'cvb cgb'
    material_property_names = 'kToverV nQ Va b f0 kpen kgbub kvbub cvbubeq cgbubeq'
    function = '0.5*kgbub*(cvb-cvbubeq)^2 + 0.5*kvbub*(cgb-cgbubeq)^2'
  [../]

# Elastic energy of the bubble
  [./elastic_free_energy_p]
    type = ElasticEnergyMaterial
    base_name = bub
    f_name = fe_b
    args = ' '
  [../]

# Total free energy of the bubble
  [./Total_energy_bub]
    type = DerivativeSumMaterial
    f_name = f_total_bub
    sum_materials = 'fb fe_b'
    # sum_materials = 'fb'
    args = 'cvb cgb'
  [../]

  # h(eta)
  [./h_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta
  [../]

  # g(eta)
  [./g_eta]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'M   L   kappa  Va      kvmatrix  kgmatrix  kgbub kvbub f0      kpen  cvbubeq cgbubeq b      T'
    prop_values = '0.7 0.7 0.0368 0.03629 223.16    223.16    2.23  2.23  0.0224  1.0   0.6076  0.3924  0.085  800'
  [../]
  [./cvmatrixeq]
    type = ParsedMaterial
    f_name = cvmatrixeq
    material_property_names = 'T'
    constant_names        = 'kB           Efv'
    constant_expressions  = '8.6173324e-5 1.69'
    function = 'exp(-Efv/(kB*T))'
  [../]
  [./cgmatrixeq]
    type = ParsedMaterial
    f_name = cgmatrixeq
    material_property_names = 'T'
    constant_names        = 'kB           Efg'
    constant_expressions  = '8.6173324e-5 4.92'
    function = 'exp(-Efg/(kB*T))'
  [../]
  [./kToverV]
    type = ParsedMaterial
    f_name = kToverV
    material_property_names = 'T Va'
    constant_names        = 'k          C44dim' #k in J/K and dimensional C44 in J/m^3
    constant_expressions  = '1.38e-23   63e9'
    function = 'k*T*1e27/Va/C44dim'
  [../]
  [./nQ]
    type = ParsedMaterial
    f_name = nQ
    material_property_names = 'T'
    constant_names        = 'k          Pi      M         hbar' #k in J/K, M is Xe atomic mass in kg, hbar in J s
    constant_expressions  = '1.38e-23   3.14159 2.18e-25  1.05459e-34'
    function = '(M*k*T/2/Pi/hbar^2)^1.5 * 1e-27' #1e-27 converts from #/m^3 to #/nm^3
  [../]

  #Mechanical properties
  [./Stiffness_matrix]
    type = ComputeElasticityTensor
    C_ijkl = '0.778 0.7935'
    fill_method = symmetric_isotropic
    base_name = matrix
  [../]
  [./Stiffness_bub]
    type = ComputeElasticityTensor
    C_ijkl = '0.0778 0.07935'
    fill_method = symmetric_isotropic
    base_name = bub
  [../]
  [./strain_matrix]
    type = ComputeRSphericalSmallStrain
    base_name = matrix
  [../]
  [./strain_bub]
    type = ComputeRSphericalSmallStrain
    base_name = bub
  [../]
  [./stress_matrix]
    type = ComputeLinearElasticStress
    base_name = matrix
  [../]
  [./stress_bub]
    type = ComputeLinearElasticStress
    base_name = bub
  [../]
  [./global_stress]
    type = TwoPhaseStressMaterial
    base_A = matrix
    base_B = bub
  [../]
  [./surface_tension]
    type = ComputeSurfaceTensionKKS
    v = eta
    kappa_name = kappa
    w = 0.356
  [../]
  [./gas_pressure]
    type = ComputeExtraStressVDWGas
    T = T
    b = b
    cg = cgb
    Va = Va
    nondim_factor = 63e9
    base_name = bub
    outputs = exodus
  [../]
[]

[BCs]
  [./left_r]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
[]

[Preconditioning]
  [./full]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -sub_pc_type   -sub_pc_factor_shift_type'
  petsc_options_value = 'asm       lu            nonzero'

  l_max_its = 30
  nl_max_its = 15
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-10
  nl_abs_tol = 1e-11
  num_steps = 2
  dt = 0.5
[]

[Outputs]
  exodus = true
[]

(test/tests/postprocessors/displaced_mesh/elemental.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  displacements = 'ux uy'
[]

[AuxVariables]
  [./ux]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
  [./uy]
    [./InitialCondition]
      type = FunctionIC
      function = y
    [../]
  [../]
  [./c]
    initial_condition = 1
  [../]
[]

[Variables]
  [./a]
  [../]
[]
[Kernels]
  [./a]
    type = Diffusion
    variable = a
  [../]
[]

[Postprocessors]
  [./without]
    type = ElementIntegralVariablePostprocessor
    variable = c
    execute_on = initial
  [../]
  [./with]
    type = ElementIntegralVariablePostprocessor
    variable = c
    use_displaced_mesh = true
    execute_on = initial
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 0
[]

[Outputs]
  [./out]
    type = Exodus
  [../]
[]

(test/tests/functions/image_function/threshold_adapt.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    threshold = 2.7e4
    upper_value = 1
    lower_value = -1
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Adaptivity]
  max_h_level = 5
  initial_steps = 5
  initial_marker = marker
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = u
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      refine = 0.9
    []
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/function_file_test6.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    x = '1'
    y = '2'
    xy_data = '1 2'
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/phase_field/test/tests/feature_flood_test/parallel_feature_count.i)

[Mesh]
  type = ImageMesh
  dim = 2
  file = spiral_16x16.png
  scale_to_one = false
[]

[Variables]
  [./u]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxVariables]
  [./feature]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./proc_id]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./feature_ghost]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./nodal_flood_aux]
    type = FeatureFloodCountAux
    variable = feature
    flood_counter = flood_count_pp
    execute_on = 'initial timestep_end'
  [../]
  [./proc_id]
    type = ProcessorIDAux
    variable = proc_id
    execute_on = 'initial timestep_end'
  [../]
  [./ghost]
    type = FeatureFloodCountAux
    variable = feature_ghost
    field_display = GHOSTED_ENTITIES
    flood_counter = flood_count_pp
    execute_on = 'initial timestep_end'
  [../]
[]

[Functions]
  [./tif]
    type = ImageFunction
    component = 0
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    function = tif
    variable = u
  [../]
[]

[Postprocessors]
  [./flood_count_pp]
    type = FeatureFloodCount
    variable = u
    threshold = 1.0
    execute_on = 'initial timestep_end'
  [../]
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/userobject/HLLC/hllc_uo_2D_tri.i)

rho_left = 1.162633159
E_left = 2.1502913276e+05
v_left = 40

rho_right = 1.116127833
E_right = 1.7919094397e+05
v_right = 50

[Mesh]
  [./cartesian]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 2
    nx = 1
    ny = 1
    elem_type = 'TRI3'
  [../]
[]

[Modules]
  [./FluidProperties]
    [./fp]
      type = IdealGasFluidProperties
      allow_imperfect_jacobians = true
    [../]
  [../]
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./rho]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./rho_v]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./rho_E]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./rho_ic]
    type = FunctionIC
    variable = rho
    function = 'if (y / (2 * x) < 0.5, ${rho_left}, ${rho_right})'
  [../]

  [./rho_v_ic]
    type = FunctionIC
    variable = rho_v
    function = 'if (y / (2 * x) < 0.5, ${fparse rho_left * v_left}, ${fparse rho_right * v_right})'
  [../]

  [./rho_E_ic]
    type = FunctionIC
    variable = rho_E
    function = 'if (y / (2 * x) < 0.5, ${fparse E_left * rho_left}, ${fparse E_right * rho_right})'
  [../]
[]

[Materials]
  [./var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = 0
    rhov = rho_v
    rho_et = rho_E
    fp = fp
  [../]
[]

[UserObjects]
  [./hllc]
    type = HLLCUserObject
    fp = fp
  [../]
[]

[VectorPostprocessors]
  [./wave_speeds]
    type = WaveSpeedVPP
    hllc_uo = hllc
    elem_id = 0
    side_id = 2
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/level_set/examples/rotating_circle/circle_rotate.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 32
  ny = 32
  uniform_refine = 2
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[Variables]
  [./phi]
  [../]
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '4*y'
    value_y = '-4*x'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial' #timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1.570796
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/porous_flow/test/tests/numerical_diffusion/pffltvd_action.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, employing PorousFlow Kernels and UserObjects, with superbee flux-limiter
# Using the PorousFlowFullySaturated Action
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[PorousFlowFullySaturated]
  porepressure = porepressure
  coupling_type = Hydro
  fp = the_simple_fluid
  mass_fraction_vars = tracer
  stabilization = KT
  flux_limiter_type = superbee
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  file_base = pffltvd_out
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/richards/test/tests/gravity_head_2/gh_fu_02.i)

# unsaturated = true
# gravity = true
# supg = false
# transient = false

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmin = 0
  xmax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1.0E2
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 0.5
    bulk_mod = 0.5E2
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.15
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.05
    sum_s_res = 0.15
  [../]
  [./SUPGwater]
    type = RichardsSUPGnone
  [../]
  [./SUPGgas]
    type = RichardsSUPGnone
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  # get nonconvergence if initial condition is too crazy
  [./water_ic]
    type = FunctionIC
    function = pwater_initial
    variable = pwater
  [../]
  [./gas_ic]
    type = FunctionIC
    function = pgas_initial
    variable = pgas
  [../]
[]


[Kernels]
  active = 'richardsfwater richardsfgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFullyUpwindFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFullyUpwindFlux
    variable = pgas
  [../]
[]


[AuxVariables]
  [./seffgas]
  [../]
  [./seffwater]
  [../]
[]

[AuxKernels]
  [./seffgas_kernel]
    type = RichardsSeffAux
    pressure_vars = 'pwater pgas'
    seff_UO = SeffGas
    variable = seffgas
  [../]
  [./seffwater_kernel]
    type = RichardsSeffAux
    pressure_vars = 'pwater pgas'
    seff_UO = SeffWater
    variable = seffwater
  [../]
[]

[Postprocessors]
  [./mwater_init]
    type = RichardsMass
    variable = pwater
    execute_on = timestep_begin
    outputs = none
  [../]
  [./mgas_init]
    type = RichardsMass
    variable = pgas
    execute_on = timestep_begin
    outputs = none
  [../]
  [./mwater_fin]
    type = RichardsMass
    variable = pwater
    execute_on = timestep_end
    outputs = none
  [../]
  [./mgas_fin]
    type = RichardsMass
    variable = pgas
    execute_on = timestep_end
    outputs = none
  [../]

  [./mass_error_water]
    type = FunctionValuePostprocessor
    function = fcn_mass_error_w
    outputs = none # no reason why mass should be conserved
  [../]
  [./mass_error_gas]
    type = FunctionValuePostprocessor
    function = fcn_mass_error_g
    outputs = none # no reason why mass should be conserved
  [../]

  [./pw_left]
    type = PointValue
    point = '0 0 0'
    variable = pwater
    outputs = none
  [../]
  [./pw_right]
    type = PointValue
    point = '1 0 0'
    variable = pwater
    outputs = none
  [../]
  [./error_water]
    type = FunctionValuePostprocessor
    function = fcn_error_water
  [../]

  [./pg_left]
    type = PointValue
    point = '0 0 0'
    variable = pgas
    outputs = none
  [../]
  [./pg_right]
    type = PointValue
    point = '1 0 0'
    variable = pgas
    outputs = none
  [../]
  [./error_gas]
    type = FunctionValuePostprocessor
    function = fcn_error_gas
  [../]
[]

[Functions]
  [./pwater_initial]
    type = ParsedFunction
    value = 1-x/2
  [../]
  [./pgas_initial]
    type = ParsedFunction
    value = 2-x/5
  [../]

  [./fcn_mass_error_w]
    type = ParsedFunction
    value = 'abs(0.5*(mi-mf)/(mi+mf))'
    vars = 'mi mf'
    vals = 'mwater_init mwater_fin'
  [../]
  [./fcn_mass_error_g]
    type = ParsedFunction
    value = 'abs(0.5*(mi-mf)/(mi+mf))'
    vars = 'mi mf'
    vals = 'mgas_init mgas_fin'
  [../]
  [./fcn_error_water]
    type = ParsedFunction
    value = 'abs((-b*log(-(gdens0*xval+(-b*exp(-p0/b)))/b)-p1)/p1)'
    vars = 'b gdens0 p0 xval p1'
    vals = '1E2 -1 pw_left 1 pw_right'
  [../]
  [./fcn_error_gas]
    type = ParsedFunction
    value = 'abs((-b*log(-(gdens0*xval+(-b*exp(-p0/b)))/b)-p1)/p1)'
    vars = 'b gdens0 p0 xval p1'
    vals = '0.5E2 -0.5 pg_left 1 pg_right'
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    viscosity = '1E-3 0.5E-3'
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]



[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres asm lu NONZERO 1E-10 1E-10 10000'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = gh_fu_02
  csv = true
[]

(test/tests/time_steppers/timesequence_stepper/timesequence_restart2.i)

[Mesh]
  file = timesequence_restart1_cp/0002_mesh.cpr
[]

[Problem]
  restart_file_base = timesequence_restart1_cp/0002
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  end_time = 4.0
  [./TimeStepper]
    type = TimeSequenceStepper
    time_sequence  = '0   0.85 1.3 2 4'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_pflow/pffltvd_3D.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, employing PorousFlow Kernels and UserObjects, with superbee flux-limiter
# 3D version
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  xmin = 0
  xmax = 1
  ny = 4
  ymin = 0
  ymax = 0.5
  nz = 3
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0.5 2'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 0.3
  dt = 6E-2
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/porous_flow/test/tests/sinks/s13.i)

# Apply a PorousFlowOutflowBC to the right-hand side and watch fluid flow to it
#
# This test has a single phase with two components.  The test initialises with
# the porous material fully filled with component=1.  The left-hand side is fixed
# at porepressure=1 and mass-fraction of the zeroth component being unity.
# The right-hand side has
# - porepressure fixed at zero via a DirichletBC: physically this removes component=1
#   to ensure that porepressure remains fixed
# - a PorousFlowOutflowBC for the component=0 to allow that component to exit the boundary freely
#
# Therefore, the zeroth fluid component will flow from left to right (down the
# pressure gradient).
#
# The important DE is
# porosity * dc/dt = (perm / visc) * grad(P) * grad(c)
# which is true for c = mass-fraction, and very large bulk modulus of the fluid.
# For grad(P) constant in time and space (as in this example) this is just the
# advection equation for c, with velocity = perm / visc / porosity.  The parameters
# are chosen to velocity = 1 m/s.
# In the numerical world, and especially with full upwinding, the advection equation
# suffers from diffusion.  In this example, the diffusion is obvious when plotting
# the mass-fraction along the line, but the average velocity of the front is still
# correct at 1 m/s.
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [pp]
  []
  [frac]
  []
[]

[PorousFlowFullySaturated]
  fp = simple_fluid
  porepressure = pp
  mass_fraction_vars = frac
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = 1-x
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1e10 # need large in order for constant-velocity advection
      density0 = 1 # irrelevant
      thermal_expansion = 0
      viscosity = 11
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 1.1 0 0 0 1.1'
  []
[]


[BCs]
  [lhs_fixed_b]
    type = DirichletBC
    boundary = left
    variable = pp
    value = 1
  []
  [rhs_fixed_b]
    type = DirichletBC
    boundary = right
    variable = pp
    value = 0
  []
  [lhs_fixed_a]
    type = DirichletBC
    boundary = left
    variable = frac
    value = 1
  []
  [outflow_a]
    type = PorousFlowOutflowBC
    boundary = right
    include_relperm = false # no need for relperm in this fully-saturated simulation
    mass_fraction_component = 0
    variable = frac
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'asm lu NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-2
  end_time = 1
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[VectorPostprocessors]
  [mf]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 100
    sort_by = x
    variable = frac
  []
[]

[Outputs]
  [console]
    type = Console
    execute_on = 'nonlinear linear'
  []
  [csv]
    type = CSV
    sync_times = '0.1 0.5 1'
    sync_only = true
  []
  interval = 10
[]

(modules/chemical_reactions/test/tests/parser/equilibrium_action.i)

# Test AqueousEquilibriumReactions parser

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./a]
  [../]
  [./b]
  [../]
[]

[AuxVariables]
  [./pressure]
  [../]
[]

[ICs]
  [./a]
    type = BoundingBoxIC
    variable = a
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 1
    inside = 1.0e-2
    outside = 1.0e-10
  [../]
  [./b]
    type = BoundingBoxIC
    variable = b
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 1
    inside = 1.0e-2
    outside = 1.0e-10
  [../]
  [./pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  [../]
[]

[ReactionNetwork]
  [./AqueousEquilibriumReactions]
    primary_species = 'a b'
    reactions = '2a = pa2 2,
                 (1.0)a + (1.0)b = pab -2'
    secondary_species = 'pa2 pab'
    pressure = pressure
  [../]
[]

[Kernels]
  [./a_ie]
    type = PrimaryTimeDerivative
    variable = a
  [../]
  [./a_diff]
    type = PrimaryDiffusion
    variable = a
  [../]
  [./a_conv]
    type = PrimaryConvection
    variable = a
    p = pressure
  [../]
  [./b_ie]
    type = PrimaryTimeDerivative
    variable = b
  [../]
  [./b_diff]
    type = PrimaryDiffusion
    variable = b
  [../]
  [./b_conv]
    type = PrimaryConvection
    variable = b
    p = pressure
  [../]
[]

[BCs]
  [./a_left]
    type = DirichletBC
    variable = a
    boundary = left
    value = 1.0e-2
  [../]
  [./a_right]
    type = ChemicalOutFlowBC
    variable = a
    boundary = right
  [../]
  [./b_left]
    type = DirichletBC
    variable = b
    boundary = left
    value = 1.0e-2
  [../]
  [./b_right]
    type = ChemicalOutFlowBC
    variable = b
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-4 1e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  nl_abs_tol = 1e-12
  end_time = 10
  dt = 10
[]

[Outputs]
  file_base = equilibrium_out
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

(test/tests/misc/check_error/function_file_test16.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_rows_more_data.csv
    xy_in_file_only = false
    y_index_in_file = 3 # will generate an error because no forth row of data
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/xfem/test/tests/switching_material/one_cut_stationary.i)

[Problem]
  solve = false
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [levelset_cut]
    type = LevelSetCutUserObject
    level_set_var = phi
    negative_id = 1
    positive_id = 33
  []
[]

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
[]

[AuxVariables]
  [phi]
    [InitialCondition]
      type = FunctionIC
      function = 'x-0.213'
    []
  []
[]

[Materials]
  [diffusivity_A]
    type = GenericConstantMaterial
    prop_names = 'A_D'
    prop_values = '5'
  []
  [diffusivity_B]
    type = GenericConstantMaterial
    prop_names = 'B_D'
    prop_values = '0.5'
  []
  [diff_combined]
    type = XFEMCutSwitchingMaterialReal
    cut_subdomain_ids = '1 33'
    base_names = 'A B'
    prop_name = D
    geometric_cut_userobject = levelset_cut
    outputs = 'exodus'
    output_properties = 'D'
  []
[]

[Executioner]
  type = Transient

  num_steps = 1

  max_xfem_update = 1
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/dirac/bh09.i)

# fully-saturated
# production
# with anisotropic permeability
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh02.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = 1
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '2E-12 1E-12 0  1E-12 2E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 0.5
  dt = 1E-2
  solve_type = NEWTON

[]

[Outputs]
  file_base = bh09
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/phase_field/test/tests/GrandPotentialPFM/SinteringParabolic.i)

#input file to test the GrandPotentialSinteringMaterial using the parabolic energy profile

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 17
  ny = 10
  xmin = 0
  xmax = 660
  ymin = 0
  ymax = 380
[]

[GlobalParams]
  op_num = 2
  var_name_base = gr
  int_width = 40
[]

[Variables]
  [./w]
    [./InitialCondition]
      type = FunctionIC
      variable = w
      function = f_w
    [../]
  [../]
  [./phi]
  [../]
  [./PolycrystalVariables]
  [../]
[]

[AuxVariables]
  [./T]
    order = CONSTANT
    family = MONOMIAL
    [./InitialCondition]
      type = FunctionIC
      variable = T
      function = f_T
    [../]
  [../]
[]

[ICs]
  [./phi_IC]
    type = SpecifiedSmoothCircleIC
    variable = phi
    x_positions = '190 470'
    y_positions = '190 190'
    z_positions = '  0   0'
    radii = '150 150'
    invalue = 0
    outvalue = 1
  [../]
  [./gr0_IC]
    type = SmoothCircleIC
    variable = gr0
    x1 = 190
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
  [./gr1_IC]
    type = SmoothCircleIC
    variable = gr1
    x1 = 470
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
[]

[Functions]
  [./f_T]
    type = ConstantFunction
    value = 1600
  [../]
  [./f_w]
    type = ParsedFunction
    value = '1.515e-7 * x'
  [../]
[]

[Materials]
  # Free energy coefficients for parabolic curve
  [./ks]
    type = ParsedMaterial
    f_name = ks
    args = 'T'
    constant_names = 'a b'
    constant_expressions = '-0.0025 157.16'
    function = 'a*T + b'
  [../]
  [./kv]
    type = ParsedMaterial
    f_name = kv
    material_property_names = 'ks'
    function = '10 * ks'
  [../]
  # Diffusivity and mobilities
  [./chiD]
    type = GrandPotentialTensorMaterial
    f_name = chiD
    solid_mobility = L
    void_mobility = Lv
    chi = chi
    surface_energy = 19.7
    c = phi
    T = T
    D0 = 2.0e11
    GBmob0 = 1.4759e9
    Q = 2.77
    Em = 2.40
    bulkindex = 1
    gbindex = 20
    surfindex = 100
  [../]
  # Equilibrium vacancy concentration
  [./cs_eq]
    type = DerivativeParsedMaterial
    f_name = cs_eq
    args = 'gr0 gr1 T'
    constant_names = 'Ef Egb kB'
    constant_expressions = '2.69 2.1 8.617343e-5'
    function = 'bnds:=gr0^2 + gr1^2; cb:=exp(-Ef/kB/T); cgb:=exp(-(Ef-Egb)/kB/T);
                cb + 4.0*(cgb-cb)*(1.0 - bnds)^2'
  [../]
  # Everything else
  [./sintering]
    type = GrandPotentialSinteringMaterial
    chemical_potential = w
    void_op = phi
    Temperature = T
    surface_energy = 19.7
    grainboundary_energy = 9.86
    void_energy_coefficient = kv
    equilibrium_vacancy_concentration = cs_eq
    solid_energy_model = PARABOLIC
    outputs = exodus
  [../]

  # Concentration is only meant for output
  [./c]
    type = ParsedMaterial
    f_name = c
    material_property_names = 'hs rhos hv rhov'
    constant_names = 'Va'
    constant_expressions = '0.04092'
    function = 'Va*(hs*rhos + hv*rhov)'
    outputs = exodus
  [../]
[]

[Kernels]
  [./dt_gr0]
    type = TimeDerivative
    variable = gr0
  [../]
  [./dt_gr1]
    type = TimeDerivative
    variable = gr1
  [../]
  [./dt_phi]
    type = TimeDerivative
    variable = phi
  [../]
  [./dt_w]
    type = TimeDerivative
    variable = w
  [../]
[]

[AuxKernels]
  [./T_aux]
    type = FunctionAux
    variable = T
    function = f_T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = JFNK
  dt = 1
  num_steps = 2
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/basic_advection/except2.i)

# PorousFlowDarcyVelocityMaterial attempts to have at_nodes = true
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 4
      thermal_expansion = 0
      viscosity = 150.0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
    at_nodes = true
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/richards/test/tests/uo_egs/relperm.i)

# Outputs a relative permeability curve into an exodus file
# and into a CSV file.
# In the exodus file, the relperm will be a function of "x", and
# this "x" is actually effective saturation.
# In the CSV file you will find the relperm at the "x" point
# specified by you below.
#
# You may specify:
#  - the "type" of relative permeability in the UserObjects block
#  - the parameters of this relative permeability curve in the UserObjects block
#  - the "x" point (which is effective saturation) that you want to extract
#       the relative permeability at, if you want a value at a particular point


[UserObjects]
  [./relperm]
    type = RichardsRelPermPower
    simm = 0.1
    n = 3
  [../]
[]

[Postprocessors]
  [./point_val]
    type = PointValue
    execute_on = timestep_begin
    point = '0.5 0 0'
    variable = relperm
  [../]
[]


############################
# You should not need to change any of the stuff below
############################

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = x
  [../]
[]

[AuxVariables]
  [./relperm]
  [../]
[]

[AuxKernels]
  [./relperm_AuxK]
    type = RichardsRelPermAux
    variable = relperm
    relperm_UO = relperm
    execute_on = timestep_begin
    seff_var = u
  [../]
[]

[Kernels]
  [./dummy]
    type = Diffusion
    variable = u
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 0
[]

[Outputs]
  file_base = relperm
  [./csv]
    type = CSV
  [../]
  [./exodus]
    type = Exodus
    hide = u
  [../]
[]

(modules/chemical_reactions/test/tests/parser/equilibrium_without_action.i)

# Test AqueousEquilibriumReactions parser

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./a]
  [../]
  [./b]
  [../]
[]

[AuxVariables]
  [./pressure]
  [../]
  [./pa2]
  [../]
  [./pab]
  [../]
[]

[AuxKernels]
  [./pa2]
    type = AqueousEquilibriumRxnAux
    variable = pa2
    v = a
    log_k = 2
    sto_v = 2
  [../]
  [./pab]
    type = AqueousEquilibriumRxnAux
    variable = pab
    v = 'a b'
    log_k = -2
    sto_v = '1 1'
  [../]
[]

[ICs]
  [./a]
    type = BoundingBoxIC
    variable = a
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 1
    inside = 1.0e-2
    outside = 1.0e-10
  [../]
  [./b]
    type = BoundingBoxIC
    variable = b
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 1
    inside = 1.0e-2
    outside = 1.0e-10
  [../]
  [./pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  [../]
[]

[Kernels]
  [./a_ie]
    type = PrimaryTimeDerivative
    variable = a
  [../]
  [./a_diff]
    type = PrimaryDiffusion
    variable = a
  [../]
  [./a_conv]
    type = PrimaryConvection
    variable = a
    p = pressure
  [../]
  [./b_ie]
    type = PrimaryTimeDerivative
    variable = b
  [../]
  [./b_diff]
    type = PrimaryDiffusion
    variable = b
  [../]
  [./b_conv]
    type = PrimaryConvection
    variable = b
    p = pressure
  [../]
  [./a1_eq]
    type = CoupledBEEquilibriumSub
    variable = a
    log_k = 2
    weight = 2
    sto_u = 2
  [../]
  [./a1_diff]
    type = CoupledDiffusionReactionSub
    variable = a
    log_k = 2
    weight = 2
    sto_u = 2
  [../]
  [./a1_conv]
    type = CoupledConvectionReactionSub
    variable = a
    log_k = 2
    weight = 2
    sto_u = 2
    p = pressure
  [../]
  [./a2_eq]
    type = CoupledBEEquilibriumSub
    variable = a
    v = b
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./a2_diff]
    type = CoupledDiffusionReactionSub
    variable = a
    v = b
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./a2_conv]
    type = CoupledConvectionReactionSub
    variable = a
    v = b
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
    p = pressure
  [../]
  [./b2_eq]
    type = CoupledBEEquilibriumSub
    variable = b
    v = a
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./b2_diff]
    type = CoupledDiffusionReactionSub
    variable = b
    v = a
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./b2_conv]
    type = CoupledConvectionReactionSub
    variable = b
    v = a
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
    p = pressure
  [../]
[]

[BCs]
  [./a_left]
    type = DirichletBC
    variable = a
    boundary = left
    value = 1.0e-2
  [../]
  [./a_right]
    type = ChemicalOutFlowBC
    variable = a
    boundary = right
  [../]
  [./b_left]
    type = DirichletBC
    variable = b
    boundary = left
    value = 1.0e-2
  [../]
  [./b_right]
    type = ChemicalOutFlowBC
    variable = b
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-4 1e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  nl_abs_tol = 1e-12
  end_time = 10
  dt = 10
[]

[Outputs]
  file_base = equilibrium_out
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

(modules/level_set/test/tests/verification/1d_level_set_supg_mms/1d_level_set_supg_mms.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 32
  nx = 64
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[ICs]
  [./phi_ic]
    function = phi_exact
    variable = phi
    type = FunctionIC
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Functions]
  [./phi_exact]
    type = ParsedFunction
    value = 'a*exp(1/(10*t))*sin(2*pi*x/b) + 1'
    vars = 'a b'
    vals = '1 8'
  [../]
  [./phi_mms]
    type = ParsedFunction
    value = '-a*exp(1/(10*t))*sin(2*pi*x/b)/(10*t^2) + 2*pi*a*exp(1/(10*t))*cos(2*pi*x/b)/b'
    vars = 'a b'
    vals = '1 8'
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '1'
    value_y = '1'
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./time_supg]
    type = LevelSetTimeDerivativeSUPG
    variable = phi
    velocity = velocity
  [../]
  [./phi_advection]
    type = LevelSetAdvection
    variable = phi
    velocity = velocity
  [../]
  [./phi_forcing]
    type = BodyForce
    variable = phi
    function = phi_mms
  [../]
  [./phi_advection_supg]
    type = LevelSetAdvectionSUPG
    variable = phi
    velocity = velocity
  [../]
  [./phi_forcing_supg]
    type = LevelSetForcingFunctionSUPG
    velocity = velocity
    variable = phi
    function = phi_mms
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = phi_exact
    variable = phi
  [../]
  [./h]
    type = AverageElementSize
  [../]
  [./point]
    type = PointValue
    point = '0.1 0 0'
    variable = phi
  [../]
[]

[Executioner]
  type = Transient
  start_time = 1
  dt = 0.01
  end_time = 1.25
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  scheme = bdf2
  nl_rel_tol = 1e-12
[]

[Outputs]
  interval = 10
  execute_on = 'timestep_end'
  csv = true
[]

(test/tests/functions/image_function/flip_dual.i)

[Mesh]
  uniform_refine = 1
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 40
    ymax = 2
  []
  [top]
    type = SubdomainBoundingBoxGenerator
    input = gen
    top_right = '1 2 0'
    bottom_left = '0 1 0'
    block_id = 1
  []
[]

[Variables]
  [u]
  []
[]

[Functions]
  [top]
    type = ImageFunction
    origin = '0 1 0'
    file_base = stack/test
    file_suffix = png
    flip_y = true
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    dimensions = '1 1 0'
  []
  [bottom]
    type = ImageFunction
    origin = '0 0 0'
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    dimensions = '1 1 0'
  []
[]

[ICs]
  [top_ic]
    function = top
    variable = u
    type = FunctionIC
    block = 1
  []
  [bottom_ic]
    function = bottom
    variable = u
    type = FunctionIC
    block = 0
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/initial_solution_copy/solutions_equal.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[Functions]
  [./initial_func]
    type = ParsedFunction
    value = sin(pi*x)*sin(pi*y)
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  [../]
  [./time]
    type = TimeDerivative
    variable = u
  [../]
  [./source]
    type = BodyForce
    variable = u
    value = 1
  [../]
[]

[BCs]
  active = 'func_bc'
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
  [./func_bc]
    type = FunctionDirichletBC
    variable = u
    boundary = 'bottom right top left'
    function = initial_func
  [../]
[]

[Postprocessors]
  [./test_pp]
    type = TestCopyInitialSolution
    execute_on = timestep_begin
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./initial]
    function = initial_func
    variable = u
    type = FunctionIC
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/pins/mms/porosity_change/1d-rc-continuous.i)

mu=1.5
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 1
    dx = '1 1'
    ix = '15 15'
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = u
    porosity = porosity
    pressure = pressure
  []
[]

[Problem]
  error_on_jacobian_nonzero_reallocation = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []
[]

[ICs]
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    function = smooth_jump
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1)))'
  []

  # Generated by compute-functions-1d.py
  [exact_u]
    type = ParsedFunction
    value = 'cos((1/2)*x*pi)'
  []
  [forcing_u]
    type = ADParsedFunction
    value = '-mu*(1 - 0.5/(exp(30 - 30*x) + 1))*(-1/4*pi^2*cos((1/2)*x*pi)/(1 - 0.5/(exp(30 - 30*x) + 1)) - 15.0*pi*exp(30 - 30*x)*sin((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^2) - 450.0*exp(30 - 30*x)*cos((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^2) + 900.0*exp(60 - 60*x)*cos((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^3) + 450.0*exp(60 - 60*x)*cos((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^3*(exp(30 - 30*x) + 1)^4)) + 15.0*mu*(-1/2*pi*sin((1/2)*x*pi)/(1 - 0.5/(exp(30 - 30*x) + 1)) + 15.0*exp(30 - 30*x)*cos((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^2))*exp(30 - 30*x)/(exp(30 - 30*x) + 1)^2 - pi*rho*sin((1/2)*x*pi)*cos((1/2)*x*pi)/(1 - 0.5/(exp(30 - 30*x) + 1)) + 15.0*rho*exp(30 - 30*x)*cos((1/2)*x*pi)^2/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^2) + (1 - 0.5/(exp(30 - 30*x) + 1))*cos(x)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin(x)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-1/2*pi*rho*sin((1/2)*x*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []

  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []

  [u_forcing]
    type = INSFVBodyForce
    variable = u
    functor = forcing_u
    momentum_component = 'x'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'

  # ksp_gmres_restart bumped to 200 for linear convergence
  nl_max_its = 100
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/porous_flow/test/tests/numerical_diffusion/no_action.i)

# Using upwinded and mass-lumped PorousFlow Kernels: this is equivalent of fully_saturated_action.i with stabilization = Full
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = tracer
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = porepressure
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-1
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/basic-primitive-pcnsfv-kt.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_vel_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_vel_x]
    type = FunctionIC
    variable = sup_vel_x
    function = 'exact_sup_vel_x'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = sup_vel_x
    momentum_component = x
    eqn = "momentum"
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_vel_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [pressure_right]
    type = FVFunctionDirichletBC
    variable = pressure
    function = exact_p
    boundary = 'right'
  []
  [sup_vel_x_left]
    type = FVFunctionDirichletBC
    variable = sup_vel_x
    function = exact_sup_vel_x
    boundary = 'left'
  []
  [T_fluid_left]
    type = FVFunctionDirichletBC
    variable = T_fluid
    function = exact_T
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    superficial_vel_x = sup_vel_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  value = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  value = '-3.45300378856215*sin(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  value = '3.13909435323832*cos(1.1*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  value = '-0.9*(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + 0.9*(10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) + 3.13909435323832*sin(x)*cos(1.1*x)^2/cos(x)^2 - 6.9060075771243*sin(1.1*x)*cos(1.1*x)/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  value = '26.7439413073546*cos(1.2*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  value = '0.9*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(x)*cos(1.1*x)/cos(x)^2 - 0.99*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(1.1*x)/cos(x) + 0.9*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) - 32.0927295688256*sin(1.2*x))*cos(1.1*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  value = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  value = '3.13909435323832*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  value = '0.9*cos(1.1*x)/cos(x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  value_x = '0.9*cos(1.1*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  value = '0.9'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_vel_x]
    variable = sup_vel_x
    function = exact_sup_vel_x
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/kernels/ad_coupled_value/ad_aux_coupled_value.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 4
  ny = 4
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [v]
    initial_condition = 2
  []
  [exact]
  []
[]

[ICs]
  [exact]
    type = FunctionIC
    function = 'x*(2-x)'
    variable = exact
  []
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./ad_coupled_value]
    type = ADCoupledValueTest
    variable = u
    v = v
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'Newton'
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/examples/groundwater/ex02_abstraction.i)

# Abstraction groundwater model.  See groundwater_models.md for a detailed description
[Mesh]
  [from_steady_state]
    type = FileMeshGenerator
    file = gold/ex02_steady_state_ex.e
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = steady_state_pp
  []
[]

[BCs]
  [rainfall_recharge]
    type = PorousFlowSink
    boundary = zmax
    variable = pp
    flux_function = -1E-6  # recharge of 0.1mm/day = 1E-4m3/m2/day = 0.1kg/m2/day ~ 1E-6kg/m2/s
  []
  [evapotranspiration]
    type = PorousFlowHalfCubicSink
    boundary = zmax
    variable = pp
    center = 0.0
    cutoff = -5E4 # roots of depth 5m.  5m of water = 5E4 Pa
    use_mobility = true
    fluid_phase = 0
    # Assume pan evaporation of 4mm/day = 4E-3m3/m2/day = 4kg/m2/day ~ 4E-5kg/m2/s
    # Assume that if permeability was 1E-10m^2 and water table at topography then ET acts as pan strength
    # Because use_mobility = true, then 4E-5 = maximum_flux = max * perm * density / visc = max * 1E-4, so max = 40
    max = 40
  []
[]

[DiracKernels]
  inactive = polyline_sink_borehole
  [river]
    type = PorousFlowPolyLineSink
    SumQuantityUO = baseflow
    point_file = ex02_river.bh
    # Assume a perennial river.
    # Assume the river has an incision depth of 1m and a stage height of 1.5m, and these are constant in time and uniform over the whole model.  Hence, if groundwater head is 0.5m (5000Pa) there will be no baseflow and leakage.
    p_or_t_vals = '-999995000 5000 1000005000'
    # Assume the riverbed conductance, k_zz*density*river_segment_length*river_width/riverbed_thickness/viscosity = 1E-6*river_segment_length kg/Pa/s
    fluxes = '-1E3 0 1E3'
    variable = pp
  []
  [horizontal_borehole]
    type = PorousFlowPeacemanBorehole
    SumQuantityUO = abstraction
    bottom_p_or_t = -1E5
    unit_weight = '0 0 -1E4'
    character = 1.0
    point_file = ex02.bh
    variable = pp
  []
  [polyline_sink_borehole]
    type = PorousFlowPolyLineSink
    SumQuantityUO = abstraction
    fluxes = '-0.4 0 0.4'
    p_or_t_vals = '-1E8 0 1E8'
    point_file = ex02.bh
    variable = pp
  []
[]

[Functions]
  [steady_state_pp]
    type = SolutionFunction
    from_variable = pp
    solution = steady_state_solution
  []
  [baseflow_rate]
    type = ParsedFunction
    vars = 'baseflow_kg dt'
    vals = 'baseflow_kg dt'
    value = 'baseflow_kg / dt * 24.0 * 3600.0 / 400.0'
  []
  [abstraction_rate]
    type = ParsedFunction
    vars = 'abstraction_kg dt'
    vals = 'abstraction_kg dt'
    value = 'abstraction_kg / dt * 24.0 * 3600.0'
  []
[]

[AuxVariables]
  [ini_pp]
  []
  [pp_change]
  []
[]

[AuxKernels]
  [ini_pp]
    type = FunctionAux
    variable = ini_pp
    function = steady_state_pp
    execute_on = INITIAL
  []
  [pp_change]
    type = ParsedAux
    variable = pp_change
    args = 'pp ini_pp'
    function = 'pp - ini_pp'
  []
[]

[PorousFlowUnsaturated]
  fp = simple_fluid
  porepressure = pp
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [porosity_everywhere]
    type = PorousFlowPorosityConst
    porosity = 0.05
  []
  [permeability_aquifers]
    type = PorousFlowPermeabilityConst
    block = 'top_aquifer bot_aquifer'
    permeability = '1E-12 0 0 0 1E-12 0 0 0 1E-13'
  []
  [permeability_aquitard]
    type = PorousFlowPermeabilityConst
    block = aquitard
    permeability = '1E-16 0 0 0 1E-16 0 0 0 1E-17'
  []
[]

[UserObjects]
  [steady_state_solution]
    type = SolutionUserObject
    execute_on = INITIAL
    mesh = gold/ex02_steady_state_ex.e
    timestep = LATEST
    system_variables = pp
  []
  [baseflow]
    type = PorousFlowSumQuantity
  []
  [abstraction]
    type = PorousFlowSumQuantity
  []
[]

[Postprocessors]
  [baseflow_kg]
    type = PorousFlowPlotQuantity
    uo = baseflow
    outputs = 'none'
  []
  [dt]
    type = TimestepSize
    outputs = 'none'
  []
  [baseflow_l_per_m_per_day]
    type = FunctionValuePostprocessor
    function = baseflow_rate
  []
  [abstraction_kg]
    type = PorousFlowPlotQuantity
    uo = abstraction
    outputs = 'none'
  []
  [abstraction_kg_per_day]
    type = FunctionValuePostprocessor
    function = abstraction_rate
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    # following 2 lines are not mandatory, but illustrate a popular preconditioner choice in groundwater models
    petsc_options_iname = '-pc_type -sub_pc_type  -pc_asm_overlap'
    petsc_options_value = ' asm      ilu           2              '
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 100
  [TimeStepper]
    type = FunctionDT
    function = 'max(100, t)'
  []
  end_time = 8.64E5 # 10 days
  nl_abs_tol = 1E-11
[]

[Outputs]
  print_linear_residuals = false
  [ex]
    type = Exodus
    execute_on = final
  []
  [csv]
    type = CSV
  []
[]

(modules/phase_field/examples/kim-kim-suzuki/kks_example_noflux.i)

#
# KKS simple example in the split form
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 150
  ny = 15
  nz = 0
  xmin = -25
  xmax = 25
  ymin = -2.5
  ymax = 2.5
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[AuxVariables]
  [./Fglobal]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Variables]
  # order parameter
  [./eta]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute concentration
  [./c]
    order = FIRST
    family = LAGRANGE
  [../]

  # chemical potential
  [./w]
    order = FIRST
    family = LAGRANGE
  [../]

  # Liquid phase solute concentration
  [./cl]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  [../]
  # Solid phase solute concentration
  [./cs]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.9
  [../]
[]

[Functions]
  [./ic_func_eta]
    type = ParsedFunction
    value = '0.5*(1.0-tanh((x)/sqrt(2.0)))'
  [../]
  [./ic_func_c]
    type = ParsedFunction
    value = '0.9*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.1*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
  [../]
[]


[ICs]
  [./eta]
    variable = eta
    type = FunctionIC
    function = ic_func_eta
  [../]
  [./c]
    variable = c
    type = FunctionIC
    function = ic_func_c
  [../]
[]

[Materials]
  # Free energy of the liquid
  [./fl]
    type = DerivativeParsedMaterial
    f_name = fl
    args = 'cl'
    function = '(0.1-cl)^2'
  [../]

  # Free energy of the solid
  [./fs]
    type = DerivativeParsedMaterial
    f_name = fs
    args = 'cs'
    function = '(0.9-cs)^2'
  [../]

  # h(eta)
  [./h_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta
  [../]

  # g(eta)
  [./g_eta]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'M   L   eps_sq'
    prop_values = '0.7 0.7 1.0  '
  [../]
[]

[Kernels]
  active = 'PhaseConc ChemPotSolute CHBulk ACBulkF ACBulkC ACInterface dcdt detadt ckernel'

  # enforce c = (1-h(eta))*cl + h(eta)*cs
  [./PhaseConc]
    type = KKSPhaseConcentration
    ca       = cl
    variable = cs
    c        = c
    eta      = eta
  [../]

  # enforce pointwise equality of chemical potentials
  [./ChemPotSolute]
    type = KKSPhaseChemicalPotential
    variable = cl
    cb       = cs
    fa_name  = fl
    fb_name  = fs
  [../]

  #
  # Cahn-Hilliard Equation
  #
  [./CHBulk]
    type = KKSSplitCHCRes
    variable = c
    ca       = cl
    fa_name  = fl
    w        = w
  [../]

  [./dcdt]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
  [./ckernel]
    type = SplitCHWRes
    mob_name = M
    variable = w
  [../]

  #
  # Allen-Cahn Equation
  #
  [./ACBulkF]
    type = KKSACBulkF
    variable = eta
    fa_name  = fl
    fb_name  = fs
    w        = 1.0
    args = 'cl cs'
  [../]
  [./ACBulkC]
    type = KKSACBulkC
    variable = eta
    ca       = cl
    cb       = cs
    fa_name  = fl
  [../]
  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = eps_sq
  [../]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[AuxKernels]
  [./GlobalFreeEnergy]
    variable = Fglobal
    type = KKSGlobalFreeEnergy
    fa_name = fl
    fb_name = fs
    w = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      ilu          nonzero'

  l_max_its = 100
  nl_max_its = 100

  num_steps = 50
  dt = 0.1
[]

#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
  [./full]
    type = SMP
    full = true
  [../]
[]


[VectorPostprocessors]
  [./c]
    type =  LineValueSampler
    start_point = '-25 0 0'
    end_point = '25 0 0'
    variable = c
    num_points = 151
    sort_by =  id
    execute_on = timestep_end
  [../]
  [./eta]
    type =  LineValueSampler
    start_point = '-25 0 0'
    end_point = '25 0 0'
    variable = eta
    num_points = 151
    sort_by =  id
    execute_on = timestep_end
  [../]

[]

[Outputs]
  exodus = true
  [./csv]
    type = CSV
    execute_on = final
  [../]
[]

(modules/porous_flow/examples/ates/ates.i)

# Simulation designed to assess the recovery efficiency of a single-well ATES system
# Using KT stabilisation
# Boundary conditions: fixed porepressure and temperature at top, bottom and far end of model.

#####################################
flux_limiter = minmod # minmod, vanleer, mc, superbee, none
# depth of top of aquifer (m)
depth = 400

inject_fluid_mass = 1E8 # kg
produce_fluid_mass = ${inject_fluid_mass} # kg
inject_temp = 90 # degC

inject_time = 91 # days
store_time = 91 # days
produce_time = 91 # days
rest_time = 91 # days
num_cycles = 5 # Currently needs to be <= 10

cycle_length = ${fparse inject_time + store_time + produce_time + rest_time}

end_simulation = ${fparse cycle_length * num_cycles}

# Note: I have setup 10 cycles but you can set num_cycles less than 10.
start_injection1 = 0
start_injection2 = ${cycle_length}
start_injection3 = ${fparse cycle_length * 2}
start_injection4 = ${fparse cycle_length * 3}
start_injection5 = ${fparse cycle_length * 4}
start_injection6 = ${fparse cycle_length * 5}
start_injection7 = ${fparse cycle_length * 6}
start_injection8 = ${fparse cycle_length * 7}
start_injection9 = ${fparse cycle_length * 8}
start_injection10 = ${fparse cycle_length * 9}

end_injection1 = ${fparse start_injection1 + inject_time}
end_injection2 = ${fparse start_injection2 + inject_time}
end_injection3 = ${fparse start_injection3 + inject_time}
end_injection4 = ${fparse start_injection4 + inject_time}
end_injection5 = ${fparse start_injection5 + inject_time}
end_injection6 = ${fparse start_injection6 + inject_time}
end_injection7 = ${fparse start_injection7 + inject_time}
end_injection8 = ${fparse start_injection8 + inject_time}
end_injection9 = ${fparse start_injection9 + inject_time}
end_injection10 = ${fparse start_injection10 + inject_time}

start_production1 = ${fparse end_injection1 + store_time}
start_production2 = ${fparse end_injection2 + store_time}
start_production3 = ${fparse end_injection3 + store_time}
start_production4 = ${fparse end_injection4 + store_time}
start_production5 = ${fparse end_injection5 + store_time}
start_production6 = ${fparse end_injection6 + store_time}
start_production7 = ${fparse end_injection7 + store_time}
start_production8 = ${fparse end_injection8 + store_time}
start_production9 = ${fparse end_injection9 + store_time}
start_production10 = ${fparse end_injection10 + store_time}

end_production1 = ${fparse start_production1 + produce_time}
end_production2 = ${fparse start_production2 + produce_time}
end_production3 = ${fparse start_production3 + produce_time}
end_production4 = ${fparse start_production4 + produce_time}
end_production5 = ${fparse start_production5 + produce_time}
end_production6 = ${fparse start_production6 + produce_time}
end_production7 = ${fparse start_production7 + produce_time}
end_production8 = ${fparse start_production8 + produce_time}
end_production9 = ${fparse start_production9 + produce_time}
end_production10 = ${fparse start_production10 + produce_time}

synctimes = '${start_injection1} ${end_injection1} ${start_production1} ${end_production1}
             ${start_injection2} ${end_injection2} ${start_production2} ${end_production2}
             ${start_injection3} ${end_injection3} ${start_production3} ${end_production3}
             ${start_injection4} ${end_injection4} ${start_production4} ${end_production4}
             ${start_injection5} ${end_injection5} ${start_production5} ${end_production5}
             ${start_injection6} ${end_injection6} ${start_production6} ${end_production6}
             ${start_injection7} ${end_injection7} ${start_production7} ${end_production7}
             ${start_injection8} ${end_injection8} ${start_production8} ${end_production8}
             ${start_injection9} ${end_injection9} ${start_production9} ${end_production9}
             ${start_injection10} ${end_injection10} ${start_production10} ${end_production10}'

#####################################
# Geometry in RZ coordinates
# borehole radius (m)
bh_r = 0.1
# model radius (m)
max_r = 1000
# aquifer thickness (m)
aq_thickness = 20
# cap thickness (m)
cap_thickness = 40
# injection region top and bottom (m).  Note, the mesh is created with the aquifer in y = (-0.5 * aq_thickness, 0.5 * aq_thickness), irrespective of depth (depth only sets the insitu porepressure and temperature)
screen_top = ${fparse 0.5 * aq_thickness}
screen_bottom = ${fparse -0.5 * aq_thickness}

# number of elements in radial direction
num_r = 25
# number of elements across half height of aquifer
num_y_aq = 10
# number of elements across height of cap
num_y_cap = 8

# mesh bias in radial direction
bias_r = 1.22
# mesh bias in vertical direction in aquifer top
bias_y_aq_top = 0.9
# mesh bias in vertical direction in cap top
bias_y_cap_top = 1.3
# mesh bias in vertical direction in aquifer bottom
bias_y_aq_bottom = ${fparse 1.0 / bias_y_aq_top}
# mesh bias in vertical direction in cap bottom
bias_y_cap_bottom = ${fparse 1.0 / bias_y_cap_top}
depth_centre = ${fparse depth + aq_thickness/2}

#####################################
# temperature at ground surface (degC)
temp0 = 20
# Vertical geothermal gradient (K/m).  A positive number means temperature increases downwards.
geothermal_gradient = 20E-3

#####################################
# Gravity
gravity = -9.81

#####################################
half_aq_thickness = ${fparse aq_thickness * 0.5}
half_height = ${fparse half_aq_thickness + cap_thickness}
approx_screen_length = ${fparse screen_top - screen_bottom}

# Thermal radius (note this is not strictly correct, it should use the bulk specific heat
#  capacity as defined below, but it doesn't matter here because this is purely for
#  defining the region of refined mesh)
th_r = ${fparse sqrt(inject_fluid_mass / 1000 * 4.12e6 / (approx_screen_length * 3.1416 * aq_specific_heat_cap * aq_density))}
# radius of fine mesh
fine_r = ${fparse th_r * 2}
bias_r_fine = 1
num_r_fine = ${fparse int(fine_r/1)}

######################################
# aquifer properties
aq_porosity = 0.25
aq_hor_perm = 1E-11 # m^2
aq_ver_perm = 2E-12 # m^2
aq_density = 2650 # kg/m^3
aq_specific_heat_cap = 800 # J/Kg/K
aq_hor_thermal_cond = 3 # W/m/K
aq_ver_thermal_cond = 3 # W/m/K
aq_disp_parallel = 0 # m
aq_disp_perp = 0 # m
# Bulk volumetric heat capacity of aquifer:
aq_vol_cp = ${fparse aq_specific_heat_cap * aq_density * (1 - aq_porosity) + 4180 * 1000 * aq_porosity}
# Thermal radius (correct version using bulk cp):
R_th = ${fparse sqrt(inject_fluid_mass * 4180 / (approx_screen_length * 3.1416 * aq_vol_cp))}
aq_lambda_eff_hor = ${fparse aq_hor_thermal_cond + 0.3 * aq_disp_parallel * R_th * aq_vol_cp / (inject_time * 60 * 60 * 24)}
aq_lambda_eff_ver = ${fparse aq_ver_thermal_cond + 0.3 * aq_disp_perp * R_th * aq_vol_cp / (inject_time * 60 * 60 * 24)}
aq_hor_dry_thermal_cond = ${fparse aq_lambda_eff_hor * 60 * 60 * 24} # J/day/m/K
aq_ver_dry_thermal_cond = ${fparse aq_lambda_eff_ver * 60 * 60 * 24} # J/day/m/K
aq_hor_wet_thermal_cond = ${fparse aq_lambda_eff_hor * 60 * 60 * 24} # J/day/m/K
aq_ver_wet_thermal_cond = ${fparse aq_lambda_eff_ver * 60 * 60 * 24} # J/day/m/K
# cap-rock properties
cap_porosity = 0.25
cap_hor_perm = 1E-16 # m^2
cap_ver_perm = 1E-17 # m^2
cap_density = 2650 # kg/m^3
cap_specific_heat_cap = 800 # J/kg/K
cap_hor_thermal_cond = 3 # W/m/K
cap_ver_thermal_cond = 3 # W/m/K
cap_hor_dry_thermal_cond = ${fparse cap_hor_thermal_cond * 60 * 60 * 24} # J/day/m/K
cap_ver_dry_thermal_cond = ${fparse cap_ver_thermal_cond * 60 * 60 * 24} # J/day/m/K
cap_hor_wet_thermal_cond = ${fparse cap_hor_thermal_cond * 60 * 60 * 24} # J/day/m/K
cap_ver_wet_thermal_cond = ${fparse cap_ver_thermal_cond * 60 * 60 * 24} # J/day/m/K

######################################

[Mesh]
  [aq_top_fine]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r_fine}
    xmin = ${bh_r}
    xmax = ${fine_r}
    bias_x = ${bias_r_fine}
    bias_y = ${bias_y_aq_top}
    ny = ${num_y_aq}
    ymin = 0
    ymax = ${half_aq_thickness}
  []
  [cap_top_fine]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r_fine}
    xmin = ${bh_r}
    xmax = ${fine_r}
    bias_x = ${bias_r_fine}
    bias_y = ${bias_y_cap_top}
    ny = ${num_y_cap}
    ymax = ${half_height}
    ymin = ${half_aq_thickness}
  []
  [aq_and_cap_top_fine]
    type = StitchedMeshGenerator
    inputs = 'aq_top_fine cap_top_fine'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'top bottom'
  []
  [aq_bottom_fine]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r_fine}
    xmin = ${bh_r}
    xmax = ${fine_r}
    bias_x = ${bias_r_fine}
    bias_y = ${bias_y_aq_bottom}
    ny = ${num_y_aq}
    ymax = 0
    ymin = -${half_aq_thickness}
  []
  [cap_bottom_fine]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r_fine}
    xmin = ${bh_r}
    xmax = ${fine_r}
    bias_x = ${bias_r_fine}
    bias_y = ${bias_y_cap_bottom}
    ny = ${num_y_cap}
    ymin = -${half_height}
    ymax = -${half_aq_thickness}
  []
  [aq_and_cap_bottom_fine]
    type = StitchedMeshGenerator
    inputs = 'aq_bottom_fine cap_bottom_fine'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'bottom top'
  []
  [aq_and_cap_fine]
    type = StitchedMeshGenerator
    inputs = 'aq_and_cap_bottom_fine aq_and_cap_top_fine'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'top bottom'
  []

  [aq_top]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r}
    xmin = ${fine_r}
    xmax = ${max_r}
    bias_x = ${bias_r}
    bias_y = ${bias_y_aq_top}
    ny = ${num_y_aq}
    ymin = 0
    ymax = ${half_aq_thickness}
  []
  [cap_top]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r}
    xmin = ${fine_r}
    xmax = ${max_r}
    bias_x = ${bias_r}
    bias_y = ${bias_y_cap_top}
    ny = ${num_y_cap}
    ymax = ${half_height}
    ymin = ${half_aq_thickness}
  []
  [aq_and_cap_top]
    type = StitchedMeshGenerator
    inputs = 'aq_top cap_top'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'top bottom'
  []
  [aq_bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r}
    xmin = ${fine_r}
    xmax = ${max_r}
    bias_x = ${bias_r}
    bias_y = ${bias_y_aq_bottom}
    ny = ${num_y_aq}
    ymax = 0
    ymin = -${half_aq_thickness}
  []
  [cap_bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${num_r}
    xmin = ${fine_r}
    xmax = ${max_r}
    bias_x = ${bias_r}
    bias_y = ${bias_y_cap_bottom}
    ny = ${num_y_cap}
    ymin = -${half_height}
    ymax = -${half_aq_thickness}
  []
  [aq_and_cap_bottom]
    type = StitchedMeshGenerator
    inputs = 'aq_bottom cap_bottom'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'bottom top'
  []
  [aq_and_cap]
    type = StitchedMeshGenerator
    inputs = 'aq_and_cap_bottom aq_and_cap_top'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'top bottom'
  []

  [aq_and_cap_all]
    type = StitchedMeshGenerator
    inputs = 'aq_and_cap_fine aq_and_cap'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'right left'
  []

  [aquifer]
    type = ParsedSubdomainMeshGenerator
    input = aq_and_cap_all
    combinatorial_geometry = 'y >= -${half_aq_thickness} & y <= ${half_aq_thickness}'
    block_id = 1
  []
  [top_cap]
    type = ParsedSubdomainMeshGenerator
    input = aquifer
    combinatorial_geometry = 'y >= ${half_aq_thickness}'
    block_id = 2
  []
  [bottom_cap]
    type = ParsedSubdomainMeshGenerator
    input = top_cap
    combinatorial_geometry = 'y <= -${half_aq_thickness}'
    block_id = 3
  []
  [injection_area]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'x<=${bh_r}*1.000001 & y >= ${screen_bottom} & y <= ${screen_top}'
    included_subdomain_ids = 1
    new_sideset_name = 'injection_area'
    input = 'bottom_cap'
  []
  [rename]
    type = RenameBlockGenerator
    old_block = '1 2 3'
    new_block = 'aquifer caps caps'
    input = 'injection_area'
  []
[]

[Problem]
  coord_type = RZ
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 ${gravity} 0'
[]

[Variables]
  [porepressure]
  []
  [temperature]
    scaling = 1E-5
  []
[]

[PorousFlowFullySaturated]
  coupling_type = ThermoHydro
  porepressure = porepressure
  temperature = temperature
  fp = tabulated_water
  stabilization = KT
  flux_limiter_type = ${flux_limiter}
  use_displaced_mesh = false
  temperature_unit = Celsius
  pressure_unit = Pa
  time_unit = days
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = insitu_pressure
  []
  [temperature]
    type = FunctionIC
    variable = temperature
    function = insitu_temperature
  []
[]

[BCs]
  [outer_boundary_porepressure]
    type = FunctionDirichletBC
    preset = true
    variable = porepressure
    function = insitu_pressure
    boundary = 'bottom right top'
  []
  [outer_boundary_temperature]
    type = FunctionDirichletBC
    preset = true
    variable = temperature
    function = insitu_temperature
    boundary = 'bottom right top'
  []
  [inject_heat]
    type = FunctionDirichletBC
    variable = temperature
    function = ${inject_temp}
    boundary = 'injection_area'
  []
  [inject_fluid]
    type = PorousFlowSink
    variable = porepressure
    boundary = injection_area
    flux_function = injection_rate_value
  []
  [produce_heat]
    type = PorousFlowSink
    variable = temperature
    boundary = injection_area
    flux_function = production_rate_value
    fluid_phase = 0
    use_enthalpy = true
    save_in = heat_flux_out
  []
  [produce_fluid]
    type = PorousFlowSink
    variable = porepressure
    boundary = injection_area
    flux_function = production_rate_value
  []
[]

[Controls]
  [inject_on]
    type = ConditionalFunctionEnableControl
    enable_objects = 'BCs::inject_heat BCs::inject_fluid'
    conditional_function = inject
    implicit = false
    execute_on = 'initial timestep_begin'
  []
  [produce_on]
    type = ConditionalFunctionEnableControl
    enable_objects = 'BCs::produce_heat BCs::produce_fluid'
    conditional_function = produce
    implicit = false
    execute_on = 'initial timestep_begin'
  []
[]

[Functions]
  [insitu_pressure]
    type = ParsedFunction
    value = '(y - ${depth_centre}) * 1000 * ${gravity} + 1E5'  # approx insitu pressure in Pa
  []
  [insitu_temperature]
    type = ParsedFunction
    value = '${temp0} + (${depth_centre} - y) * ${geothermal_gradient}'
  []

  [inject]
    type = ParsedFunction
    value = 'if(t >= ${start_injection1} & t < ${end_injection1}, 1,
             if(t >= ${start_injection2} & t < ${end_injection2}, 1,
             if(t >= ${start_injection3} & t < ${end_injection3}, 1,
             if(t >= ${start_injection4} & t < ${end_injection4}, 1,
             if(t >= ${start_injection5} & t < ${end_injection5}, 1,
             if(t >= ${start_injection6} & t < ${end_injection6}, 1,
             if(t >= ${start_injection7} & t < ${end_injection7}, 1,
             if(t >= ${start_injection8} & t < ${end_injection8}, 1,
             if(t >= ${start_injection9} & t < ${end_injection9}, 1,
             if(t >= ${start_injection10} & t < ${end_injection10}, 1, 0))))))))))'
  []
  [produce]
    type = ParsedFunction
    value = 'if(t >= ${start_production1} & t < ${end_production1}, 1,
             if(t >= ${start_production2} & t < ${end_production2}, 1,
             if(t >= ${start_production3} & t < ${end_production3}, 1,
             if(t >= ${start_production4} & t < ${end_production4}, 1,
             if(t >= ${start_production5} & t < ${end_production5}, 1,
             if(t >= ${start_production6} & t < ${end_production6}, 1,
             if(t >= ${start_production7} & t < ${end_production7}, 1,
             if(t >= ${start_production8} & t < ${end_production8}, 1,
             if(t >= ${start_production9} & t < ${end_production9}, 1,
             if(t >= ${start_production10} & t < ${end_production10}, 1, 0))))))))))'
  []

  [injection_rate_value]
    type = ParsedFunction
    vars = true_screen_area
    vals = true_screen_area
    value = '-${inject_fluid_mass}/(true_screen_area * ${inject_time})'
  []
  [production_rate_value]
    type = ParsedFunction
    vars = true_screen_area
    vals = true_screen_area
    value = '${produce_fluid_mass}/(true_screen_area * ${produce_time})'
  []

  [heat_out_in_timestep]
    type = ParsedFunction
    vars = 'dt heat_out'
    vals = 'dt heat_out_fromBC'
    value = 'dt*heat_out'
  []
  [produced_T_time_integrated]
    type = ParsedFunction
    vars = 'dt produced_T'
    vals = 'dt produced_T'
    value = 'dt*produced_T / ${produce_time}'
  []
[]

[AuxVariables]
  [density]
    family = MONOMIAL
    order = CONSTANT
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
  []
  [heat_flux_out]
    outputs = none
  []
[]

[AuxKernels]
  [density]
    type = PorousFlowPropertyAux
    variable = density
    property = density
  []
  [porosity]
    type = PorousFlowPropertyAux
    variable = porosity
    property = porosity
  []
[]

[Modules]
  [FluidProperties]
    [true_water]
      type = Water97FluidProperties
    []
    [tabulated_water]
      type = TabulatedFluidProperties
      fp = true_water
      temperature_min = 275 # K
      temperature_max = 600
      interpolated_properties = 'density viscosity enthalpy internal_energy'
      fluid_property_file = water97_tabulated_modified.csv
    []
  []
[]

[Materials]
  [porosity_aq]
    type = PorousFlowPorosityConst
    porosity = ${aq_porosity}
    block = aquifer
  []
  [porosity_caps]
    type = PorousFlowPorosityConst
    porosity = ${cap_porosity}
    block = caps
  []

  [permeability_aquifer]
    type = PorousFlowPermeabilityConst
    block = aquifer
    permeability = '${aq_hor_perm} 0 0   0 ${aq_ver_perm} 0   0 0 0'
  []
  [permeability_caps]
    type = PorousFlowPermeabilityConst
    block = caps
    permeability = '${cap_hor_perm} 0 0   0 ${cap_ver_perm} 0   0 0 0'
  []

  [aq_internal_energy]
    type = PorousFlowMatrixInternalEnergy
    block = aquifer
    density = ${aq_density}
    specific_heat_capacity = ${aq_specific_heat_cap}
  []
  [caps_internal_energy]
    type = PorousFlowMatrixInternalEnergy
    block = caps
    density = ${cap_density}
    specific_heat_capacity = ${cap_specific_heat_cap}
  []

  [aq_thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    block = aquifer
    dry_thermal_conductivity = '${aq_hor_dry_thermal_cond} 0 0  0 ${aq_ver_dry_thermal_cond} 0  0 0 0'
    wet_thermal_conductivity = '${aq_hor_wet_thermal_cond} 0 0  0 ${aq_ver_wet_thermal_cond} 0  0 0 0'
  []
  [caps_thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    block = caps
    dry_thermal_conductivity = '${cap_hor_dry_thermal_cond} 0 0  0 ${cap_ver_dry_thermal_cond} 0  0 0 0'
    wet_thermal_conductivity = '${cap_hor_wet_thermal_cond} 0 0  0 ${cap_ver_wet_thermal_cond} 0  0 0 0'
  []
[]

[Postprocessors]
  [true_screen_area] # this accounts for meshes that do not match screen_top and screen_bottom exactly
    type = AreaPostprocessor
    boundary = injection_area
    execute_on = 'initial'
    outputs = 'none'
  []
  [dt]
    type = TimestepSize
  []

  [heat_out_fromBC]
    type = NodalSum
    variable = heat_flux_out
    boundary = injection_area
    execute_on = 'initial timestep_end'
    outputs = 'none'
  []
  [heat_out_per_timestep]
    type = FunctionValuePostprocessor
    function = heat_out_in_timestep
    execute_on = 'timestep_end'
    outputs = 'none'
  []
  [heat_out_cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = heat_out_per_timestep
    execute_on = 'timestep_end'
    outputs = 'csv console'
  []
  [produced_T]
    type = SideAverageValue
    boundary = injection_area
    variable = temperature
    execute_on = 'initial timestep_end'
    outputs = 'csv console'
  []
  [produced_T_time_integrated]
    type = FunctionValuePostprocessor
    function = produced_T_time_integrated
    execute_on = 'timestep_end'
    outputs = 'none'
  []
  [produced_T_cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = produced_T_time_integrated
    execute_on = 'timestep_end'
    outputs = 'csv console'
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = ${end_simulation}
  timestep_tolerance = 1e-5

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e-3
    growth_factor = 2
  []

  dtmax = 1
  dtmin = 1e-5
  # rough calc for fluid, |R| ~ V*k*1E6 ~ V*1E-5
  # rough calc for heat, |R| ~ V*(lam*1E-3 + h*1E-5)  ~ V*(1E3 + 1E-2)
  # so scale heat by 1E-7 and go for nl_abs_tol = 1E-4, which should give a max error of
  # ~1Pa and ~0.1K in the first metre around the borehole
  nl_abs_tol = 1E-4
  nl_rel_tol = 1E-5
[]

[Outputs]
  sync_times = ${synctimes}
  [ex]
    type = Exodus
    interval = 20
  []
  [csv]
    type = CSV
    execute_postprocessors_on = 'initial timestep_end'
  []
[]

(test/tests/transfers/multiapp_userobject_transfer/two_pipe_sub.i)

[Mesh]
  type = FileMesh
  file = two_pipe.e
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [u]
  []
[]


[AuxVariables]
  [./var]
    order = CONSTANT
    family = MONOMIAL
    block = p1
  [../]
[]

[ICs]
  [./var]
    type = FunctionIC
    variable = var
    function = setvar
    block = p1
  [../]
[]

[Functions]
  [./setvar]
    type = ParsedFunction
    value = '1 + z * z'
  [../]
[]

[UserObjects]
  [./sub_app_uo]
    type = LayeredAverage
    direction = z
    variable = var
    num_layers = 10
    execute_on = TIMESTEP_END
    block = p1
  [../]
[]

[Executioner]
  type = Transient
[]

(modules/porous_flow/test/tests/poroperm/poro_tm.i)

# Test that porosity is correctly calculated.
# Porosity = 1 + (phi0 - 1) * exp(-vol_strain + thermal_exp_coeff * (temperature - ref_temperature))
# The parameters used are:
# phi0 = 0.5
# vol_strain = 0.5
# thermal_exp_coeff = 0.5
# temperature = 4
# ref_temperature = 3.5
# which yield porosity = 0.610599608464
[Mesh]
  type = GeneratedMesh
  dim = 3
[]

[GlobalParams]
  PorousFlowDictator = dictator
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [porepressure]
    initial_condition = 2
  []
  [temperature]
    initial_condition = 4
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[ICs]
  [disp_x]
    type = FunctionIC
    function = '0.5 * x'
    variable = disp_x
  []
[]

[Kernels]
  [dummy_p]
    type = TimeDerivative
    variable = porepressure
  []
  [dummy_t]
    type = TimeDerivative
    variable = temperature
  []
  [dummy_x]
    type = TimeDerivative
    variable = disp_x
  []
  [dummy_y]
    type = TimeDerivative
    variable = disp_y
  []
  [dummy_z]
    type = TimeDerivative
    variable = disp_z
  []
[]

[AuxVariables]
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [porosity]
    type = PorousFlowPropertyAux
    property = porosity
    variable = porosity
  []
[]

[Postprocessors]
  [porosity]
    type = PointValue
    variable = porosity
    point = '0 0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure temperature'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [eff_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [total_strain]
    type = ComputeSmallStrain
  []
  [vol_strain]
    type = PorousFlowVolumetricStrain
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [porosity]
    type = PorousFlowPorosity
    mechanical = true
    thermal = true
    ensure_positive = false
    porosity_zero = 0.5
    thermal_expansion_coeff = 0.5
    reference_temperature = 3.5
  []
[]

[Executioner]
  solve_type = Newton
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/energy_conservation/heat01.i)

# checking that the heat-energy postprocessor correctly calculates the energy
# 0phase, constant porosity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 3
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [tinit]
    type = FunctionIC
    function = '100*x'
    variable = temp
  []
[]

[Kernels]
  [dummy]
    type = TimeDerivative
    variable = temp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp'
    number_fluid_phases = 0
    number_fluid_components = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 2.2
    density = 0.5
  []
[]

[Postprocessors]
  [total_heat]
    type = PorousFlowHeatEnergy
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = heat01
  csv = true
[]

(modules/porous_flow/test/tests/relperm/unity.i)

# Test perfectly mobile relative permeability curve by varying saturation over the mesh

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [kr1]
    type = PorousFlowRelativePermeabilityConst
    phase = 1
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/cns/symmetry_test/2D_symmetry.i)

rho_inside = 1
E_inside = 2.501505578

rho_outside = 0.125
E_outside = 1.999770935

radius = 0.1
angle = 45

[GlobalParams]
  fp = fp
[]

[Debug]
   show_material_props = true
[]

[Mesh]
  [file]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -0.5
    xmax = 0.5
    nx = 10
    ymin = -0.5
    ymax = 0.5
    ny = 10
  [../]


  [rotate]
    type = TransformGenerator
    vector_value = '${angle} 0 0'
    transform = ROTATE
    input = file
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
      allow_imperfect_jacobians = true
    []
  []
[]

[Variables]
  [rho]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  [../]

  [rho_u]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 1e-15
    outputs = none
  []

  [rho_v]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 1e-15
    outputs = none
  []

  [rho_E]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []
[]

[ICs]
  [rho_ic]
    type = FunctionIC
    variable = rho
    function = 'if (abs(x) < ${radius} & abs(y) < ${radius}, ${rho_inside}, ${rho_outside})'
  []

  [rho_E_ic]
    type = FunctionIC
    variable = rho_E
    function = 'if (abs(x) < ${radius} & abs(y) < ${radius}, ${fparse E_inside * rho_inside}, ${fparse E_outside * rho_outside})'
  []
[]

[FVKernels]
  # Mass conservation
  [mass_time]
    type = FVTimeKernel
    variable = rho
  []

  [mass_advection]
    type = CNSFVMassHLLC
    variable = rho
    fp = fp
  []

  # Momentum x conservation
  [momentum_x_time]
    type = FVTimeKernel
    variable = rho_u
  []

  [momentum_x_advection]
    type = CNSFVMomentumHLLC
    variable = rho_u
    momentum_component = x
    fp = fp
  []

  # Momentum y conservation
  [momentum_y_time]
    type = FVTimeKernel
    variable = rho_v
  []

  [./momentum_y_advection]
    type = CNSFVMomentumHLLC
    variable = rho_v
    momentum_component = y
  []

  # Fluid energy conservation
  [./fluid_energy_time]
    type = FVTimeKernel
    variable = rho_E
  []

  [./fluid_energy_advection]
    type = CNSFVFluidEnergyHLLC
    variable = rho_E
    fp = fp
  []
[]

[FVBCs]
  ## outflow implicit conditions
  [mass_outflow]
    type = CNSFVHLLCMassImplicitBC
    variable = rho
    fp = fp
    boundary = 'left right top bottom'
  []

  [./momentum_x_outflow]
    type = CNSFVHLLCMomentumImplicitBC
    variable = rho_u
    momentum_component = x
    fp = fp
    boundary = 'left right top bottom'
  []

  [momentum_y_outflow]
    type = CNSFVHLLCMomentumImplicitBC
    variable = rho_v
    momentum_component = y
    fp = fp
    boundary = 'left right top bottom'
  []

  [fluid_energy_outflow]
    type = CNSFVHLLCFluidEnergyImplicitBC
    variable = rho_E
    fp = fp
    boundary = 'left right top bottom'
  []
[]

[AuxVariables]
  [Ma]
    family = MONOMIAL
    order = CONSTANT
  []

  [p]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [Ma_aux]
    type = NSMachAux
    variable = Ma
    fluid_properties = fp
    use_material_properties = true
  []

  [p_aux]
    type = ADMaterialRealAux
    variable = p
    property = pressure
  []
[]

[Materials]
  [var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = rho_u
    rhov = rho_v
    rho_et = rho_E
  []
  [sound_speed]
    type = SoundspeedMat
    fp = fp
  []
[]

[Postprocessors]
  [cfl_dt]
    type = ADCFLTimeStepSize
    c_names = 'sound_speed'
    vel_names = 'speed'
    CFL = 0.5
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
[]

[Executioner]
  type = Transient
  end_time = 0.2

  [TimeIntegrator]
    type = ExplicitSSPRungeKutta
    order = 2
  []
  l_tol = 1e-8

  [TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl_dt
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/materials/derivative_material_interface/ad_construction_order.i)

#
# Test the the getDefaultMaterialProperty in DerivativeMaterialInterface.
# This test should only pass, if the construction order of the Materials
# using this interface does not influence the outcome.
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 0.1
  elem_type = QUAD4
[]

[GlobalParams]
  derivative_order = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
[]

[Kernels]
  [./dummy1]
    type = ADDiffusion
    variable = c
  [../]
  [./dummy2]
    type = ADTimeDerivative
    variable = c
  [../]
[]

[Materials]
  # derivatives used both before and after being declared
  [./sum_a_1]
    type = ADDerivativeSumMaterial
    f_name = Fa1
    sum_materials = 'Fa'
    args = 'c'
    outputs = exodus
  [../]
  [./free_energy_a]
    type = ADDerivativeParsedMaterial
    f_name = Fa
    args = 'c'
    function = 'c^4'
  [../]
  [./sum_a_2]
    type = ADDerivativeSumMaterial
    f_name = Fa2
    sum_materials = 'Fa'
    args = 'c'
    outputs = exodus
  [../]

  # derivatives declared after being used
  [./sum_b_1]
    type = ADDerivativeSumMaterial
    f_name = Fb1
    sum_materials = 'Fb'
    args = 'c'
    outputs = exodus
  [../]
  [./free_energy_b]
    type = ADDerivativeParsedMaterial
    f_name = Fb
    args = 'c'
    function = 'c^4'
  [../]

  # derivatives declared before being used
  [./free_energy_c]
    type = ADDerivativeParsedMaterial
    f_name = Fc
    args = 'c'
    function = 'c^4'
  [../]
  [./sum_c_2]
    type = ADDerivativeSumMaterial
    f_name = Fc2
    sum_materials = 'Fc'
    args = 'c'
    outputs = exodus
  [../]

  # non-existing derivatives
  [./free_energy_d]
    type = ADParsedMaterial
    f_name = Fd
    args = 'c'
    function = 'c^4'
  [../]
  [./sum_d_1]
    type = ADDerivativeSumMaterial
    f_name = Fd1
    sum_materials = 'Fd'
    args = 'c'
    outputs = exodus
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2

  solve_type = 'NEWTON'
  num_steps = 1
  dt = 1e-5
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(modules/richards/test/tests/gravity_head_2/gh02.i)

# unsaturated = true
# gravity = true
# supg = false
# transient = false

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmin = 0
  xmax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1.0E2
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 0.5
    bulk_mod = 0.5E2
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.15
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.05
    sum_s_res = 0.15
  [../]
  [./SUPGwater]
    type = RichardsSUPGnone
  [../]
  [./SUPGgas]
    type = RichardsSUPGnone
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  # get nonconvergence if initial condition is too crazy
  [./water_ic]
    type = FunctionIC
    function = pwater_initial
    variable = pwater
  [../]
  [./gas_ic]
    type = FunctionIC
    function = pgas_initial
    variable = pgas
  [../]
[]


[Kernels]
  active = 'richardsfwater richardsfgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]


[AuxVariables]
  [./seffgas]
  [../]
  [./seffwater]
  [../]
[]

[AuxKernels]
  [./seffgas_kernel]
    type = RichardsSeffAux
    pressure_vars = 'pwater pgas'
    seff_UO = SeffGas
    variable = seffgas
  [../]
  [./seffwater_kernel]
    type = RichardsSeffAux
    pressure_vars = 'pwater pgas'
    seff_UO = SeffWater
    variable = seffwater
  [../]
[]

[Postprocessors]
  [./mwater_init]
    type = RichardsMass
    variable = pwater
    execute_on = timestep_begin
    outputs = none
  [../]
  [./mgas_init]
    type = RichardsMass
    variable = pgas
    execute_on = timestep_begin
    outputs = none
  [../]
  [./mwater_fin]
    type = RichardsMass
    variable = pwater
    execute_on = timestep_end
    outputs = none
  [../]
  [./mgas_fin]
    type = RichardsMass
    variable = pgas
    execute_on = timestep_end
    outputs = none
  [../]

  [./mass_error_water]
    type = FunctionValuePostprocessor
    function = fcn_mass_error_w
    outputs = none # no reason why mass should be conserved
  [../]
  [./mass_error_gas]
    type = FunctionValuePostprocessor
    function = fcn_mass_error_g
    outputs = none # no reason why mass should be conserved
  [../]

  [./pw_left]
    type = PointValue
    point = '0 0 0'
    variable = pwater
    outputs = none
  [../]
  [./pw_right]
    type = PointValue
    point = '1 0 0'
    variable = pwater
    outputs = none
  [../]
  [./error_water]
    type = FunctionValuePostprocessor
    function = fcn_error_water
  [../]

  [./pg_left]
    type = PointValue
    point = '0 0 0'
    variable = pgas
    outputs = none
  [../]
  [./pg_right]
    type = PointValue
    point = '1 0 0'
    variable = pgas
    outputs = none
  [../]
  [./error_gas]
    type = FunctionValuePostprocessor
    function = fcn_error_gas
  [../]
[]

[Functions]
  [./pwater_initial]
    type = ParsedFunction
    value = 1-x/2
  [../]
  [./pgas_initial]
    type = ParsedFunction
    value = 2-x/5
  [../]

  [./fcn_mass_error_w]
    type = ParsedFunction
    value = 'abs(0.5*(mi-mf)/(mi+mf))'
    vars = 'mi mf'
    vals = 'mwater_init mwater_fin'
  [../]
  [./fcn_mass_error_g]
    type = ParsedFunction
    value = 'abs(0.5*(mi-mf)/(mi+mf))'
    vars = 'mi mf'
    vals = 'mgas_init mgas_fin'
  [../]
  [./fcn_error_water]
    type = ParsedFunction
    value = 'abs((-b*log(-(gdens0*xval+(-b*exp(-p0/b)))/b)-p1)/p1)'
    vars = 'b gdens0 p0 xval p1'
    vals = '1E2 -1 pw_left 1 pw_right'
  [../]
  [./fcn_error_gas]
    type = ParsedFunction
    value = 'abs((-b*log(-(gdens0*xval+(-b*exp(-p0/b)))/b)-p1)/p1)'
    vars = 'b gdens0 p0 xval p1'
    vals = '0.5E2 -0.5 pg_left 1 pg_right'
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 0.5E-3'
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]



[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres asm lu NONZERO 1E-10 1E-10 10000'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = gh02
  csv = true
[]

(test/tests/functions/image_function/image_3d.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 20
  ny = 20
  nz = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/rdg/test/tests/advection_1d/block_restrictable.i)

############################################################
[GlobalParams]
  order = CONSTANT
  family = MONOMIAL
  u = u
  slope_limiting = lslope
  implicit = false
[]
############################################################
[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 100
  []
  [./subdomain1]
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0.5 0 0'
    block_id = 1
    top_right = '1.0 1.0 0'
    input = gen
  [../]
  [./interface]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
    input = subdomain1
  [../]
  [./interface_again]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'primary1_interface'
    input = interface
  [../]
[]
############################################################
[Functions]
  [./ic_u]
    type = PiecewiseConstant
    axis = x
    direction = right
    xy_data = '0.1 0.5
               0.4 1.0
               0.5 0.5'
  [../]
[]
############################################################
[UserObjects]
  [./lslope]
    type = AEFVSlopeLimitingOneD
    execute_on = 'linear'
    scheme = 'superbee' #none | minmod | mc | superbee
    block = 0
  [../]

  [./internal_side_flux]
    type = AEFVUpwindInternalSideFlux
    execute_on = 'linear'
  [../]

  [./free_outflow_bc]
    type = AEFVFreeOutflowBoundaryFlux
    execute_on = 'linear'
  [../]
[]
############################################################
[Variables]
  [./u]
    block = 0
  [../]
  [./v]
    block = 1
    family = LAGRANGE
    order = FIRST
  [../]
[]
############################################################
[ICs]
  [./u_ic]
    type = FunctionIC
    variable = 'u'
    function = ic_u
  [../]
[]
############################################################
[Kernels]
  [./time_u]
    implicit = true
    type = TimeDerivative
    variable = u
    block = 0
  [../]
  [./diff_v]
    implicit = true
    type = Diffusion
    variable = v
    block = 1
  [../]
  [./time_v]
    implicit = true
    type = TimeDerivative
    variable = v
    block = 1
  [../]
[]
############################################################
[DGKernels]
  [./concentration]
    type = AEFVKernel
    variable = u
    component = 'concentration'
    flux = internal_side_flux
    block = 0
  [../]
[]
############################################################
[BCs]
  [./concentration]
    type = AEFVBC
    boundary = 'left primary0_interface'
    variable = u
    component = 'concentration'
    flux = free_outflow_bc
  [../]
  [./v_left]
    type = DirichletBC
    boundary = 'primary1_interface'
    variable = v
    value = 1
  [../]
  [./v_right]
    type = DirichletBC
    boundary = 'right'
    variable = v
    value = 0
  [../]
[]
############################################################
[Materials]
  [./aefv]
    type = AEFVMaterial
    block = 0
  [../]
  [./dummy_1]
    type = GenericConstantMaterial
    block = 1
    prop_names = ''
    prop_values = ''
  [../]
[]
############################################################
[Executioner]
  type = Transient
  [./TimeIntegrator]
    type = ExplicitMidpoint
  [../]
  solve_type = 'LINEAR'

  l_tol = 1e-4
  nl_rel_tol = 1e-20
  nl_abs_tol = 1e-8
  nl_max_its = 60

  start_time = 0.0
  num_steps = 4 # 4 | 400 for complete run
  dt = 5e-4
  dtmin = 1e-6
[]

[Outputs]
  [./out]
    type = Exodus
    interval = 2
  [../]
  perf_graph = true
[]

(test/tests/time_steppers/function_dt/function_dt_no_interpolation.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]

  [./dts]
    type = PiecewiseConstant
    x = '0  4  8 12  20'
    y = '0  1  2  4  8'
    direction = right
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  start_time = 0
  end_time = 20
  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/dirac/bh07.i)

[Mesh]
  type = FileMesh
  file = bh07_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1000 10000'
    x = '100 1000'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[BCs]
  [./fix_outer]
    type = DirichletBC
    boundary = perimeter
    variable = pressure
    value = 1E7
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh07.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    re_constant = 0.1594
    character = 2
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
    execute_on = 'initial timestep_end'
  [../]

  [./fluid_mass]
    type = RichardsMass
    variable = pressure
    execute_on = 'initial timestep_end'
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-11 0 0  0 1E-11 0  0 0 1E-11'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1000
  solve_type = NEWTON

  [./TimeStepper]
    # get only marginally better results for smaller time steps
    type = FunctionDT
    function = dts
  [../]

[]

[Outputs]
  file_base = bh07
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
[]

(test/tests/functions/solution_function/solution_function_rot1.i)

# checking rotation of points by 45 deg about z axis in a SolutionUserObject
[Mesh]
  # this is chosen so when i rotate through 45deg i get a length of "1" along the x or y or z direction
  type = GeneratedMesh
  dim = 3
  xmin = -0.70710678
  xmax = 0.70710678
  nx = 3
  ymin = -0.70710678
  ymax = 0.70710678
  ny = 3
  zmin = -0.70710678
  zmax = 0.70710678
  nz = 3
[]

[UserObjects]
  [./solution_uo]
    type = SolutionUserObject
    mesh = cube_with_u_equals_x.e
    timestep = LATEST
    system_variables = u
    rotation0_vector = '0 0 1'
    rotation0_angle = 45
    transformation_order = rotation0
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = solution_fcn
  [../]
[]

[Functions]
  [./solution_fcn]
    type = SolutionFunction
    from_variable = u
    solution = solution_uo
  [../]
[]

[Kernels]
  [./diff]
    type = TimeDerivative
    variable = u
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  l_max_its = 800
  nl_rel_tol = 1e-10
  num_steps = 1
  end_time = 1
  dt = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = solution_function_rot1
  exodus = true
[]

(test/tests/functions/image_function/flip_quad.i)

[Mesh]
  uniform_refine = 1
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 20
    xmax = 2
    ymax = 2
  []
  # Define block IDs for the four quadrants in CCW order:
  # 1=top_right
  # 2=top_left
  # 3=bottom_left
  # 4=bottom_right
  [top_right_modifier]
    input = gen
    type = SubdomainBoundingBoxGenerator
    top_right = '2 2 0'
    bottom_left = '1 1 0'
    block_id = 1
  []
  [top_left_modifier]
    input = top_right_modifier
    type = SubdomainBoundingBoxGenerator
    top_right = '1 2 0'
    bottom_left = '0 1 0'
    block_id = 2
  []
  [bottom_left_modifier]
    input = top_left_modifier
    type = SubdomainBoundingBoxGenerator
    top_right = '1 1 0'
    bottom_left = '0 0 0'
    block_id = 3
  []
  [bottom_right_modifier]
    input = bottom_left_modifier
    type = SubdomainBoundingBoxGenerator
    top_right = '2 1 0'
    bottom_left = '1 0 0'
    block_id = 4
  []
[]

[Variables]
  [u]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Functions]
  [bottom_left_func]
    type = ImageFunction
    file_base = stack/test
    flip_x = true
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    file_suffix = png
    origin = '0 0 0'
    dimensions = '1 1 0'
  []
  [top_left_func]
    type = ImageFunction
    file_base = stack/test
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    file_suffix = png
    origin = '0 1 0'
    dimensions = '1 1 0'
    flip_x = true
    flip_y = true
  []
  [top_right_func]
    type = ImageFunction
    origin = '1 1 0'
    file_base = stack/test
    file_suffix = png
    flip_y = true
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    dimensions = '1 1 0'
  []
  [bottom_right_func]
    type = ImageFunction
    origin = '1 0 0'
    file_base = stack/test
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    file_suffix = png
    dimensions = '1 1 0'
  []
[]

[ICs]
  # Defined the same way as the MeshGenerators
  [top_right_ic]
    function = top_right_func
    variable = u
    type = FunctionIC
    block = 1
  []
  [top_left_ic]
    function = top_left_func
    variable = u
    type = FunctionIC
    block = 2
  []
  [bottom_left_ic]
    function = bottom_left_func
    variable = u
    type = FunctionIC
    block = 3
  []
  [bottom_right_ic]
    function = bottom_right_func
    variable = u
    type = FunctionIC
    block = 4
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/boundary_intersecting_features/boundary_intersecting_features.i)

[Mesh]
  # ImageMesh ignores nx, xmin, xmax (and similarly for y and z) and
  # tries to read them from the image file...
  type = ImageMesh
  dim = 2

  # Be sure to choose a corresponding image name below!
  # file = image001_cropped3_closing_298.png         # full size, 157 Mb Exodus file!
  # file = eighth_image001_cropped3_closing_298.png  # 1/8
  file = sixteenth_image001_cropped3_closing_298.png # 1/16

  # Uncomment to maintain 1:1 ratio between number of pixels and mesh size.
  # scale_to_one = false

  # Uncomment to set cells_per_pixel to something other than the default value of 1.0.
  # Must be <= 1.
  # cells_per_pixel = .75

  # To crop an image to e.g. 1/8th size, install ImageMagick and run:
  #  convert image001_cropped3_closing_298.png -crop 230x198+100+100 eighth_image001_cropped3_closing_298.png
  # Note: Do not use 'sips' on OSX to crop!  It actually interpolates
  # the colors in the image instead of just cropping.
[]

[Variables]
  [./u]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxVariables]
  [./grain_auxvar]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./centroids]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./nodal_flood_aux]
    variable = grain_auxvar
    type = FeatureFloodCountAux
    flood_counter = flood_count_pp
    execute_on = 'initial timestep_end'
  [../]

  [./centroids]
    type = FeatureFloodCountAux
    variable = centroids
    flood_counter = flood_count_pp
    field_display = CENTROID
    execute_on = 'initial timestep_end'
  [../]
[]

[Functions]
  [./tif]
    # ImageFunction gets its file range parameters from ImageMesh,
    # when it is present.  This prevents duplicating information in
    # input files.
    type = ImageFunction

    # In these sample images the features we want to analyze are RED (or close to pure red). The
    # background is BLUE so we can easily distinguish between the two by selecting only the red channel.
    component = 0
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    function = tif
    variable = u
  [../]
[]

[Postprocessors]
  [./flood_count_pp]
    type = FeatureFloodCount
    variable = u
    threshold = 1.0
    compute_var_to_feature_map = true
    execute_on = 'initial timestep_end'
  [../]
[]

[VectorPostprocessors]
  [./grain_volumes]
    type = FeatureVolumeVectorPostprocessor
    flood_counter = flood_count_pp
    execute_on = 'initial timestep_end'
  [../]
[]

[Problem]
  type = FEProblem
  solve = false
[../]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  csv = true
[]

(test/tests/meshgenerators/file_mesh_generator/2d_diffusion_iga_nosplines.i)

[Mesh]
  [cyl2d_iga]
    type = FileMeshGenerator
    file = PressurizedCyl_Patch6_4Elem.e
    clear_spline_nodes = true
  []
  allow_renumbering = false
  parallel_type = replicated
[]

[Variables]
  [u]
    order = SECOND  # Must match mesh order
    family = RATIONAL_BERNSTEIN
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'sin(x)'
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
  solve_type = NEWTON
  dtmin = 1
[]

[Outputs]
  vtk = true
[]

(test/tests/time_integrators/actually_explicit_euler_verification/ee-1d-linear.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 200
  elem_type = EDGE2
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    lumping = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    preset = false
    boundary = '0 1'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  start_time = 0.0
  num_steps = 20
  dt = 0.00005

  [./TimeIntegrator]
    type = ActuallyExplicitEuler
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(test/tests/functions/image_function/image_mesh_2d.i)

[Mesh]
  type = ImageMesh
  dim = 2
  file = stack/test_00.png
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    # ImageFunction gets its file range parameters from ImageMesh,
    # when it is present.  This prevents duplicating information in
    # input files.
    type = ImageFunction
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/function_ic/function_ic_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = initial_cond_func
    [../]
  [../]
[]

[AuxVariables]
  active = 'u_aux'

  [./u_aux]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = initial_cond_func
    [../]
  [../]
[]

[Functions]
  [./initial_cond_func]
    type = ParsedFunction
    value = x+2
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
  nl_rel_tol = 1e-10
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/userobjects/shape_element_user_object/shape_element_user_object.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = (x-0.5)^2
    [../]
  [../]
  [./v]
    order = THIRD
    family = HERMITE
    [./InitialCondition]
      type = FunctionIC
      function = (y-0.5)^2
    [../]
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./time_u]
    type = TimeDerivative
    variable = u
  [../]
  [./time_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[UserObjects]
  [./test]
    type = TestShapeElementUserObject
    u = u
    # first order lagrange variables have 4 DOFs per element
    u_dofs = 4
    v = v
    # third order hermite variables have 16 DOFs per element
    v_dofs = 16
    # as this userobject computes quantities for both the residual AND the jacobian
    # it needs to have these execute_on flags set.
    execute_on = 'linear nonlinear'
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.1
  num_steps = 2
[]

(test/tests/time_integrators/tvdrk2/2d-quadratic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 20
  ny = 20
  elem_type = QUAD9
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*((x*x)+(y*y))-(4*t*t)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*t*((x*x)+(y*y))
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = ic
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = ExplicitTVDRK2
  [../]
  solve_type = 'LINEAR'

  start_time = 0.0
  num_steps = 10
  dt = 0.0001
  l_tol = 1e-8
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/level_set/test/tests/kernels/olsson_reinitialization/olsson_1d.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 8
  ny = 8
  uniform_refine = 2
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./phi_0]
    family = MONOMIAL
    order = FIRST
  [../]
  [./phi_exact]
  [../]
[]

[AuxKernels]
  [./phi_exact]
    type = FunctionAux
    function = phi_exact
    variable = phi_exact
  [../]
[]

[Functions]
  [./phi_initial]
    type = ParsedFunction
    value = '1-x'
  [../]
  [./phi_exact]
    type = ParsedFunction
    vars = epsilon
    vals = 0.05
    value = '1 / (1+exp((x-0.5)/epsilon))'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_initial
    variable = phi
  [../]
  [./phi_0_ic]
    type = FunctionIC
    function = phi_initial
    variable = phi_0
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.05
  [../]
[]

[UserObjects]
  [./arnold]
    type = LevelSetOlssonTerminator
    tol = 0.1
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = phi_exact
    execute_on = 'initial timestep_end'
  [../]
  [./ndofs]
    type = NumDOFs
  [../]
[]

[VectorPostprocessors]
  [./line]
    type = LineValueSampler
    start_point = '0 0.5 0'
    end_point =  '1 0.5 0'
    variable = phi
    num_points = 100
    sort_by = x
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  l_max_its = 100
  nl_max_its = 100
  solve_type = PJFNK
  num_steps = 10
  start_time = 0
  nl_abs_tol = 1e-13
  scheme = implicit-euler
  dt = 0.05
  petsc_options_iname = '-pc_type -pc_sub_type -ksp_gmres_restart'
  petsc_options_value = 'hypre    boomeramg    300'
[]

[Outputs]
  exodus = true
  [./out]
    type = CSV
    time_data = true
    file_base = output/olsson_1d_out
  [../]
[]

(modules/phase_field/test/tests/misc/equal_gradient_lagrange.i)

#
# This test demonstrates an InterfaceKernel set that can enforce the componentwise
# continuity of the gradient of a variable using the Lagrange multiplier method.
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    ymax = 0.5
  []
  [./box1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.51 1 0'
    input = gen
  [../]
  [./box2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.49 0 0'
    top_right = '1 1 0'
    input = box1
  [../]
  [./iface_u]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = 10
    input = box2
  [../]
[]

[Variables]
  [./u2]
    block = 1
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.4)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
  [./v2]
    block = 2
    initial_condition = 0.8
  [../]
  [./lambda]
  [../]
[]

[Kernels]
  [./u2_diff]
    type = Diffusion
    variable = u2
    block = 1
  [../]
  [./u2_dt]
    type = TimeDerivative
    variable = u2
    block = 1
  [../]
  [./v2_diff]
    type = Diffusion
    variable = v2
    block = 2
  [../]
  [./v2_dt]
    type = TimeDerivative
    variable = v2
    block = 2
  [../]
  [./lambda]
    type = NullKernel
    variable = lambda
  [../]
[]

[InterfaceKernels]
  [./iface]
    type = InterfaceDiffusionBoundaryTerm
    boundary = 10
    variable = u2
    neighbor_var = v2
  [../]
  [./lambda]
    type = EqualGradientLagrangeMultiplier
    variable = lambda
    boundary = 10
    element_var = u2
    neighbor_var = v2
    component = 0
  [../]
  [./constraint]
    type = EqualGradientLagrangeInterface
    boundary = 10
    lambda = lambda
    variable = u2
    neighbor_var = v2
    component = 0
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[VectorPostprocessors]
  [./uv]
    type = LineValueSampler
    variable = 'u2 v2'
    start_point = '0 0.5 0'
    end_point = '1 0.5 0'
    sort_by = x
    num_points = 100
  [../]
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type -pc_factor_shift_type'
  petsc_options_value = ' asm    lu          nonzero                    nonzero'

  dt = 0.002
  num_steps = 10
[]

[Outputs]
  exodus = true
  csv = true
  hide = lambda
  print_linear_residuals = false
[]

(test/tests/time_integrators/explicit-euler/ee-1d-quadratic-neumann.i)

[GlobalParams]
  implicit = false
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 10
  elem_type = EDGE3
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x*x-2*t+t*x*x
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x*x
  [../]

  [./left_bc_fn]
    type = ParsedFunction
    value = -t*2*x
  [../]
  [./right_bc_fn]
    type = ParsedFunction
    value = t*2*x
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./abs]
    type = Reaction
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./left]
    type = FunctionNeumannBC
    variable = u
    boundary = '0'
    function = left_bc_fn
  [../]

  [./right]
    type = FunctionNeumannBC
    variable = u
    boundary = '1'
    function = right_bc_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'explicit-euler'
  solve_type = 'LINEAR'

  l_tol = 1e-12
  start_time = 0.0
  num_steps = 10
  dt = 0.001
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(test/tests/materials/piecewise_by_block_material/test.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 10
    xmax = 2
  []
  [subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1.0 0 0'
    block_id = 1
    top_right = '2.0 1.0 0'
  []
  [middle]
    input = subdomain1
    type = SideSetsBetweenSubdomainsGenerator
    new_boundary = middle
    paired_block = 1
    primary_block = 0
  []
[]

[Variables]
  [dummy]
    type = MooseVariableFVReal
  []
[]

# This is added to have sufficient ghosting layers, see #19534
[FVKernels]
  [diff]
    type = FVDiffusion
    variable = 'dummy'
    coeff = 1
  []
[]

[AuxVariables]
  [u]
    type = MooseVariableFVReal
  []
  [v]
    type = MooseVariableFVReal
    [InitialCondition]
      type = FunctionIC
      function = '4 * (x - 7) * (x - 8)'
    []
  []
[]

[AuxKernels]
  # to trigger off-boundary element computations
  [to_var]
    type = ADMaterialRealAux
    variable = 'u'
    property = coeff
  []
[]

[Materials]
  [coeff_mat]
    type = ADPiecewiseConstantByBlockMaterial
    prop_name = 'coeff'
    subdomain_to_prop_value = '0 4
                               1 2'
  []
[]

[Postprocessors]
  # to trigger on boundary element computations
  [flux]
    type = ADSideDiffusiveFluxIntegral
    boundary = left
    variable = v
    diffusivity = 'coeff'
  []

  # to trigger ghost evaluations
  [flux_mid]
    type = ADInterfaceDiffusiveFluxIntegral
    boundary = middle
    variable = v
    diffusivity = 'coeff'
  []
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[]

[Outputs]
  exodus = true
  # To get level of ghosting
  [console]
    type = Console
    system_info = 'framework mesh aux nonlinear execution relationship'
  []
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/fltvd_3D.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, with antidiffusion from superbee flux limiting
# 3D version
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  xmin = 0
  xmax = 1
  ny = 4
  ymin = 0
  ymax = 0.5
  nz = 3
  zmin = 0
  zmax = 2
[]

[Variables]
  [tracer]
  []
[]

[Problem]
  error_on_jacobian_nonzero_reallocation=true
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0.5 2'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  nl_max_its = 500
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(test/tests/functions/image_function/image_2d_elemental.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    # file range is parsed as a vector of unsigned.  If it only has 1
    # entry, only a single file is read.
    file_range = '0'
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/eigenstrain/composite.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./TensorMechanics]
  [../]
[]

[AuxVariables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
  [./s11]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./s22]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./ds11]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./ds22]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = eigenstrain
    index_i = 0
    index_j = 0
  [../]
  [./s22]
    type = RankTwoAux
    variable = s22
    rank_two_tensor = eigenstrain
    index_i = 1
    index_j = 1
  [../]
  [./ds11]
    type = RankTwoAux
    variable = ds11
    rank_two_tensor = delastic_strain/dc
    index_i = 0
    index_j = 0
  [../]
  [./ds22]
    type = RankTwoAux
    variable = ds22
    rank_two_tensor = delastic_strain/dc
    index_i = 1
    index_j = 1
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
  [./strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
    eigenstrain_names = 'eigenstrain'
  [../]
  [./eigen1]
    type = GenericConstantRankTwoTensor
    tensor_values = '1 -1 0 0 0 0'
    tensor_name = eigen1
  [../]
  [./eigen2]
    type = GenericConstantRankTwoTensor
    tensor_values = '-1 1 0 0 0 0'
    tensor_name = eigen2
  [../]
  [./weight1]
    type = DerivativeParsedMaterial
    function = 0.02*c^2
    f_name = weight1
    args = c
  [../]
  [./weight2]
    type = DerivativeParsedMaterial
    function = 0.02*(1-c)^2
    f_name = weight2
    args = c
  [../]

  [./eigenstrain]
    type = CompositeEigenstrain
    tensors = 'eigen1  eigen2'
    weights = 'weight1 weight2'
    args = c
    eigenstrain_name = eigenstrain
  [../]
[]

[BCs]
  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  exodus = true
  execute_on = final
[]

(test/tests/mortar/continuity-2d-conforming/equalgradient.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-conf.e
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lmx]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]
  [./lmy]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]
[]

[ICs]
  [./block1]
    type = FunctionIC
    variable = u
    block = 1
    function = y
  [../]
  [./block2]
    type = FunctionIC
    variable = u
    block = 2
    function = y-0.5
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./dt]
    type = TimeDerivative
    variable = u
  [../]
[]

[Constraints]
  [./cedx]
    type = EqualGradientConstraint
    secondary_variable = u
    variable = lmx
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
    component = 0
  [../]
  [./cedy]
    type = EqualGradientConstraint
    secondary_variable = u
    variable = lmy
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
    component = 1
  [../]
[]

[BCs]
  [./all]
    type = DiffusionFluxBC
    variable = u
    boundary = '2 4 100 101'
  [../]
  [./boundary]
    type = DirichletBC
    boundary = 1
    variable = u
    value = 0.0
  [../]
  [./top]
    type = FunctionDirichletBC
    boundary = 3
    variable = u
    function = 0.5-t
  [../]
[]

[Preconditioning]
  [./fmp]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  nl_rel_tol = 1e-11
  l_tol = 1e-10
  l_max_its = 10
  dt = 0.05
  num_steps = 3
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(test/tests/postprocessors/side_integral/side_integral_functor.i)

[Mesh]
  inactive = 'refine'
  # U-shaped domains to have internal boundaries in
  # a variety of directions
  [cmg]
     type = CartesianMeshGenerator
     dim = 2
     dx = '1 1 1'
     dy = '3 1'
     ix = '4 5 3'
     iy = '12 4'
     subdomain_id = '1 2 1
                     1 1 1'
  []
  [internal_boundary_dir1]
     type = SideSetsBetweenSubdomainsGenerator
     input = cmg
     primary_block = 1
     paired_block = 2
     new_boundary = 'inside_1'
  []
  [internal_boundary_dir2]
     type = SideSetsBetweenSubdomainsGenerator
     input = internal_boundary_dir1
     primary_block = 2
     paired_block = 1
     new_boundary = 'inside_2'
  []
  [refine]
    type = RefineBlockGenerator
    input = internal_boundary_dir2
    block = '1 2'
    refinement = '2 1'
  []
[]

[Variables]
  [u]
    type = MooseVariableFVReal
    block = 1
  []
[]

[AuxVariables]
  [v1]
    type = MooseVariableFVReal
    block = 1
    [InitialCondition]
      type = FunctionIC
      function = 'x + y'
    []
  []
  [v2]
    type = MooseVariableFVReal
    block = 2
    [InitialCondition]
      type = FunctionIC
      function = '2*x*x - y'
    []
  []
[]

[Functions]
  [f1]
    type = ADParsedFunction
    value = 'exp(x - y)'
  []
[]

[Materials]
  [m1]
    type = ADGenericFunctorMaterial
    prop_names = 'm1'
    prop_values = 'f1'
  []
  [m2]
    type = ADPiecewiseByBlockFunctorMaterial
    prop_name = 'm2'
    subdomain_to_prop_value = '1 12
                               2 4'
  []
[]

[FVKernels]
  [diff]
    type = FVDiffusion
    variable = u
    coeff = '1'
  []
[]

[FVBCs]
  [left]
    type = FVDirichletBC
    variable = u
    boundary = 3
    value = 0
  []

  [right]
    type = FVDirichletBC
    variable = u
    boundary = 1
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Postprocessors]
  # Mesh external boundaries integration
  [ext_u]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'left top right'
    functor = u
    restrict_to_functors_domain = true
  []
  [ext_v1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'left right'
    functor = v1
  []
  [ext_v2]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'top'
    functor = v2
    restrict_to_functors_domain = true
  []
  [ext_f1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'left top right'
    functor = f1
    prefactor = f1
  []
  [ext_m1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'left top right'
    functor = m1
    restrict_to_functors_domain = true
  []
  [ext_m2]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'left top right'
    functor = m2
    restrict_to_functors_domain = true
  []

  # Internal to the mesh, but a side to the variables
  # With orientation of normal 1->2
  [int_s1_u]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_1
    functor = u
  []
  [int_s1_v1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_1
    functor = v1
  []
  [int_s1_f1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_1
    functor = f1
  []
  [int_s1_m1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_1
    functor = m1
  []
  [int_s1_m2]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_1
    functor = m2
  []
  # With orientation of normal 2->1
  [int_s2_v2]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_2
    functor = v2
  []
  [int_s2_f1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_2
    functor = f1
  []
  [int_s2_m1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_2
    functor = m1
  []
  [int_s2_m2]
    type = ADSideIntegralFunctorPostprocessor
    boundary = inside_2
    functor = m2
  []
[]

[Outputs]
  csv = true
  exodus = true
[]

[Problem]
  kernel_coverage_check = false
[]

(test/tests/kernels/conservative_advection/no_upwinding_2D.i)

# 2D test of advection with no upwinding
# Note there are overshoots or undershoots
# but numerical diffusion is minimized.
# The center of the blob advects with the correct velocity
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 40
  ny = 40
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_blob]
    type = FunctionIC
    variable = u
    function = 'if(x<0.2,if(y<0.2,1,0),0)'
  [../]
[]

[Kernels]
  [./udot]
    type = TimeDerivative
    variable = u
  [../]
  [./advection]
    type = ConservativeAdvection
    variable = u
    velocity = '2 1 0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = LINEAR
  dt = 0.01
  end_time = 0.1
  l_tol = 1E-14
[]

[Outputs]
  exodus = true
[]

(test/tests/materials/derivative_material_interface/ad_parsed_material.i)

#
# Test the parsed function free enery Allen-Cahn Bulk kernel
#

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./eta]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = ADMatDiffusion
    variable = eta
    diffusivity = F
  [../]
  [./dt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[Materials]
  [./consts]
    type = ADParsedMaterial
    args  = 'eta'
    function ='(eta-0.5)^2'
    outputs = exodus
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(modules/porous_flow/test/tests/mass_conservation/mass05.i)

# Checking that the mass postprocessor correctly calculates the mass
# of each component in each phase, as well as the total mass of each
# component in all phases.
# 2phase, 2component, constant porosity

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [sat]
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 0.3
  []
  [massfrac_ph1_sp0]
    initial_condition = 0.55
  []
[]

[ICs]
  [pinit]
    type = ConstantIC
    value = 1
    variable = pp
  []
  [satinit]
    type = FunctionIC
    function = 1-x
    variable = sat
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sat
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp sat'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 0.1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp
    phase1_saturation = sat
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [comp0_phase0_mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = 0
  []
  [comp0_phase1_mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = 1
  []
  [comp0_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 0
  []
  [comp0_total_mass2]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = '0 1'
  []
  [comp1_phase0_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = 0
  []
  [comp1_phase1_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = 1
  []
  [comp1_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
  []
  [comp1_total_mass2]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = '0 1'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  nl_abs_tol = 1e-16
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = mass05
  csv = true
[]

(modules/richards/test/tests/sinks/s_fu_03.i)

# with fully_upwind = true
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  SUPG_UO = SUPGstandard
  sat_UO = Saturation
  seff_UO = SeffVG
  fully_upwind = true
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[AuxVariables]
  [./seff]
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 2
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-lfout-rfout-mf)/2/(mi+mf))
    vars = 'mi mf lfout rfout'
    vals = 'mass_init mass_fin left_flux_out right_flux_out'
  [../]
[]

[Postprocessors]
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]
  [./mass_fin]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]
  [./left_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = left
    variable = pressure
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    use_mobility = true
    use_relperm = true
  [../]
  [./right_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = right
    variable = pressure
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    use_mobility = true
    use_relperm = true
  [../]
  [./p0]
    type = PointValue
    point = '0 0 0'
    variable = pressure
  [../]
  [./s0]
    type = PointValue
    point = '0 0 0'
    variable = seff
  [../]
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]

[BCs]
  [./left_flux]
    type = RichardsPiecewiseLinearSink
    boundary = left
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    variable = pressure
    use_mobility = true
    use_relperm = true
  [../]
  [./right_flux]
    type = RichardsPiecewiseLinearSink
    boundary = right
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    variable = pressure
    use_mobility = true
    use_relperm = true
  [../]
[]

[Kernels]
  active = 'richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
[]

[AuxKernels]
  [./seff_auxk]
    type = RichardsSeffAux
    variable = seff
    seff_UO = SeffVG
    pressure_vars = 'pressure'
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 2.1E-5 2.2E-5  2.1E-5 0.1E-5 3.3E-5  2.2E-5 3.3E-5 2E-5'
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2E-3
  end_time = 0.2
[]

[Outputs]
  file_base = s_fu_03
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/jacobian/fflux01.i)

# 1phase, 1component, constant viscosity, constant insitu permeability
# density with constant bulk, Corey relative perm, nonzero gravity, unsaturated with vanGenuchten
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  xmin = 0
  xmax = 1
  ny = 1
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = -0.7+x+y
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      density0 = 1
      thermal_expansion = 0
      viscosity = 1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0 0 2 0 0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Preconditioning]
  active = check
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000'
  []
  [check]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  exodus = false
[]

(modules/richards/test/tests/buckley_leverett/bl02.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2.0E6
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-3
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]


[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]

[AuxKernels]
  active = 'calculate_seff'
  [./calculate_seff]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffVG
    pressure_vars = pressure
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[BCs]
  active = 'left'
  [./left]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 980000
  [../]
[]

[Kernels]
  active = 'richardsf richardst'

  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]


[Functions]
 active = 'initial_pressure'
  [./initial_pressure]
    type = ParsedFunction
    value = max((1000000-x/5*1000000)-20000,-20000)
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'andy'

  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 20'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 50

  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.01
  [../]

[]

[Outputs]
  file_base = bl02
  interval = 1000000
  exodus = true
[]

(test/tests/kernels/material_derivatives/material_derivatives_test.i)

###########################################################
# This is a test of the material derivatives test kernel.
###########################################################

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Functions]
  [./u_IC_fn]
    type = ParsedFunction
    value = 'x'
  [../]
  [./v_IC_fn]
    type = ParsedFunction
    value = 'sin(x)'
  [../]
[]

[ICs]
  [./u_IC]
    type = FunctionIC
    variable = u
    function = u_IC_fn
  [../]
  [./v_IC]
    type = FunctionIC
    variable = v
    function = v_IC_fn
  [../]
[]

[Kernels]
  [./test_kernel]
    type = MaterialDerivativeTestKernel
    variable = u
    args = 'u v'
    material_property = material_derivative_test_property
  [../]
  # add a dummy kernel for v to prevent singular Jacobian
  [./dummy_kernel]
    type = Diffusion
    variable = v
  [../]
[]

[Materials]
  [./material_derivative_test_material]
    type = MaterialDerivativeTestMaterial
    var1 = u
    var2 = v
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    solve_type = newton
    petsc_options_iname = '-snes_type -snes_test_err'
    petsc_options_value = 'test       1e-10'
  [../]
[]

[Executioner]
  type = Steady
[]

(test/tests/auxkernels/solution_aux/aux_nonlinear_solution_adapt_xda.i)

[Mesh]
  # This test uses SolutionUserObject which doesn't work with DistributedMesh.
  type = FileMesh
  file = aux_nonlinear_solution_adapt_out_0004_mesh.xda
  parallel_type = replicated
[]

[Adaptivity]
  marker = error_frac
  steps = 2
  [./Indicators]
    [./jump_indicator]
      type = GradientJumpIndicator
      variable = u
    [../]
  [../]
  [./Markers]
    [./error_frac]
      type = ErrorFractionMarker
      indicator = jump_indicator
      refine = 0.7
    [../]
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./u_aux]
  [../]
[]

[Functions]
  [./u_xda_func]
    type = SolutionFunction
    solution = xda_u
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[AuxKernels]
  [./aux_xda_kernel]
    type = SolutionAux
    variable = u_aux
    solution = xda_u_aux
    execute_on = initial
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 2
  [../]
[]

[UserObjects]
  [./xda_u_aux]
    type = SolutionUserObject
    system = aux0
    mesh = aux_nonlinear_solution_adapt_out_0004_mesh.xda
    es = aux_nonlinear_solution_adapt_out_0004.xda
    system_variables = u_aux
    execute_on = initial
  [../]
  [./xda_u]
    type = SolutionUserObject
    system = nl0
    mesh = aux_nonlinear_solution_adapt_out_0004_mesh.xda
    es = aux_nonlinear_solution_adapt_out_0004.xda
    system_variables = u
    execute_on = initial
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_rel_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./u_func_ic]
    function = u_xda_func
    variable = u
    type = FunctionIC
  [../]
[]

(modules/richards/test/tests/dirac/bh_fu_07.i)

#fullyupwind
[Mesh]
  type = FileMesh
  file = bh07_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1000 10000'
    x = '100 1000'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[BCs]
  [./fix_outer]
    type = DirichletBC
    boundary = perimeter
    variable = pressure
    value = 1E7
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFullyUpwindFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh07.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    re_constant = 0.1594
    character = 2
    fully_upwind = true
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
    execute_on = 'initial timestep_end'
  [../]

  [./fluid_mass]
    type = RichardsMass
    variable = pressure
    execute_on = 'initial timestep_end'
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-11 0 0  0 1E-11 0  0 0 1E-11'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1000
  solve_type = NEWTON

  [./TimeStepper]
    # get only marginally better results for smaller time steps
    type = FunctionDT
    function = dts
  [../]

[]

[Outputs]
  file_base = bh_fu_07
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
[]

(modules/porous_flow/test/tests/sinks/s07.i)

# apply a sink flux on just one component of a 3-component system and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp frac0 frac1'
    number_fluid_phases = 1
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1.1
  []
[]

[Variables]
  [pp]
  []
  [frac0]
    initial_condition = 0.1
  []
  [frac1]
    initial_condition = 0.6
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = y
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = frac0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = frac1
  []
  [mass2]
    type = PorousFlowMassTimeDerivative
    fluid_component = 2
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'frac0 frac1'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '0.2 0 0 0 0.1 0 0 0 0.1'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[AuxVariables]
  [flux_out]
  []
[]

[Functions]
  [mass1_00]
    type = ParsedFunction
    value = 'frac*vol*por*dens0*exp(pp/bulk)*pow(1+pow(-al*pp,1.0/(1-m)),-m)'
    vars = 'frac  vol  por dens0 pp bulk al m'
    vals = 'f1_00 0.25 0.1 1.1  p00 1.3 1.1 0.5'
  []
  [expected_mass_change1_00]
    type = ParsedFunction
    value = 'frac*fcn*area*dt'
    vars = 'frac fcn area dt'
    vals = 'f1_00 6  0.5  1E-3'
  []
  [mass1_00_expect]
    type = ParsedFunction
    value = 'mass_prev-mass_change'
    vars = 'mass_prev mass_change'
    vals = 'm1_00_prev  del_m1_00'
  []
  [mass1_01]
    type = ParsedFunction
    value = 'frac*vol*por*dens0*exp(pp/bulk)*pow(1+pow(-al*pp,1.0/(1-m)),-m)'
    vars = 'frac  vol  por dens0 pp bulk al m'
    vals = 'f1_01 0.25 0.1 1.1  p01 1.3 1.1 0.5'
  []
  [expected_mass_change1_01]
    type = ParsedFunction
    value = 'frac*fcn*area*dt'
    vars = 'frac fcn area dt'
    vals = 'f1_01 6  0.5  1E-3'
  []
  [mass1_01_expect]
    type = ParsedFunction
    value = 'mass_prev-mass_change'
    vars = 'mass_prev mass_change'
    vals = 'm1_01_prev  del_m1_01'
  []
[]

[Postprocessors]
  [f1_00]
    type = PointValue
    point = '0 0 0'
    variable = frac1
    execute_on = 'initial timestep_end'
  []
  [flux_00]
    type = PointValue
    point = '0 0 0'
    variable = flux_out
    execute_on = 'initial timestep_end'
  []
  [p00]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m1_00]
    type = FunctionValuePostprocessor
    function = mass1_00
    execute_on = 'initial timestep_end'
  []
  [m1_00_prev]
    type = FunctionValuePostprocessor
    function = mass1_00
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [del_m1_00]
    type = FunctionValuePostprocessor
    function = expected_mass_change1_00
    execute_on = 'timestep_end'
    outputs = 'console'
  []
  [m1_00_expect]
    type = FunctionValuePostprocessor
    function = mass1_00_expect
    execute_on = 'timestep_end'
  []
  [f1_01]
    type = PointValue
    point = '0 1 0'
    variable = frac1
    execute_on = 'initial timestep_end'
  []
  [flux_01]
    type = PointValue
    point = '0 1 0'
    variable = flux_out
    execute_on = 'initial timestep_end'
  []
  [p01]
    type = PointValue
    point = '0 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m1_01]
    type = FunctionValuePostprocessor
    function = mass1_01
    execute_on = 'initial timestep_end'
  []
  [m1_01_prev]
    type = FunctionValuePostprocessor
    function = mass1_01
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [del_m1_01]
    type = FunctionValuePostprocessor
    function = expected_mass_change1_01
    execute_on = 'timestep_end'
    outputs = 'console'
  []
  [m1_01_expect]
    type = FunctionValuePostprocessor
    function = mass1_01_expect
    execute_on = 'timestep_end'
  []
  [f1_11]
    type = PointValue
    point = '1 1 0'
    variable = frac1
    execute_on = 'initial timestep_end'
  []
  [flux_11]
    type = PointValue
    point = '1 1 0'
    variable = flux_out
    execute_on = 'initial timestep_end'
  []
  [p11]
    type = PointValue
    point = '1 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [flux]
    type = PorousFlowSink
    boundary = 'left'
    variable = frac1
    use_mobility = false
    use_relperm = false
    mass_fraction_component = 1
    fluid_phase = 0
    flux_function = 6
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-3
  end_time = 0.01
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s07
  [console]
    type = Console
    execute_on = 'nonlinear linear'
  []
  [csv]
    type = CSV
    execute_on = 'timestep_end'
  []
[]

(modules/richards/test/tests/dirac/bh10.i)

# fully-saturated
# production
# with anisotropic and nonsymmetric (!) permeability
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh02.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = 1
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '2E-12 0 0  1E-12 3E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 0.5
  dt = 1E-2
  solve_type = NEWTON

[]

[Outputs]
  file_base = bh10
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(test/tests/time_steppers/timesequence_stepper/timesequence_failed_solve.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  # This timestepper does not use dt to set the timestep, it uses the time_sequence.
  # dt = 250
  dtmin=250
  end_time = 3000.0
  [./TimeStepper]
    type = TimeSequenceStepperFailTest
    time_sequence  = '0  1000.0 2000.0'
  [../]
  nl_rel_tol=1.e-10
[]

[Outputs]
  file_base = timesequence_failed_solve
  exodus = true
[]

(test/tests/time_integrators/explicit-euler/ee-1d-linear.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 200
  elem_type = EDGE2
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    lumping = true
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[BCs]
  active = 'all'

  [./all]
    type = FunctionDirichletBC
    variable = u
    preset = false
    boundary = '0 1'
    function = exact_fn
    implicit = true
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'explicit-euler'
  solve_type = 'LINEAR'

  start_time = 0.0
  num_steps = 20
  dt = 0.00005
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(test/tests/fvkernels/fv_constant_scalar_advection/2D_constant_scalar_advection.i)

[Mesh]
  [gen_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 4
    nx = 10
    ny = 20
  []
[]

[Variables]
  [v]
    type = MooseVariableFVReal
    two_term_boundary_expansion = false
  []
[]

[ICs]
  [v_ic]
    type = FunctionIC
    variable = v
    function = 'r2 := (x - 0.5)*(x - 0.5) + (y - 0.3)*(y - 0.3); exp(-r2 * 20)'
  []
[]

[FVKernels]
  [advection]
    type = FVAdvection
    variable = v
    velocity = '1 0.5 0'
  []
  [time]
    type = FVTimeKernel
    variable = v
  []
[]

[FVBCs]
  [fv_outflow]
    type = FVConstantScalarOutflowBC
    velocity = '1 0.5 0'
    variable = v
    boundary = 'right top'
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  num_steps = 10
  dt = 0.25
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/tensor_mechanics/test/tests/auxkernels/tensorelasticenergyaux.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  nz = 0
  xmax = 3
  ymax = 2
  zmax = 0
  elem_type = QUAD4
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = sin(x)*0.1
    [../]
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = cos(y)*0.05
    [../]
  [../]
  [./E]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./elastic_energy]
    type = ElasticEnergyAux
    variable = E
  [../]
[]

[Materials]
  [./elasticity]
    type = ComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1 2 4 3 2 5 1 3 1'
  [../]
  [./strain]
    type = ComputeSmallStrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Problem]
  kernel_coverage_check = false
[]

[Outputs]
  exodus = true
[]

(modules/level_set/test/tests/verification/1d_level_set_mms/level_set_mms.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 32
  nx = 64
  uniform_refine = 0
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[ICs]
  [./phi_ic]
    function = phi_exact
    variable = phi
    type = FunctionIC
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Functions]
  [./phi_exact]
    type = ParsedFunction
    value = 'a*exp(1/(10*t))*sin(2*pi*x/b) + 1'
    vars = 'a b'
    vals = '1 8'
  [../]
  [./phi_mms]
    type = ParsedFunction
    value = '-a*exp(1/(10*t))*sin(2*pi*x/b)/(10*t^2) + 2*pi*a*exp(1/(10*t))*cos(2*pi*x/b)/b'
    vars = 'a b'
    vals = '1 8'
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '1'
    value_y = '1'
  [../]
[]

[Kernels]
  [./phi_advection]
    type = LevelSetAdvection
    variable = phi
    velocity = velocity
  [../]
  [./phi_time]
    type = TimeDerivative
    variable = phi
  [../]
  [./phi_forcing]
    type = BodyForce
    variable = phi
    function = phi_mms
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = phi_exact
    variable = phi
  [../]
  [./h]
    type = AverageElementSize
  [../]
  [./point]
    type = PointValue
    point = '0.1 0 0'
    variable = phi
  [../]
[]

[Executioner]
  type = Transient
  start_time = 1
  dt = 0.01
  end_time = 1.25
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  scheme = bdf2
  nl_rel_tol = 1e-12
[]

[Outputs]
  interval = 10
  execute_on = 'timestep_end'
  csv = true
[]

(modules/phase_field/test/tests/free_energy_material/RegularSolutionFreeEnergy_plog.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 50
  xmax = 1
[]

[Variables]
  [./c]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = c
  [../]
[]

[BCs]
  [./left]
    type = FunctionDirichletBC
    variable = c
    boundary = left
    function = x
  [../]
  [./right]
    type = FunctionDirichletBC
    variable = c
    boundary = right
    function = x
  [../]
[]

[Materials]
  [./free_energy]
    type = RegularSolutionFreeEnergy
    f_name = F
    c = c
    outputs = out
    log_tol = 0.2
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  l_max_its = 1
  nl_max_its = 1
  nl_abs_tol = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  [./out]
    type = Exodus
    execute_on = timestep_end
  [../]
[]

(test/tests/misc/check_error/function_file_test10.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    xy_data = '1 2'
    scale_factor = 1.0
    axis = 3
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/porous_flow/test/tests/recover/pffltvd.i)

# Tests that PorousFlow can successfully recover using a checkpoint file.
# This test contains stateful material properties, adaptivity, integrated
# boundary conditions with nodal-sized materials, and TVD flux limiting.
#
# This test file is run three times:
# 1) The full input file is run to completion
# 2) The input file is run for half the time and checkpointing is included
# 3) The input file is run in recovery using the checkpoint data
#
# The final output of test 3 is compared to the final output of test 1 to verify
# that recovery was successful.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[Adaptivity]
  initial_steps = 1
  initial_marker = tracer_marker
  marker = tracer_marker
  max_h_level = 1
  [Markers]
    [tracer_marker]
      type = ValueRangeMarker
      variable = tracer
      lower_bound = 0.02
      upper_bound = 0.98
    []
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '2 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 2
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = NodalValueSampler
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 0.2
  dt = 0.05
[]

[Outputs]
  csv = true
[]

(modules/phase_field/test/tests/GrandPotentialPFM/SinteringBase.i)

#input file to test the materials GrandPotentialTensorMaterial and GrandPotentialSinteringMaterial

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 17
  ny = 17
  xmin = 0
  xmax = 680
  ymin = 0
  ymax = 680
[]

[GlobalParams]
  op_num = 4
  var_name_base = gr
  int_width = 40
[]

[Variables]
  [./w]
  [../]
  [./phi]
  [../]
  [./PolycrystalVariables]
  [../]
[]

[AuxVariables]
  [./bnds]
  [../]
  [./T]
    order = CONSTANT
    family = MONOMIAL
    [./InitialCondition]
      type = FunctionIC
      variable = T
      function = f_T
    [../]
  [../]
[]

[ICs]
  [./phi_IC]
    type = SpecifiedSmoothCircleIC
    variable = phi
    x_positions = '190 490 190 490'
    y_positions = '190 190 490 490'
    z_positions = '  0   0   0   0'
    radii = '150 150 150 150'
    invalue = 0
    outvalue = 1
  [../]
  [./gr0_IC]
    type = SmoothCircleIC
    variable = gr0
    x1 = 190
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
  [./gr1_IC]
    type = SmoothCircleIC
    variable = gr1
    x1 = 490
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
  [./gr2_IC]
    type = SmoothCircleIC
    variable = gr2
    x1 = 190
    y1 = 490
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
  [./gr3_IC]
    type = SmoothCircleIC
    variable = gr3
    x1 = 490
    y1 = 490
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
[]

[Functions]
  [./f_T]
    type = ConstantFunction
    value = 1600
  [../]
[]

[Materials]
  # Free energy coefficients for parabolic curves
  [./ks]
    type = ParsedMaterial
    f_name = ks
    args = 'T'
    constant_names = 'a b'
    constant_expressions = '-0.0025 157.16'
    function = 'a*T + b'
  [../]
  [./kv]
    type = ParsedMaterial
    f_name = kv
    material_property_names = 'ks'
    function = '10*ks'
  [../]
  # Diffusivity and mobilities
  [./chiD]
    type = GrandPotentialTensorMaterial
    f_name = chiD
    solid_mobility = L
    void_mobility = Lv
    chi = chi
    surface_energy = 19.7
    c = phi
    T = T
    D0 = 2.0e11
    GBmob0 = 1.4759e9
    Q = 2.77
    Em = 2.40
    bulkindex = 1
    gbindex = 20
    surfindex = 100
    outputs = exodus
  [../]
  # Equilibrium vacancy concentration
  [./cs_eq]
    type = DerivativeParsedMaterial
    f_name = cs_eq
    args = 'gr0 gr1 gr2 gr3 T'
    constant_names = 'Ef c_GB kB'
    constant_expressions = '2.69 0.189 8.617343e-5'
    function = 'bnds:=gr0^2 + gr1^2 + gr2^2 + gr3^2; exp(-Ef/kB/T) + 4.0 * c_GB * (1 - bnds)^2'
  [../]
  # Everything else
  [./sintering]
    type = GrandPotentialSinteringMaterial
    chemical_potential = w
    void_op = phi
    Temperature = T
    surface_energy = 19.7
    grainboundary_energy = 9.86
    void_energy_coefficient = kv
    solid_energy_coefficient = ks
    equilibrium_vacancy_concentration = cs_eq
    solid_energy_model = PARABOLIC
  [../]
[]

[Kernels]
  [./dt_gr0]
    type = TimeDerivative
    variable = gr0
  [../]
  [./dt_gr1]
    type = TimeDerivative
    variable = gr1
  [../]
  [./dt_gr2]
    type = TimeDerivative
    variable = gr2
  [../]
  [./dt_gr3]
    type = TimeDerivative
    variable = gr3
  [../]
  [./dt_phi]
    type = TimeDerivative
    variable = phi
  [../]
  [./dt_w]
    type = TimeDerivative
    variable = w
  [../]
[]

[AuxKernels]
  [./bnds_aux]
    type = BndsCalcAux
    variable = bnds
    execute_on = 'initial timestep_end'
  [../]
  [./T_aux]
    type = FunctionAux
    variable = T
    function = f_T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = JFNK
  dt = 1
  num_steps = 1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/examples/tutorial/06_KT.i)

# Darcy flow with a tracer
[Mesh]
  [annular]
    type = AnnularMeshGenerator
    nr = 10
    rmin = 1.0
    rmax = 10
    growth_r = 1.4
    nt = 4
    dmin = 0
    dmax = 90
  []
  [make3D]
    type = MeshExtruderGenerator
    extrusion_vector = '0 0 12'
    num_layers = 3
    bottom_sideset = 'bottom'
    top_sideset = 'top'
    input = annular
  []
  [shift_down]
    type = TransformGenerator
    transform = TRANSLATE
    vector_value = '0 0 -6'
    input = make3D
  []
  [aquifer]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 -2'
    top_right = '10 10 2'
    input = shift_down
  []
  [injection_area]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'x*x+y*y<1.01'
    included_subdomain_ids = 1
    new_sideset_name = 'injection_area'
    input = 'aquifer'
  []
  [rename]
    type = RenameBlockGenerator
    old_block = '0 1'
    new_block = 'caps aquifer'
    input = 'injection_area'
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [porepressure]
  []
  [tracer_concentration]
  []
[]

[ICs]
  [tracer_concentration]
    type = FunctionIC
    function = '0.5*if(x*x+y*y<1.01,1,0)'
    variable = tracer_concentration
  []
[]

[PorousFlowFullySaturated]
  porepressure = porepressure
  coupling_type = Hydro
  gravity = '0 0 0'
  fp = the_simple_fluid
  mass_fraction_vars = tracer_concentration
  stabilization = KT
  flux_limiter_type = superbee
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1E6
    boundary = injection_area
  []
  [constant_outer_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 0
    boundary = rmax
  []
  [injected_tracer]
    type = DirichletBC
    variable = tracer_concentration
    value = 0.5
    boundary = injection_area
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      viscosity = 1.0E-3
      density0 = 1000.0
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability_aquifer]
    type = PorousFlowPermeabilityConst
    block = aquifer
    permeability = '1E-14 0 0   0 1E-14 0   0 0 1E-14'
  []
  [permeability_caps]
    type = PorousFlowPermeabilityConst
    block = caps
    permeability = '1E-15 0 0   0 1E-15 0   0 0 1E-16'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1E6
  dt = 1E5
  nl_rel_tol = 1E-14
[]

[Outputs]
  exodus = true
[]

(test/tests/userobjects/element_subdomain_modifier/reversible.i)

[Problem]
  solve = false
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 16
    ny = 16
  []
  [left]
    type = SubdomainBoundingBoxGenerator
    input = 'gen'
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.25 1 1'
  []
  [right]
    type = SubdomainBoundingBoxGenerator
    input = 'left'
    block_id = 2
    bottom_left = '0.25 0 0'
    top_right = '1 1 1'
  []
[]

[UserObjects]
  [moving_circle]
    type = CoupledVarThresholdElementSubdomainModifier
    coupled_var = 'phi'
    criterion_type = BELOW
    threshold = 0
    subdomain_id = 1
    complement_subdomain_id = 2
    moving_boundary_name = moving_boundary
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []
[]

[Functions]
  [moving_circle]
    type = ParsedFunction
    value = '(x-t)^2+(y)^2-0.5^2'
  []
[]

[AuxVariables]
  [phi]
    [InitialCondition]
      type = FunctionIC
      function = moving_circle
    []
  []
[]

[AuxKernels]
  [phi]
    type = FunctionAux
    variable = phi
    function = moving_circle
    execute_on = 'INITIAL TIMESTEP_BEGIN TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  dt = 0.3
  num_steps = 3
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/fltvd_2D.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, with antidiffusion from superbee flux limiting
# 2D version
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  xmin = 0
  xmax = 1
  ny = 4
  ymin = 0
  ymax = 0.5
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0.5 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  nl_max_its = 500
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/heat_conduction/test/tests/verify_against_analytical/ad_1D_transient.i)

# This test solves a 1D transient heat equation
# The error is caclulated by comparing to the analytical solution
# The problem setup and analytical solution are taken from "Advanced Engineering
# Mathematics, 10th edition" by Erwin Kreyszig.
# http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364
# It is Example 1 in section 12.6 on page 561

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 160
  xmax = 80
[]

[Variables]
  [./T]
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '100*sin(pi*x/80)'
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = ADHeatConduction
    variable = T
  [../]
  [./HeatTdot]
    type = ADHeatConductionTimeDerivative
    variable = T
  [../]
[]

[BCs]
  [./sides]
    type = DirichletBC
    variable = T
    boundary = 'left right'
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '0.95' #copper in cal/(cm sec C)
  [../]
  [./cp]
    type = ADGenericConstantMaterial
    prop_names = 'specific_heat'
    prop_values = '0.092' #copper in cal/(g C)
  [../]
  [./rho]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = '8.92' #copper in g/(cm^3)
  [../]
[]

[Postprocessors]
  [./error]
    type = NodalL2Error
    function = '100*sin(pi*x/80)*exp(-0.95/(0.092*8.92)*pi^2/80^2*t)'
    variable = T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  l_tol = 1e-6
  dt = 2
  end_time = 100
[]

[Outputs]
  exodus = true
[]

(modules/xfem/test/tests/moving_interface/ad_phase_transition_2d.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 11
    ny = 1
    xmin = 0.0
    xmax = 20.0
    ymin = 0.0
    ymax = 5.0
    elem_type = QUAD4
  []
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [velocity]
    type = XFEMPhaseTransitionMovingInterfaceVelocity
    diffusivity_at_positive_level_set = 5
    diffusivity_at_negative_level_set = 1
    equilibrium_concentration_jump = 1
    value_at_interface_uo = value_uo
  []
  [value_uo]
    type = NodeValueAtXFEMInterface
    variable = 'u'
    interface_mesh_cut_userobject = 'cut_mesh'
    execute_on = TIMESTEP_END
    level_set_var = ls
  []
  [cut_mesh]
    type = InterfaceMeshCut2DUserObject
    mesh_file = flat_interface_1d.e
    interface_velocity_uo = velocity
    heal_always = true
  []
[]

[Variables]
  [u]
  []
[]

[ICs]
  [ic_u]
    type = FunctionIC
    variable = u
    function = 'if(x<5.01, 2, 1)'
  []
[]

[AuxVariables]
  [ls]
    order = FIRST
    family = LAGRANGE
  []
[]

[Constraints]
  [u_constraint]
    type = XFEMEqualValueAtInterface
    geometric_cut_userobject = 'cut_mesh'
    use_displaced_mesh = false
    variable = u
    value = 2
    alpha = 1e6
  []
[]

[Kernels]
  [diff]
    type = ADMatDiffusion
    variable = u
    diffusivity = diffusion_coefficient
  []
  [time]
    type = ADTimeDerivative
    variable = u
  []
[]

[AuxKernels]
  [ls]
    type = MeshCutLevelSetAux
    mesh_cut_user_object = cut_mesh
    variable = ls
    execute_on = 'TIMESTEP_BEGIN'
  []
[]

[Materials]
  [diffusivity_A]
    type = ADGenericConstantMaterial
    prop_names = A_diffusion_coefficient
    prop_values = 5
  []
  [diffusivity_B]
    type = ADGenericConstantMaterial
    prop_names = B_diffusion_coefficient
    prop_values = 1
  []
  [diff_combined]
    type = ADLevelSetBiMaterialReal
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = diffusion_coefficient
  []
[]

[BCs]
  # Define boundary conditions
  [left_u]
    type = ADDirichletBC
    variable = u
    value = 2
    boundary = left
  []

  [right_u]
    type = ADNeumannBC
    variable = u
    boundary = right
    value = 0
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = 'none'

  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  start_time = 0.0
  dt = 1
  num_steps = 5
  max_xfem_update = 1
[]

[Outputs]
  file_base = phase_transition_2d_out
  execute_on = timestep_end
  exodus = true
  perf_graph = true
  csv = true
[]

(modules/porous_flow/examples/tutorial/06.i)

# Darcy flow with a tracer
[Mesh]
  [annular]
    type = AnnularMeshGenerator
    nr = 10
    rmin = 1.0
    rmax = 10
    growth_r = 1.4
    nt = 4
    dmin = 0
    dmax = 90
  []
  [make3D]
    type = MeshExtruderGenerator
    extrusion_vector = '0 0 12'
    num_layers = 3
    bottom_sideset = 'bottom'
    top_sideset = 'top'
    input = annular
  []
  [shift_down]
    type = TransformGenerator
    transform = TRANSLATE
    vector_value = '0 0 -6'
    input = make3D
  []
  [aquifer]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 -2'
    top_right = '10 10 2'
    input = shift_down
  []
  [injection_area]
    type = ParsedGenerateSideset
    combinatorial_geometry = 'x*x+y*y<1.01'
    included_subdomain_ids = 1
    new_sideset_name = 'injection_area'
    input = 'aquifer'
  []
  [rename]
    type = RenameBlockGenerator
    old_block = '0 1'
    new_block = 'caps aquifer'
    input = 'injection_area'
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [porepressure]
  []
  [tracer_concentration]
  []
[]

[ICs]
  [tracer_concentration]
    type = FunctionIC
    function = '0.5*if(x*x+y*y<1.01,1,0)'
    variable = tracer_concentration
  []
[]

[PorousFlowFullySaturated]
  porepressure = porepressure
  coupling_type = Hydro
  gravity = '0 0 0'
  fp = the_simple_fluid
  mass_fraction_vars = tracer_concentration
  stabilization = none # Note to reader: 06_KT.i uses KT stabilization - compare the results
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1E6
    boundary = injection_area
  []
  [constant_outer_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 0
    boundary = rmax
  []
  [injected_tracer]
    type = DirichletBC
    variable = tracer_concentration
    value = 0.5
    boundary = injection_area
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      viscosity = 1.0E-3
      density0 = 1000.0
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability_aquifer]
    type = PorousFlowPermeabilityConst
    block = aquifer
    permeability = '1E-14 0 0   0 1E-14 0   0 0 1E-14'
  []
  [permeability_caps]
    type = PorousFlowPermeabilityConst
    block = caps
    permeability = '1E-15 0 0   0 1E-15 0   0 0 1E-16'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1E6
  dt = 1E5
  nl_rel_tol = 1E-14
[]

[Outputs]
  exodus = true
[]

(test/tests/bcs/mat_neumann_bc/mat_neumann.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 10
  ymax = 10
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./phi]
  [../]
[]

[ICs]
  [./phi_IC]
    type = FunctionIC
    variable = phi
    function = ic_func_phi
  [../]
[]

[Functions]
  [./ic_func_phi]
    type = ParsedFunction
    value = '0.5 * (1 - tanh((x - 5) / 0.8))'
  [../]
[]

[BCs]
  [./top]
    type = MatNeumannBC
    variable = u
    boundary = top
    value = 2
    boundary_material = hm
  [../]
[]

[Kernels]
  [./dudt]
    type = TimeDerivative
    variable = u
  [../]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[Materials]
  [./hm]
    type = ParsedMaterial
    f_name = hm
    args = 'phi'
    function = '3*phi^2 - 2*phi^3'
    outputs = exodus
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  end_time = 10
[]

[Outputs]
  exodus = true
[]

(test/tests/restart/restart_subapp_not_master/two_step_solve_master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  active = ''
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./average]
    type = ElementAverageValue
    variable = u
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  start_time = 2.0
  end_time = 4.0
  dt = 1.0
[]

[MultiApps]
  [./full_solve]
    type = FullSolveMultiApp
    execute_on = initial
    positions = '0 0 0'
    # input file will come from cli-args
  [../]
[]

[Transfers]
  [./transfer_u]
    type = MultiAppProjectionTransfer
    multi_app = full_solve
    direction = FROM_MULTIAPP
    variable = u
    source_variable = u
  [../]
[]

[Outputs]
  #file_base will come from cli-args
  exodus = true
[]

(modules/level_set/test/tests/functions/olsson_plane/olsson_plane.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 1
  ymax = 1
  nx = 100
  ny = 100
  elem_type = QUAD9
[]

[AuxVariables/phi]
  family = LAGRANGE
  order = FIRST
[]

[Functions/phi_exact]
  type = LevelSetOlssonPlane
  epsilon = 0.04
  point = '0.5 0.5 0'
  normal = '0 1 0'
[]

[ICs/phi_ic]
  type = FunctionIC
  function = phi_exact
  variable = phi
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/free_energy_material/RegularSolutionFreeEnergy_const_T.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmax = 1
[]

[Variables]
  [./c]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = c
  [../]
[]

[BCs]
  [./left]
    type = FunctionDirichletBC
    variable = c
    boundary = left
    function = x
  [../]
  [./right]
    type = FunctionDirichletBC
    variable = c
    boundary = right
    function = x
  [../]
[]

[Materials]
  [./free_energy]
    type = RegularSolutionFreeEnergy
    f_name = F
    c = c
    outputs = out
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  l_max_its = 1
  nl_max_its = 1
  nl_abs_tol = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  [./out]
    type = Exodus
    execute_on = timestep_end
  [../]
[]

(modules/richards/test/tests/sinks/s01.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1 # same deal with PETScs constant state
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 2
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-lfout-rfout-mf)/2/(mi+mf))
    vars = 'mi mf lfout rfout'
    vals = 'mass_init mass_fin left_flux_out right_flux_out'
  [../]
[]

[Postprocessors]
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]
  [./mass_fin]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]
  [./left_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = left
    variable = pressure
    pressures = '0 1'
    bare_fluxes = '1 2'
    use_mobility = false
    use_relperm = false
  [../]
  [./right_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = right
    variable = pressure
    pressures = '0 1'
    bare_fluxes = '1 2'
    use_mobility = false
    use_relperm = false
  [../]
  [./p0]
    type = PointValue
    point = '0 0 0'
    variable = pressure
  [../]
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]

[BCs]
  [./left_flux]
    type = RichardsPiecewiseLinearSink
    boundary = left
    pressures = '0 1'
    bare_fluxes = '1 2'
    variable = pressure
    use_mobility = false
    use_relperm = false
  [../]
  [./right_flux]
    type = RichardsPiecewiseLinearSink
    boundary = right
    pressures = '0 1'
    bare_fluxes = '1 2'
    variable = pressure
    use_mobility = false
    use_relperm = false
  [../]
[]

[Kernels]
  active = 'richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
[]

[AuxVariables]
  [./one]
    initial_condition = 1
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2E-3
  end_time = 0.2
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s01
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/examples/tidal/atm_tides_open_hole.i)

# A 100m x 10m "slab" of height 100m is subjected to cyclic pressure at its top
# Assumptions:
# the boundaries are impermeable, except the top boundary
# only vertical displacement is allowed
# the atmospheric pressure sets the total stress at the top of the model
# at the slab left-hand side there is a borehole that taps into the base of the slab.
[Mesh]
  [the_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 1
    nz = 10
    xmin = 0
    xmax = 100
    ymin = -5
    ymax = 5
    zmin = -100
    zmax = 0
  []
  [bh_back]
    type = ExtraNodesetGenerator
    coord = '0 -5 -100'
    input = the_mesh
    new_boundary = 11
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  PorousFlowDictator = dictator
  block = 0
  biot_coefficient = 0.6
  multiply_by_density = false
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [porepressure]
    scaling = 1E11
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '-10000*z'  # this is only approximately correct
  []
[]

[Functions]
  [ini_stress_zz]
    type = ParsedFunction
    value = '(25000 - 0.6*10000)*z' # remember this is effective stress
  []
  [cyclic_porepressure]
    type = ParsedFunction
    value = 'if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
  [cyclic_porepressure_at_depth]
    type = ParsedFunction
    value = '-10000*z + if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
  [neg_cyclic_porepressure]
    type = ParsedFunction
    value = '-if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
[]

[BCs]
  # zmin is called 'back'
  # zmax is called 'front'
  # ymin is called 'bottom'
  # ymax is called 'top'
  # xmin is called 'left'
  # xmax is called 'right'
  [no_x_disp]
    type = DirichletBC
    variable = disp_x
    value = 0
    boundary = 'bottom top' # because of 1-element meshing, this fixes u_x=0 everywhere
  []
  [no_y_disp]
    type = DirichletBC
    variable = disp_y
    value = 0
    boundary = 'bottom top' # because of 1-element meshing, this fixes u_y=0 everywhere
  []
  [no_z_disp_at_bottom]
    type = DirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
  [pp]
    type = FunctionDirichletBC
    variable = porepressure
    function = cyclic_porepressure
    boundary = front
  []
  [pp_downhole]
    type = FunctionDirichletBC
    variable = porepressure
    function = cyclic_porepressure_at_depth
    boundary = 11
  []
  [total_stress_at_top]
    type = FunctionNeumannBC
    variable = disp_z
    function = neg_cyclic_porepressure
    boundary = front
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      thermal_expansion = 0.0
      bulk_modulus = 2E9
      viscosity = 1E-3
      density0 = 1000.0
    []
  []
[]

[PorousFlowBasicTHM]
  coupling_type = HydroMechanical
  displacements = 'disp_x disp_y disp_z'
  porepressure = porepressure
  gravity = '0 0 -10'
  fp = the_simple_fluid
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    bulk_modulus = 10.0E9 # drained bulk modulus
    poissons_ratio = 0.25
  []
  [strain]
    type = ComputeSmallStrain
    eigenstrain_names = ini_stress
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [ini_stress]
    type = ComputeEigenstrainFromInitialStress
    initial_stress = '0 0 0  0 0 0  0 0 ini_stress_zz'
    eigenstrain_name = ini_stress
  []
  [porosity]
    type = PorousFlowPorosityConst # only the initial value of this is ever used
    porosity = 0.1
  []
  [biot_modulus]
    type = PorousFlowConstantBiotModulus
    solid_bulk_compliance = 1E-10
    fluid_bulk_modulus = 2E9
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-14 0 0   0 1E-14 0   0 0 1E-14'
  []
  [density]
    type = GenericConstantMaterial
    prop_names = density
    prop_values = 2500.0
  []
[]

[Postprocessors]
  [p0_0]
    type = PointValue
    outputs = csv
    point = '0 0 0'
    variable = porepressure
  []
  [p100_0]
    type = PointValue
    outputs = csv
    point = '100 0 0'
    variable = porepressure
  []
  [p0_100]
    type = PointValue
    outputs = csv
    point = '0 0 -100'
    variable = porepressure
  []
  [p100_100]
    type = PointValue
    outputs = csv
    point = '100 0 -100'
    variable = porepressure
  []
  [uz0]
    type = PointValue
    outputs = csv
    point = '0 0 0'
    variable = disp_z
  []
  [uz100]
    type = PointValue
    outputs = csv
    point = '100 0 0'
    variable = disp_z
  []
[]


[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  start_time = -3600
  dt = 3600
  end_time = 172800
  nl_rel_tol = 1E-10
  nl_abs_tol = 1E-5
[]

[Outputs]
  print_linear_residuals = false
  csv = true
[]

(modules/porous_flow/test/tests/mass_conservation/mass07.i)

# Checking that the mass postprocessor throws the correct error if
# too many phases are supplied

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [sat]
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[ICs]
  [pinit]
    type = ConstantIC
    value = 1
    variable = pp
  []
  [satinit]
    type = FunctionIC
    function = 1-x
    variable = sat
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sat
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp sat'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 0.1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp
    phase1_saturation = sat
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [comp1_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = '0 1 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

(modules/porous_flow/test/tests/capillary_pressure/brooks_corey2.i)

# Test Brooks-Corey capillary pressure curve by varying saturation over the mesh
# lambda = 2, sat_lr = 0.1, log_extension = true

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [p0]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 0
    variable = p0aux
  []
  [p1]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = p1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureBC
    lambda = 2
    log_extension = true
    pe = 1e5
    sat_lr = 0.1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    variable = 's0aux s1aux p0aux p1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 500
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-6
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/jacobian/fflux01_fully_saturated.i)

# 1phase, 3components, constant viscosity, constant insitu permeability
# density with constant bulk, nonzero gravity
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  xmin = 0
  xmax = 1
  ny = 1
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [massfrac0]
  []
  [massfrac1]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = -0.7+x+y
  []
  [massfrac0]
    type = RandomIC
    variable = massfrac0
    min = 0
    max = 0.3
  []
  [massfrac1]
    type = RandomIC
    variable = massfrac1
    min = 0
    max = 0.4
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowFullySaturatedDarcyFlow
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
  []
  [flux1]
    type = PorousFlowFullySaturatedDarcyFlow
    fluid_component = 1
    variable = massfrac0
    gravity = '-1 -0.1 0'
  []
  [flux2]
    type = PorousFlowFullySaturatedDarcyFlow
    fluid_component = 2
    variable = massfrac1
    gravity = '-1 -0.1 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0 massfrac1'
    number_fluid_phases = 1
    number_fluid_components = 3
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      density0 = 1
      thermal_expansion = 0
      viscosity = 1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac0 massfrac1'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0 0 2 0 0 0 3'
  []
[]

[Preconditioning]
  active = check
  [check]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  exodus = false
[]

(modules/porous_flow/test/tests/relperm/corey3.i)

# Test Corey relative permeability curve by varying saturation over the mesh
# Residual saturation of phase 0: s0r = 0.2
# Residual saturation of phase 1: s1r = 0.3

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
    family = LAGRANGE
    order = FIRST
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityCorey
    phase = 0
    n = 2
    s_res = 0.2
    sum_s_res = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
    s_res = 0.3
    sum_s_res = 0.5
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(test/tests/misc/check_error/function_file_test17.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_rows_more_data.csv
    xy_in_file_only = false
    x_index_in_file = 0
    y_index_in_file = 0 # will generate an error because x and y index are equal
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/time_integrators/actually_explicit_euler_verification/ee-1d-quadratic-neumann.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 10
  elem_type = EDGE3
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x*x-2*t+t*x*x
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x*x
  [../]

  [./left_bc_fn]
    type = ParsedFunction
    value = -t*2*x
  [../]
  [./right_bc_fn]
    type = ParsedFunction
    value = t*2*x
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./abs]
    type = Reaction
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./left]
    type = FunctionNeumannBC
    variable = u
    boundary = '0'
    function = left_bc_fn
  [../]

  [./right]
    type = FunctionNeumannBC
    variable = u
    boundary = '1'
    function = right_bc_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  l_tol = 1e-12
  start_time = 0.0
  num_steps = 10
  dt = 0.001

  [./TimeIntegrator]
    type = ActuallyExplicitEuler
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/fluid_properties/test/tests/brine/brine.i)

# Test BrineFluidProperties calculations of density, viscosity and thermal
# conductivity
#
# Experimental density values from Pitzer et al, "Thermodynamic properties
# of aqueous sodium chloride solution", Journal of Physical and Chemical
# Reference Data, 13, 1-102 (1984)
#
# Experimental viscosity values from Phillips et al, "Viscosity of NaCl and
# other solutions up to 350C and 50MPa pressures", LBL-11586 (1980)
#
# Thermal conductivity values from Ozbek and Phillips, "Thermal conductivity of
# aqueous NaCl solutions from 20C to 330C", LBL-9086 (1980)
#
#  --------------------------------------------------------------
#  Pressure (Mpa)                |   20      |    20     |   40
#  Temperature (C)               |   50      |   200     |  200
#  NaCl molality (mol/kg)        |    2      |     2     |    5
#  NaCl mass fraction (kg/kg)    |  0.1047   |  0.1047   |  0.2261
#  --------------------------------------------------------------
#  Expected values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1068.52  |  959.27   |  1065.58
#  Viscosity (1e-6Pa.s)          |  679.8    |  180.0    |  263.1
#  Thermal conductivity (W/m/K)  |  0.630    |  0.649    |  0.633
#  --------------------------------------------------------------
#  Calculated values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1067.18  |  958.68   |  1065.46
#  Viscosity (1e-6 Pa.s)         |  681.1    |  181.98    |  266.1
#  Thermal conductivity (W/m/K)  |  0.637    |   0.662    |  0.658
#  --------------------------------------------------------------
#
# All results are within expected accuracy

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 1
  xmax = 3
  # This test uses ElementalVariableValue postprocessors on specific
  # elements, so element numbering needs to stay unchanged
  allow_renumbering = false
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./pressure]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./temperature]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./xnacl]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./density]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./enthalpy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./internal_energy]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Functions]
  [./pic]
    type = ParsedFunction
    value = 'if(x<2,20e6, 40e6)'
  [../]
  [./tic]
    type = ParsedFunction
    value = 'if(x<1, 323.15, 473.15)'
  [../]
  [./xic]
    type = ParsedFunction
    value = 'if(x<2,0.1047, 0.2261)'
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    function = pic
    variable = pressure
  [../]
  [./t_ic]
    type = FunctionIC
    function = tic
    variable = temperature
  [../]
  [./x_ic]
    type = FunctionIC
    function = xic
    variable = xnacl
  [../]
[]

[AuxKernels]
  [./density]
    type = MaterialRealAux
     variable = density
     property = density
  [../]
  [./enthalpy]
    type = MaterialRealAux
     variable = enthalpy
     property = enthalpy
  [../]
  [./internal_energy]
    type = MaterialRealAux
     variable = internal_energy
     property = e
  [../]
[]

[Modules]
  [./FluidProperties]
    [./brine]
      type = BrineFluidProperties
    [../]
  [../]
[]

[Materials]
  [./fp_mat]
    type = MultiComponentFluidPropertiesMaterialPT
    pressure = pressure
    temperature = temperature
    xmass = xnacl
    fp = brine
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Postprocessors]
  [./density0]
    type = ElementalVariableValue
    variable = density
    elementid = 0
  [../]
  [./density1]
    type = ElementalVariableValue
    variable = density
    elementid = 1
  [../]
  [./density2]
    type = ElementalVariableValue
    variable = density
    elementid = 2
  [../]
  [./enthalpy0]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 0
  [../]
  [./enthalpy1]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 1
  [../]
  [./enthalpy2]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 2
  [../]
  [./e0]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 0
  [../]
  [./e1]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 1
  [../]
  [./e2]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 2
  [../]
[]

[Outputs]
  csv = true
[]

(modules/richards/test/tests/theis/th02.i)

# fully-saturated
# production
[Mesh]
  type = FileMesh
  file = th02_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1 2 4 20'
    x = '0 1 10 100'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]

  [./total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsPolyLineSink
    pressures = '-1E9 1E9'
    fluxes = '200 200'
    point_file = th01.points
    SumQuantityUO = total_outflow_mass
    variable = pressure
  [../]
[]


[Postprocessors]
  [./flow_report]
    type = RichardsPlotQuantity
    uo = total_outflow_mass
  [../]
  [./p50]
    type = PointValue
    variable = pressure
    point = '50 0 0'
    execute_on = 'initial timestep_end'
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E5
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-6 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 100
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  file_base = th02
  csv = true
[]

(test/tests/transfers/multiapp_vector_pp_transfer/master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 1
  ymax = 2
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./v]
    [./InitialCondition]
      type = FunctionIC
      function = set_v
    [../]
  [../]
[]

[Functions]
  [./set_v]
    type = ParsedFunction
    value = 'x + 2 * y'
  [../]
[]

[VectorPostprocessors]
  [./sample_points]
    type = PointValueSampler
    variable = v
    points = '0.25 1.25 0 0.5 1.5 0'
    sort_by = x
    execute_on = 'initial timestep_end'
  [../]

  [./receive_values]
    type = PointValueSampler
    variable = v
    points = '0.25 1.25 0 0.5 1.5 0'
    sort_by = x
    execute_on = initial
  [../]
[]

[MultiApps]
  [./sub]
    type = TransientMultiApp
    input_files = 'sub.i'
    positions = '0.25 1.25 0 0.5 1.5 0'
    max_procs_per_app = 1
  [../]
[]

[Transfers]
  [./send]
    type = MultiAppVectorPostprocessorTransfer
    vector_postprocessor = sample_points
    postprocessor = receive
    vector_name = v
    to_multi_app = sub
  [../]

  [./receive]
    type = MultiAppVectorPostprocessorTransfer
    vector_postprocessor = receive_values
    postprocessor = send
    vector_name = v
    from_multi_app = sub
  [../]
[]

[Executioner]
  type = Transient
  nl_abs_tol = 1e-10
  num_steps = 1
[]

[Outputs]
  csv = true
[]

(test/tests/materials/functor_properties/gradients/functor-gradients.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 4
  xmax = 2
[]

[Variables]
  [u]
    type = MooseVariableFVReal
  []
[]

[AuxVariables]
  [sink]
    type = MooseVariableFVReal
  []
  [diffusive_flux_x]
    type = MooseVariableFVReal
  []
  [diffusive_flux_y]
    type = MooseVariableFVReal
  []
  [diffusive_flux_magnitude]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [sink]
    type = FunctionIC
    variable = sink
    function = 'x^3'
  []
[]


[FVKernels]
  [diff]
    type = FVDiffusion
    variable = u
    coeff = 1.1
  []
  [sink]
    type = FVFunctorElementalKernel
    variable = u
    functor_name = 'sink_mat'
  []
[]

[FVBCs]
  [bounds]
    type = FVDirichletBC
    variable = u
    boundary = 'left right top bottom'
    value = 0
  []
[]

[Materials]
  [functor_properties]
    type = ADGenericFunctorMaterial
    prop_names = 'sink_mat diffusive_coef'
    prop_values = 'sink 4.5'
  []
  [gradient_of_u]
    type = ADGenericFunctorGradientMaterial
    prop_names = 'grad_u'
    prop_values = 'u'
  []
[]

# Compute the diffusive flux magnitude
[AuxKernels]
  [diffusive_flux_x]
    type = ADFunctorVectorElementalAux
    variable = 'diffusive_flux_x'
    functor = 'grad_u'
    factor = 'diffusive_coef'
    component = 0
  []
  [diffusive_flux_y]
    type = ADFunctorVectorElementalAux
    variable = 'diffusive_flux_y'
    functor = 'grad_u'
    factor = 'diffusive_coef'
    component = 1
  []
  [diffusive_flux_magnitude]
    type = VectorMagnitudeAux
    variable = 'diffusive_flux_magnitude'
    x = 'diffusive_flux_x'
    y = 'diffusive_flux_y'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/poroperm/except2.i)

# Exception test: fluid=true but no solid_bulk is provided
[Mesh]
  type = GeneratedMesh
  dim = 3
[]

[GlobalParams]
  PorousFlowDictator = dictator
  displacements = 'disp_x disp_y disp_z'
  biot_coefficient = 0.7
[]

[Variables]
  [porepressure]
    initial_condition = 2
  []
  [temperature]
    initial_condition = 4
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[ICs]
  [disp_x]
    type = FunctionIC
    function = '0.5 * x'
    variable = disp_x
  []
[]

[Kernels]
  [dummy_p]
    type = TimeDerivative
    variable = porepressure
  []
  [dummy_t]
    type = TimeDerivative
    variable = temperature
  []
  [dummy_x]
    type = TimeDerivative
    variable = disp_x
  []
  [dummy_y]
    type = TimeDerivative
    variable = disp_y
  []
  [dummy_z]
    type = TimeDerivative
    variable = disp_z
  []
[]

[AuxVariables]
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [porosity]
    type = PorousFlowPropertyAux
    property = porosity
    variable = porosity
  []
[]

[Postprocessors]
  [porosity]
    type = PointValue
    variable = porosity
    point = '0 0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure temperature'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [eff_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [vol_strain]
    type = PorousFlowVolumetricStrain
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [porosity]
    type = PorousFlowPorosity
    mechanical = true
    fluid = true
    thermal = true
    ensure_positive = false
    porosity_zero = 0.5
    thermal_expansion_coeff = 0.5
    reference_porepressure = 3
    reference_temperature = 3.5
  []
[]

[Executioner]
  solve_type = Newton
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/phase_field_fracture/crack2d_vi_solver.i)

#This input uses PhaseField-Nonconserved Action to add phase field fracture bulk rate kernels
[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 20
    xmax = 1
    ymax = 1
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Modules]
  [./PhaseField]
    [./Nonconserved]
      [./c]
        free_energy = F
        kappa = kappa_op
        mobility = L
      [../]
    [../]
  [../]
  [./TensorMechanics]
    [./Master]
      [./mech]
        add_variables = true
        strain = SMALL
        additional_generate_output = 'stress_yy'
        save_in = 'resid_x resid_y'
      [../]
    [../]
  [../]
[]

[ICs]
  [./c_ic]
    type = FunctionIC
    function = ic
    variable = c
  [../]
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 'if(x<0.5 & y < 0.55 & y > 0.45,1, 0)'
  [../]
[]

[AuxVariables]
  [./resid_x]
  [../]
  [./resid_y]
  [../]
  [./bounds_dummy]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./solid_x]
    type = PhaseFieldFractureMechanicsOffDiag
    variable = disp_x
    component = 0
    c = c
  [../]
  [./solid_y]
    type = PhaseFieldFractureMechanicsOffDiag
    variable = disp_y
    component = 1
    c = c
  [../]
[]

[BCs]
  [./ydisp]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = top
    function = 't'
  [../]
  [./yfix]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
  [./xfix]
    type = DirichletBC
    variable = disp_x
    boundary = 'top bottom'
    value = 0
  [../]
[]

[Materials]
  [./pfbulkmat]
    type = GenericConstantMaterial
    prop_names = 'gc_prop l visco'
    prop_values = '1e-3 0.04 1e-4'
  [../]
  [./define_mobility]
    type = ParsedMaterial
    material_property_names = 'gc_prop visco'
    f_name = L
    function = '1.0/(gc_prop * visco)'
  [../]
  [./define_kappa]
    type = ParsedMaterial
    material_property_names = 'gc_prop l'
    f_name = kappa_op
    function = 'gc_prop * l'
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '120.0 80.0'
    fill_method = symmetric_isotropic
  [../]
  [./damage_stress]
    type = ComputeLinearElasticPFFractureStress
    c = c
    E_name = 'elastic_energy'
    D_name = 'degradation'
    F_name = 'local_fracture_energy'
    decomposition_type = strain_spectral
    use_snes_vi_solver = true
  [../]
  [./degradation]
    type = DerivativeParsedMaterial
    f_name = degradation
    args = 'c'
    function = '(1.0-c)^2*(1.0 - eta) + eta'
    constant_names       = 'eta'
    constant_expressions = '0.0'
    derivative_order = 2
  [../]
  [./local_fracture_energy]
    type = DerivativeParsedMaterial
    f_name = local_fracture_energy
    args = 'c'
    material_property_names = 'gc_prop l'
    function = 'c^2 * gc_prop / 2 / l'
    derivative_order = 2
  [../]
  [./fracture_driving_energy]
    type = DerivativeSumMaterial
    args = c
    sum_materials = 'elastic_energy local_fracture_energy'
    derivative_order = 2
    f_name = F
  [../]
[]

[Postprocessors]
  [./resid_x]
    type = NodalSum
    variable = resid_x
    boundary = 2
  [../]
  [./resid_y]
    type = NodalSum
    variable = resid_y
    boundary = 2
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Bounds]
  [./c_upper_bound]
    type = ConstantBoundsAux
    variable = bounds_dummy
    bounded_variable = c
    bound_type = upper
    bound_value = 1.0
  [../]
  [./c_lower_bound]
    type = VariableOldValueBoundsAux
    variable = bounds_dummy
    bounded_variable = c
    bound_type = lower
  [../]
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  petsc_options_iname = '-pc_type  -snes_type'
  petsc_options_value = 'lu vinewtonrsls'

  nl_rel_tol = 1e-8
  l_max_its = 10
  nl_max_its = 10

  dt = 1e-4
  dtmin = 1e-4
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/jacobian/offdiag.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./s]
    [./InitialCondition]
      type = FunctionIC
      function = sin(10*x+y)
    [../]
  [../]
  [./t]
    [./InitialCondition]
      type = FunctionIC
      function = sin(13*y+x)
    [../]
  [../]
[]

[Kernels]
  [./diffs]
    type = WrongJacobianDiffusion
    variable = s
    coupled = t
  [../]
  [./difft]
    type = WrongJacobianDiffusion
    variable = t
    coupled = s
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

(modules/porous_flow/test/tests/energy_conservation/except01.i)

# checking that the heat-energy postprocessor throws the correct error if the phase number is entered incorrectly
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 3
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [temp]
  []
[]

[ICs]
  [tinit]
    type = FunctionIC
    function = '100*x'
    variable = temp
  []
  [pinit]
    type = FunctionIC
    function = x
    variable = pp
  []
[]

[Kernels]
  [dummyt]
    type = TimeDerivative
    variable = temp
  []
  [dummyp]
    type = TimeDerivative
    variable = pp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      viscosity = 0.001
      thermal_expansion = 0
      cv = 1.3
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 2.2
    density = 0.5
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
[]

[Postprocessors]
  [total_heat]
    type = PorousFlowHeatEnergy
    phase = 1
  []
  [rock_heat]
    type = PorousFlowHeatEnergy
  []
  [fluid_heat]
    type = PorousFlowHeatEnergy
    include_porous_skeleton = false
    phase = 0
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = except01
  csv = true
[]

(test/tests/functions/solution_function/solution_function_scale_transl.i)

# checking scale and translation, with ordering scale first, then translation second
[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = -1
  xmax = 1
  nx = 3
  ymin = -1
  ymax = 1
  ny = 3
  zmin = -1
  zmax = 1
  nz = 3
[]

[UserObjects]
  [./solution_uo]
    type = SolutionUserObject
    mesh = cube_with_u_equals_x.e
    timestep = 1
    system_variables = u
    scale = '0.5 1 1'
    translation = '2 0 0'
    transformation_order = 'scale translation'
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = solution_fcn
  [../]
[]

[Functions]
  [./solution_fcn]
    type = SolutionFunction
    from_variable = u
    solution = solution_uo
  [../]
[]

[Kernels]
  [./diff]
    type = TimeDerivative
    variable = u
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  l_max_its = 800
  nl_rel_tol = 1e-10
  num_steps = 1
  end_time = 1
  dt = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = solution_function_scale_transl
  exodus = true
[]

(test/tests/time_steppers/function_dt/function_dt_min.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]

  [./dts]
    type = PiecewiseLinear
    x = '0   0.85 2'
    y = '0.2 0.2  0.2'
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  start_time = 0
  num_steps = 10
  [./TimeStepper]
    type = FunctionDT
    function = dts
    min_dt = 0.1
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/function_file_test1.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_columns.csv #Will generate error because data is expected in rows
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/level_set/examples/vortex/vortex_supg.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 1
  ymax = 1
  nx = 16
  ny = 16
  uniform_refine = 2
  elem_type = QUAD9
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[AuxKernels]
  [./vec]
    type = VectorFunctionAux
    variable = velocity
    function = velocity_func
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Variables]
  [./phi]
    family = LAGRANGE
    order = FIRST
  [../]
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.01184
    center = '0.5 0.75 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = LevelSetOlssonVortex
    reverse_time = 2
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
  [./advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = phi
  [../]
  [./time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 2
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/porous_flow/examples/groundwater/ex02_steady_state.i)

# Steady-state groundwater model.  See groundwater_models.md for a detailed description
[Mesh]
  [basic_mesh]
    # mesh create by external program: lies within -500<=x<=500 and -200<=y<=200, with varying z
    type = FileMeshGenerator
    file = ex02_mesh.e
  []
  [name_blocks]
    type = RenameBlockGenerator
    input = basic_mesh
    old_block = '2 3 4'
    new_block = 'bot_aquifer aquitard top_aquifer'
  []
  [zmax]
    type = SideSetsFromNormalsGenerator
    input = name_blocks
    new_boundary = zmax
    normals = '0 0 1'
  []
  [xmin_bot_aquifer]
    type = ParsedGenerateSideset
    input = zmax
    included_subdomain_ids = 2
    normal = '-1 0 0'
    combinatorial_geometry = 'x <= -500.0'
    new_sideset_name = xmin_bot_aquifer
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = initial_pp
  []
[]

[BCs]
  [rainfall_recharge]
    type = PorousFlowSink
    boundary = zmax
    variable = pp
    flux_function = -1E-6  # recharge of 0.1mm/day = 1E-4m3/m2/day = 0.1kg/m2/day ~ 1E-6kg/m2/s
  []
  [evapotranspiration]
    type = PorousFlowHalfCubicSink
    boundary = zmax
    variable = pp
    center = 0.0
    cutoff = -5E4 # roots of depth 5m.  5m of water = 5E4 Pa
    use_mobility = true
    fluid_phase = 0
    # Assume pan evaporation of 4mm/day = 4E-3m3/m2/day = 4kg/m2/day ~ 4E-5kg/m2/s
    # Assume that if permeability was 1E-10m^2 and water table at topography then ET acts as pan strength
    # Because use_mobility = true, then 4E-5 = maximum_flux = max * perm * density / visc = max * 1E-4, so max = 40
    max = 40
  []
[]

[DiracKernels]
  [river]
    type = PorousFlowPolyLineSink
    SumQuantityUO = baseflow
    point_file = ex02_river.bh
    # Assume a perennial river.
    # Assume the river has an incision depth of 1m and a stage height of 1.5m, and these are constant in time and uniform over the whole model.  Hence, if groundwater head is 0.5m (5000Pa) there will be no baseflow and leakage.
    p_or_t_vals = '-999995000 5000 1000005000'
    # Assume the riverbed conductance, k_zz*density*river_segment_length*river_width/riverbed_thickness/viscosity = 1E-6*river_segment_length kg/Pa/s
    fluxes = '-1E3 0 1E3'
    variable = pp
  []
[]

[Functions]
  [initial_pp]
    type = SolutionFunction
    scale_factor = 1E4
    from_variable = cosflow_depth
    solution = initial_mesh
  []
  [baseflow_rate]
    type = ParsedFunction
    vars = 'baseflow_kg dt'
    vals = 'baseflow_kg dt'
    value = 'baseflow_kg / dt * 24.0 * 3600.0 / 400.0'
  []
[]

[PorousFlowUnsaturated]
  fp = simple_fluid
  porepressure = pp
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [porosity_everywhere]
    type = PorousFlowPorosityConst
    porosity = 0.05
  []
  [permeability_aquifers]
    type = PorousFlowPermeabilityConst
    block = 'top_aquifer bot_aquifer'
    permeability = '1E-12 0 0 0 1E-12 0 0 0 1E-13'
  []
  [permeability_aquitard]
    type = PorousFlowPermeabilityConst
    block = aquitard
    permeability = '1E-16 0 0 0 1E-16 0 0 0 1E-17'
  []
[]

[UserObjects]
  [initial_mesh]
    type = SolutionUserObject
    execute_on = INITIAL
    mesh = ex02_mesh.e
    timestep = LATEST
    system_variables = cosflow_depth
  []
  [baseflow]
    type = PorousFlowSumQuantity
  []
[]

[Postprocessors]
  [baseflow_kg]
    type = PorousFlowPlotQuantity
    uo = baseflow
    outputs = 'none'
  []
  [dt]
    type = TimestepSize
    outputs = 'none'
  []
  [baseflow_l_per_m_per_day]
    type = FunctionValuePostprocessor
    function = baseflow_rate
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    # following 2 lines are not mandatory, but illustrate a popular preconditioner choice in groundwater models
    petsc_options_iname = '-pc_type -sub_pc_type  -pc_asm_overlap'
    petsc_options_value = ' asm      ilu           2              '
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E6
  [TimeStepper]
    type = FunctionDT
    function = 'max(1E6, t)'
  []
  end_time = 1E12
  nl_abs_tol = 1E-13
[]

[Outputs]
  print_linear_residuals = false
  [ex]
    type = Exodus
    execute_on = final
  []
  [csv]
    type = CSV
  []
[]

(test/tests/postprocessors/displaced_mesh/side.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  displacements = 'ux uy'
[]

[AuxVariables]
  [./ux]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
  [./uy]
    [./InitialCondition]
      type = FunctionIC
      function = y
    [../]
  [../]
  [./c]
    initial_condition = 1
  [../]
[]

[Variables]
  [./a]
  [../]
[]
[Kernels]
  [./a]
    type = Diffusion
    variable = a
  [../]
[]

[Postprocessors]
  [./without]
    type = SideIntegralVariablePostprocessor
    variable = c
    execute_on = initial
    boundary = left
  [../]
  [./with]
    type = SideIntegralVariablePostprocessor
    variable = c
    use_displaced_mesh = true
    execute_on = initial
    boundary = left
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 0
[]

[Outputs]
  [./out]
    type = Exodus
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/pins/mms/porosity_change/2d-rc-continuous.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = -1
    ymax = 1
    nx = 8
    ny = 8
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = u
    v = v
    porosity = porosity
    pressure = pressure
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []
[]

[ICs]
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    function = smooth_jump
  []
[]

[GlobalParams]
  porosity = porosity
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
  [u_forcing]
    type = INSFVBodyForce
    variable = u
    functor = forcing_u
    momentum_component = 'x'
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    pressure = pressure
    porosity = porosity
    momentum_component = 'y'
  []
  [v_forcing]
    type = INSFVBodyForce
    variable = v
    functor = forcing_v
    momentum_component = 'y'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 'exact_v'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1))) - 0.01 * y'
  []

  # Output from compute-functions-2d.py
  [exact_u]
    type = ParsedFunction
    value = 'sin((1/2)*y*pi)*cos((1/2)*x*pi)'
  []
  [forcing_u]
    type = ADParsedFunction
    value = '15.0*mu*(-1/2*pi*sin((1/2)*x*pi)*sin((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 15.0*exp(30 - 30*x)*sin((1/2)*y*pi)*cos((1/2)*x*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2))*exp(30 - 30*x)/(exp(30 - 30*x) + 1)^2 + 0.01*mu*((1/2)*pi*cos((1/2)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.01*sin((1/2)*y*pi)*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) - mu*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*(-1/4*pi^2*sin((1/2)*y*pi)*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.01*pi*cos((1/2)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 + 0.0002*sin((1/2)*y*pi)*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^3) - mu*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*(-1/4*pi^2*sin((1/2)*y*pi)*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - 15.0*pi*exp(30 - 30*x)*sin((1/2)*x*pi)*sin((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) - 450.0*exp(30 - 30*x)*sin((1/2)*y*pi)*cos((1/2)*x*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + 900.0*exp(60 - 60*x)*sin((1/2)*y*pi)*cos((1/2)*x*pi)/((exp(30 - 30*x) + 1)^3*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + 450.0*exp(60 - 60*x)*sin((1/2)*y*pi)*cos((1/2)*x*pi)/((exp(30 - 30*x) + 1)^4*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^3)) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + (1/2)*pi*rho*sin((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)^2/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.01*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 + 15.0*rho*exp(30 - 30*x)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi)^2/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) - 1/4*pi*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*sin((1/4)*x*pi)*sin((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    value = 'sin((1/4)*x*pi)*cos((1/2)*y*pi)'
  []
  [forcing_v]
    type = ADParsedFunction
    value = '0.01*mu*(-1/2*pi*sin((1/4)*x*pi)*sin((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.01*sin((1/4)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + 15.0*mu*((1/4)*pi*cos((1/4)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 15.0*exp(30 - 30*x)*sin((1/4)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2))*exp(30 - 30*x)/(exp(30 - 30*x) + 1)^2 - mu*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*(-1/4*pi^2*sin((1/4)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - 0.01*pi*sin((1/4)*x*pi)*sin((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 + 0.0002*sin((1/4)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^3) - mu*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*(-1/16*pi^2*sin((1/4)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - 450.0*exp(30 - 30*x)*sin((1/4)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + 7.5*pi*exp(30 - 30*x)*cos((1/4)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + 900.0*exp(60 - 60*x)*sin((1/4)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^3*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + 450.0*exp(60 - 60*x)*sin((1/4)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^4*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^3)) - pi*rho*sin((1/4)*x*pi)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + (1/4)*pi*rho*sin((1/2)*y*pi)*cos((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.01*rho*sin((1/4)*x*pi)^2*cos((1/2)*y*pi)^2/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 + 15.0*rho*exp(30 - 30*x)*sin((1/4)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + (3/2)*pi*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*cos((1/4)*x*pi)*cos((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin((3/2)*y*pi)*cos((1/4)*x*pi)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi) - 1/2*pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/porous_flow/test/tests/dirackernels/pls03_action.i)

# Test that the upwinding works correctly.
#
# A poly-line sink sits at the centre of the element.
# It has length=4 and weight=0.5, and extracts fluid
# at a constant rate of
# (1 * relative_permeability) kg.m^-1.s^-1
# Since it sits at the centre of the element, it extracts
# equally from each node, so the rate of extraction from
# each node is
# (0.5 * relative_permeability) kg.s^-1
# including the length and weight effects.
#
# There is no fluid flow.
#
# The initial conditions are such that all nodes have
# relative_permeability=0, except for one which has
# relative_permeaility = 1.  Therefore, all nodes should
# remain at their initial porepressure, except the one.
#
# The porosity is 0.1, and the elemental volume is 2,
# so the fluid mass at the node in question = 0.2 * density / 4,
# where the 4 is the number of nodes in the element.
# In this simulation density = dens0 * exp(P / bulk), with
# dens0 = 100, and bulk = 20 MPa.
# The initial porepressure P0 = 10 MPa, so the final (after
# 1 second of simulation) is
# P(t=1) = 8.748592 MPa
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 2
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      thermal_expansion = 0.0
      bulk_modulus = 2.0E7
      viscosity = 1.0
      density0 = 100.0
    []
  []
[]

[PorousFlowUnsaturated]
  porepressure = pp
  gravity = '0 0 0'
  fp = the_simple_fluid
  van_genuchten_alpha = 1.0E-7
  van_genuchten_m = 0.5
  relative_permeability_exponent = 2
  residual_saturation = 0.99
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    #function = if((x<1)&(y<0.5),1E7,-1E7)
    function = if((x<1)&(y>0.5),1E7,-1E7)
    #function = if((x>1)&(y<0.5),1E7,-1E7)
    #function = if((x>1)&(y>0.5),1E7,-1E7)
  []
[]

[UserObjects]
  [pls_total_outflow_mass]
    type = PorousFlowSumQuantity
  []
[]

[Materials]
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '0 0 0  0 0 0  0 0 0'
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]


[DiracKernels]
  [pls]
    type = PorousFlowPolyLineSink
    fluid_phase = 0
    point_file = pls03.bh
    use_relative_permeability = true
    line_length = 4
    SumQuantityUO = pls_total_outflow_mass
    variable = pp
    p_or_t_vals = '0 1E7'
    fluxes = '1 1'
  []
[]


[Postprocessors]
  [pls_report]
    type = PorousFlowPlotQuantity
    uo = pls_total_outflow_mass
  []

  [fluid_mass0]
    type = PorousFlowFluidMass
    execute_on = timestep_begin
  []

  [fluid_mass1]
    type = PorousFlowFluidMass
    execute_on = timestep_end
  []

  [zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  []

  [p00]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = timestep_end
  []
  [p01]
    type = PointValue
    variable = pp
    point = '0 1 0'
    execute_on = timestep_end
  []
  [p20]
    type = PointValue
    variable = pp
    point = '2 0 0'
    execute_on = timestep_end
  []
  [p21]
    type = PointValue
    variable = pp
    point = '2 1 0'
    execute_on = timestep_end
  []
[]


[Functions]
  [mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 pls_report'
  []
[]

[Preconditioning]
  [usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  []
[]


[Executioner]
  type = Transient
  end_time = 1
  dt = 1
  solve_type = NEWTON
[]

[Outputs]
  file_base = pls03_action
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(test/tests/time_integrators/explicit-euler/ee-2d-quadratic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD9
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = ((x*x)+(y*y))-(4*t)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*((x*x)+(y*y))
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[BCs]
  active = 'all'

  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
    implicit = true
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'explicit-euler'
  solve_type = 'LINEAR'

  l_tol = 1e-13
  start_time = 0.0
  num_steps = 20
  dt = 0.00005
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/porous_flow/test/tests/relperm/brooks_corey1.i)

# Test Brooks-Corey relative permeability curve by varying saturation over the mesh
# Exponent lambda = 2 for both phases

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityBC
    phase = 0
    lambda = 2
  []
  [kr1]
    type = PorousFlowRelativePermeabilityBC
    phase = 1
    lambda = 2
    nw_phase = true
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(test/tests/time_integrators/actually_explicit_euler_verification/ee-2d-quadratic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD9
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = ((x*x)+(y*y))-(4*t)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*((x*x)+(y*y))
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    preset = false
    boundary = '0 1 2 3'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  l_tol = 1e-13
  start_time = 0.0
  num_steps = 20
  dt = 0.00005

  [./TimeIntegrator]
    type = ActuallyExplicitEuler
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(test/tests/nodalkernels/constraint_enforcement/upper-and-lower-bound.i)

l=10
nx=100
num_steps=10

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
  [lm_upper]
  []
  [lm_lower]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[NodalKernels]
  [upper_bound]
    type = UpperBoundNodalKernel
    variable = lm_upper
    v = u
    exclude_boundaries = 'left right'
    upper_bound = 10
  []
  [forces_from_upper]
    type = CoupledForceNodalKernel
    variable = u
    v = lm_upper
    coef = -1
  []
  [lower_bound]
    type = LowerBoundNodalKernel
    variable = lm_lower
    v = u
    exclude_boundaries = 'left right'
    lower_bound = 0
  []
  [forces_from_lower]
    type = CoupledForceNodalKernel
    variable = u
    v = lm_lower
    coef = 1
  []
[]


[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type'
  petsc_options_value = '0                           30          asm      16                    basic'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [active_upper_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm_upper
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
    comparator = 'greater'
  []
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [active_lower_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm_lower
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

(modules/tensor_mechanics/test/tests/cohesive_zone_model/bilinear_mixed_scale_strength.i)

[Mesh]
  [msh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 2
    nx = 5
    ny = 10
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    input = 'msh'
    bottom_left = '0 0 0'
    top_right = '1 1 0'
    block_id = 1
    block_name = 'block1'
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    input = 'block1'
    bottom_left = '0 1 0'
    top_right = '1 2 0'
    block_id = 2
    block_name = 'block2'
  []
  [split]
    type = BreakMeshByBlockGenerator
    input = block2
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = split
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '0 0 0'
    input = top_node
    new_boundary = bottom_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Modules]
  [TensorMechanics]
    [Master]
      generate_output = 'stress_yy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
        save_in = 'resid_x resid_y'
      []
    []
  []
[]

[ICs]
  [scale_factor]
    type = FunctionIC
    variable = scale_factor
    function = 'if(x<0.5,1,100)'
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []

  [fix_top]
    type = DirichletBC
    preset = true
    boundary = top
    variable = disp_x
    value = 0
  []

  [top]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []

  [bottom]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
    preset = true
  []
[]

[AuxVariables]
  [resid_x]
  []
  [resid_y]
  []
  [mode_mixity_ratio]
    order = CONSTANT
    family = MONOMIAL
  []
  [damage]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_displacement_at_full_degradation]
    order = CONSTANT
    family = MONOMIAL
  []
  [maximum_mixed_mode_relative_displacement]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_displacement_at_damage_initiation]
    order = CONSTANT
    family = MONOMIAL
  []
  [scale_factor]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [mode_mixity_ratio]
    type = MaterialRealAux
    variable = mode_mixity_ratio
    property = mode_mixity_ratio
    execute_on = timestep_end
    boundary = interface
  []
  [damage]
    type = MaterialRealAux
    variable = damage
    property = damage
    execute_on = timestep_end
    boundary = interface
  []
  [effective_displacement_at_damage_initiation]
    type = MaterialRealAux
    variable = effective_displacement_at_damage_initiation
    property = effective_displacement_at_damage_initiation
    execute_on = timestep_end
    boundary = interface
  []
  [effective_displacement_at_full_degradation]
    type = MaterialRealAux
    variable = effective_displacement_at_full_degradation
    property = effective_displacement_at_full_degradation
    execute_on = timestep_end
    boundary = interface
  []
  [maximum_mixed_mode_relative_displacement]
    type = MaterialRealAux
    variable = maximum_mixed_mode_relative_displacement
    property = maximum_mixed_mode_relative_displacement
    execute_on = timestep_end
    boundary = interface
  []
[]

[Modules/TensorMechanics/CohesiveZoneMaster]
  [czm_ik]
    boundary = 'interface'
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  []
  [czm]
    type = BiLinearMixedModeTraction
    boundary = 'interface'
    penalty_stiffness = 1e6
    GI_C = 1e3
    GII_C = 1e2
    normal_strength = 1e4
    shear_strength = 1e3
    displacements = 'disp_x disp_y'
    eta = 2.2
    viscosity = 1e-3
    normal_strength_scale_factor = scale_factor
  []
[]

[Postprocessors]
  [resid_x]
    type = NodalSum
    variable = resid_x
    boundary = top
  []
  [resid_y]
    type = NodalSum
    variable = resid_y
    boundary = top
  []
  [disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
  []
  [disp_x]
    type = SideAverageValue
    variable = disp_x
    boundary = top
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  automatic_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  start_time = 0.0
  dt = 0.01
  end_time = 0.05
  dtmin = 0.01
[]

[Outputs]
  csv = true
  exodus = true
[]

(test/tests/ics/function_ic/parsed_function.i)

#
# Test the automatically generated gradients in ParsedFunction and the gradient pass-through in FunctionIC
# OLD MOOSE behavior was for parsed_function to behave the same as parsed_zerograd_function
# NEW MOOSE behavior is for parsed_function to behave the same as parsed_grad_function
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 3.141
  ymin = 0
  ymax = 3.141
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Functions]
  [./parsed_function]
    type = ParsedFunction
    value = 'sin(x)-cos(y/2)'
  [../]
  [./parsed_grad_function]
    type =ParsedGradFunction
    value = 'sin(x)-cos(y/2)'
    grad_x = 'cos(x)'
    grad_y = 'sin(y/2)/2'
  [../]
  [./parsed_zerograd_function]
    type = ParsedGradFunction
    value = 'sin(x)-cos(y/2)'
    grad_x = '0'
    grad_y = '0'
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = 'u'
    function = parsed_function
  [../]
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[]

[Outputs]
  file_base = parsed
  [./OverSampling]
    type = Exodus
    refinements = 3
  [../]
[]

(modules/porous_flow/test/tests/mass_conservation/mass10.i)

# Checking that the mass postprocessor throws the correct error when kernel_variable_numer is illegal

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [sat]
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[ICs]
  [pinit]
    type = ConstantIC
    value = 1
    variable = pp
  []
  [satinit]
    type = FunctionIC
    function = 1-x
    variable = sat
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sat
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp sat'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 0.1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp
    phase1_saturation = sat
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [comp1_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    kernel_variable_number = 2
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

(modules/geochemistry/test/tests/kernels/dispersion_1.i)

# Dispersion of a step-function front of concentration
# The initial condition is such that the theoretical result is exactly
# c = erf(x/sqrt(4*t*D)), where D = hydrodynamic_dispersion
#
# The finite mesh resolution and large time-step size means this is only achieved approximately (increasing nx and decreasing results in the error decreasing, but note the series approximation to the error function means that the error should never be exactly zero)

por = 2.0 # this is the porosity.  The result should not depend on por in this example since it appears in both terms of the PDE
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -5
  xmax = 5
[]

[Variables]
  [conc]
  []
[]

[ICs]
  [spike]
    type = FunctionIC
    variable = conc
    function = 'if(x<=0.0, -1.0, 1.0)'
  []
[]

[Kernels]
  [dot]
    type = GeochemistryTimeDerivative
    porosity = ${por}
    variable = conc
  []
  [disp]
    type = GeochemistryDispersion
    variable = conc
    porosity = ${por}
    tensor_coeff = '0.3 0 0  0 0 0  0 0 0'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.5
  end_time = 1.0
[]

[AuxVariables]
  [expected]
  []
  [should_be_zero]
  []
[]

[AuxKernels]
  [expected]
    type = FunctionAux
    variable = expected
    function = erf
  []
  [should_be_zero]
    type = ParsedAux
    args = 'expected conc'
    function = 'expected - conc'
    variable = should_be_zero
  []
[]

[Postprocessors]
  [error]
    type = ElementL2Norm
    variable = should_be_zero
  []
[]

[Functions]
  [erf]
    type = ParsedFunction
    # series expansion for evaluating the error function
    value = 'xi := x / sqrt(4 * t * 0.3); expxi := exp(-xi * xi); if(x < 0.0, -1.0, if(x > 0.0, 1.0, 0.0)) * 2 / sqrt(pi) * sqrt(1 - expxi) * (sqrt(pi) / 2.0 + 31.0 * expxi / 200.0 - 341.0 * expxi * expxi / 8000.0)'
  []
[]

[Outputs]
  exodus = true
  execute_on = final
[]

(modules/combined/test/tests/DiffuseCreep/strain.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.1*v'
    [../]
  [../]
  [./mu]
  [../]
  [./jx]
  [../]
  [./jy]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./creep_strain_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./creep_strain_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./creep_strain_xy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = mu_prop
    c = c
  [../]
  [./flux_x]
    type = CHSplitFlux
    variable = jx
    component = 0
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./flux_y]
    type = CHSplitFlux
    variable = jy
    component = 1
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./creep_strain_xx]
    type = RankTwoAux
    variable = creep_strain_xx
    rank_two_tensor = creep_strain
    index_i = 0
    index_j = 0
  [../]
  [./creep_strain_yy]
    type = RankTwoAux
    variable = creep_strain_yy
    rank_two_tensor = creep_strain
    index_i = 1
    index_j = 1
  [../]
  [./creep_strain_xy]
    type = RankTwoAux
    variable = creep_strain_xy
    rank_two_tensor = creep_strain
    index_i = 0
    index_j = 1
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
  [./diffuse_strain_increment]
    type = FluxBasedStrainIncrement
    xflux = jx
    yflux = jy
    gb = gb
    property_name = diffuse
  [../]
  [./diffuse_creep_strain]
    type = SumTensorIncrements
    tensor_name = creep_strain
    coupled_tensor_increment_names = diffuse
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  nl_max_its = 5
  dt = 20
  num_steps = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/auxkernels/linear_combination/test.i)

# All tested logic is in the aux system
# The non-linear problem is unrelated

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax =  1
  nx = 10
[]

[Functions]
  [./v1_func]
    type = ParsedFunction
    value = (1-x)/2
  [../]
  [./v2_func]
    type = ParsedFunction
    value = (1+x)/2
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./lc]
  [../]

  [./v1]
  [../]
  [./v2]
  [../]

  [./w1]
  [../]
  [./w2]
  [../]
[]

[ICs]
  [./v1_ic]
    type = FunctionIC
    variable = v1
    function = v1_func
  [../]
  [./v2_ic]
    type = FunctionIC
    variable = v2
    function = v2_func
  [../]

  [./w1_ic]
    type = ConstantIC
    variable = w1
    value = 0.3
  [../]
  [./w2_ic]
    type = ConstantIC
    variable = w2
    value = 0.5
  [../]
[]

[AuxKernels]
  [./lc-aux]
    type = ParsedAux
    variable = lc
    function = 'v1*w1+v2*w2'
    args = 'v1 w1 v2 w2'
    execute_on = 'timestep_end'
  [../]
[]


[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 1
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 2
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Outputs]
  [./out]
    type = Exodus
  [../]
[]

(test/tests/vectorpostprocessors/spherical_average/spherical_average.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 10
  nz = 10
  xmin = -5
  xmax = 5
  ymin = -5
  ymax = 5
  zmin = -5
  zmax = 5
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = sin(x*7.4+z*4.1)+cos(y*3.8+x*8.7)+sin(z*9.1+y*2.6)
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
[]

[VectorPostprocessors]
  [./average]
    type = SphericalAverage
    variable = c
    radius = 5
    bin_number = 10
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 1
  solve_type = PJFNK
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  csv = true
[]

(modules/level_set/test/tests/reinitialization/master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 8
  ny = 8
  uniform_refine = 3 #1/64
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[Variables]
  [./phi]
  [../]
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.05
    center = '0.5 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '1'
    value_y = '1'
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = phi
      auto_direction = 'x y'
    [../]
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]

  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]

  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1
  nl_rel_tol = 1e-12
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 1
  [../]

[]

[MultiApps]
  [./reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'reinit.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    to_multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./to_sub_init]
    type = MultiAppCopyTransfer
    variable = phi_0
    source_variable = phi
    to_multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./from_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    from_multi_app = reinit
    execute_on = timestep_end
  [../]
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower.i)

# checking that the PorousFlowDarcyVelocityComponentLowerDimensional AuxKernel works as expected
# for the fully-saturated case (relative-permeability = 1)
# The fractured_block.e has size = 10x10x10, and a fracture running through its
# centre, with normal = (0, -sin(20deg), cos(20deg))
# Porepressure is initialised to grad(P) = (0, 0, 1)
# Fluid_density = 2
# viscosity = 10
# relative_permeability = 1
# permeability = (5, 5, 5)  (in the bulk)
# permeability = (10, 10, 10)   (in the fracture)
# aperture = 1
# gravity = (1, 0.5, 0.2)
# So Darcy velocity in the bulk = (1, 0.5, -0.3)
# in the fracture grad(P) = (0, 0.3213938, 0.11697778)
# In the fracture the projected gravity vector is
# tangential_gravity = (1, 0.5057899, 0.18409245)
# So the Darcy velocity in the fracture = (2, 0.690186, 0.251207)

[Mesh]
  type = FileMesh
  file = fractured_block.e
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '1 0.5 0.2'
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = z
    variable = pp
  []
[]

[Kernels]
  [dummy]
    type = TimeDerivative
    variable = pp
  []
[]

[AuxVariables]
  [bulk_vel_x]
    order = CONSTANT
    family = MONOMIAL
  []
  [bulk_vel_y]
    order = CONSTANT
    family = MONOMIAL
  []
  [bulk_vel_z]
    order = CONSTANT
    family = MONOMIAL
  []
  [fracture_vel_x]
    order = CONSTANT
    family = MONOMIAL
    block = 3
  []
  [fracture_vel_y]
    order = CONSTANT
    family = MONOMIAL
    block = 3
  []
  [fracture_vel_z]
    order = CONSTANT
    family = MONOMIAL
    block = 3
  []
[]

[AuxKernels]
  [bulk_vel_x]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_x
    component = x
    fluid_phase = 0
  []
  [bulk_vel_y]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_y
    component = y
    fluid_phase = 0
  []
  [bulk_vel_z]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_z
    component = z
    fluid_phase = 0
  []
  [fracture_vel_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_x
    component = x
    fluid_phase = 0
  []
  [fracture_vel_y]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_y
    component = y
    fluid_phase = 0
  []
  [fracture_vel_z]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_z
    component = z
    fluid_phase = 0
 []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1E16
      viscosity = 10
      density0 = 2
      thermal_expansion = 0
    []
  []
[]

[Postprocessors]
  [bulk_vel_x]
    type = ElementAverageValue
    block = 1
    variable = bulk_vel_x
  []
  [bulk_vel_y]
    type = ElementAverageValue
    block = 1
    variable = bulk_vel_y
  []
  [bulk_vel_z]
    type = ElementAverageValue
    block = 1
    variable = bulk_vel_z
  []
  [fracture_vel_x]
    type = ElementAverageValue
    block = 3
    variable = fracture_vel_x
  []
  [fracture_vel_y]
    type = ElementAverageValue
    block = 3
    variable = fracture_vel_y
  []
  [fracture_vel_z]
    type = ElementAverageValue
    block = 3
    variable = fracture_vel_z
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
    block = '1 2'
  []
  [permeability_fracture]
    type = PorousFlowPermeabilityConst
    permeability = '10 0 0 0 10 0 0 0 10'
    block = 3
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/relperm/corey2.i)

# Test Corey relative permeability curve by varying saturation over the mesh
# Corey exponent n = 2 for both phases
# No residual saturation in either phase

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
    family = LAGRANGE
    order = FIRST
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityCorey
    phase = 0
    n = 2
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/cartesian-version/2d-rc-symmetry.i)

mu=1.1
rho=1.1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = -1
    ymax = 1
    nx = 2
    ny = 2
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  two_term_boundary_expansion = true
  advected_interp_method = 'average'
  velocity_interp_method = 'rc'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = u
    v = v
    pressure = pressure
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[ICs]
  [u]
    type = FunctionIC
    function = 'exact_u'
    variable = u
  []
  [v]
    type = FunctionIC
    function = 'exact_v'
    variable = v
  []
  [pressure]
    type = FunctionIC
    function = 'exact_p'
    variable = pressure
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = INSFVBodyForce
    variable = u
    functor = forcing_u
    momentum_component = 'x'
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = INSFVBodyForce
    variable = v
    functor = forcing_v
    momentum_component = 'y'
  []
[]

[FVBCs]
  [u_wall]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'right'
    function = 'exact_u'
  []
  [v_wall]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'right'
    function = 'exact_v'
  []
  [u_axis]
    type = INSFVSymmetryVelocityBC
    variable = u
    boundary = 'left'
    mu = ${mu}
    u = u
    v = v
    momentum_component = 'x'
  []
  [v_axis]
    type = INSFVSymmetryVelocityBC
    variable = v
    boundary = 'left'
    mu = ${mu}
    u = u
    v = v
    momentum_component = 'y'
  []
  [p_axis]
    type = INSFVSymmetryPressureBC
    variable = pressure
    boundary = 'left'
  []
  [p]
    type = INSFVOutletPressureBC
    variable = pressure
    function = 'exact_p'
    boundary = 'top'
  []
  [inlet_u]
    type = INSFVInletVelocityBC
    variable = u
    function = 'exact_u'
    boundary = 'bottom'
  []
  [inlet_v]
    type = INSFVInletVelocityBC
    variable = v
    function = 'exact_v'
    boundary = 'bottom'
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    value = 'sin(x*pi)*cos(y*pi)'
  []
  [forcing_u]
    type = ADParsedFunction
    value = '2*pi^2*mu*sin(x*pi)*cos(y*pi) - 2*pi*rho*sin(x*pi)*sin(y*pi)*cos(1.3*x)*cos(y*pi) + 2*pi*rho*sin(x*pi)*cos(x*pi)*cos(y*pi)^2 - 1.5*sin(1.5*x)*cos(1.6*y)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    value = 'cos(1.3*x)*cos(y*pi)'
  []
  [forcing_v]
    type = ADParsedFunction
    value = '1.69*mu*cos(1.3*x)*cos(y*pi) + pi^2*mu*cos(1.3*x)*cos(y*pi) - 1.3*rho*sin(1.3*x)*sin(x*pi)*cos(y*pi)^2 - 2*pi*rho*sin(y*pi)*cos(1.3*x)^2*cos(y*pi) + pi*rho*cos(1.3*x)*cos(x*pi)*cos(y*pi)^2 - 1.6*sin(1.6*y)*cos(1.5*x)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'cos(1.5*x)*cos(1.6*y)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-pi*rho*sin(y*pi)*cos(1.3*x) + pi*rho*cos(x*pi)*cos(y*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       NONZERO               superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = false
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [p_avg]
    type = ElementAverageValue
    variable = pressure
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/porous_flow/test/tests/dirackernels/injection_with_plasticity.i)

# Example: Injection into a uniform aquifer 10 x 10 x 5 km
# Drucker-Prager deformation
# Darcy flow
gravity = -9.81
solid_density = 2350
fluid_density = 1000
porosity0 = 0.1
[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = 0
  xmax = 1e4
  ymin = 0
  ymax = 1e4
  zmax = 0
  zmin = -5e3
  nx = 2
  ny = 2
  nz = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 ${gravity}'
  displacements = 'disp_x disp_y disp_z'
  strain_at_nearest_qp = true
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      thermal_expansion = 0 # Not doing a thermal simulation
      bulk_modulus = 2E9
      density0 = ${fluid_density}
      viscosity = 5E-4
    []
  []
[]

[PorousFlowFullySaturated]
  coupling_type = HydroMechanical
  porepressure = pp
  dictator_name = dictator
  fp = simple_fluid
  add_darcy_aux = false
  add_stress_aux = false
  stabilization = none
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [pp]
    scaling = 1E6
    [InitialCondition]
      type = FunctionIC
      function = ini_pp
    []
  []
[]

[Functions]
  [ini_stress]
    type = ParsedFunction
    value = '-${gravity} * z * (${solid_density} - ${fluid_density}) * (1.0 - ${porosity0})'  # initial effective stress that should result from weight force
  []

  [ini_pp]
    type = ParsedFunction
    value = '${gravity} * z * ${fluid_density} + 1E5'
  []
[]

[BCs]
  [p_top]
    type = FunctionDirichletBC
    variable = pp
    boundary = front
    function = ini_pp
  []

  [x_roller]
    type = DirichletBC
    variable = disp_x
    boundary = 'left right'
    value = 0
  []
  [y_roller]
    type = DirichletBC
    variable = disp_y
    boundary = 'top bottom'
    value = 0
  []
  [z_confined]
    type = DirichletBC
    variable = disp_z
    boundary = 'back front'
    value = 0
  []
[]

[UserObjects]
  [pls_total_outflow_mass]
    type = PorousFlowSumQuantity
  []

  # Cohesion
  [mc_coh]
    type = TensorMechanicsHardeningConstant
    value = 6.0E6
  []

  # Friction angle
  [mc_phi]
    type = TensorMechanicsHardeningConstant
    value = 35.0
    convert_to_radians = true
  []

  # Dilation angle
  [mc_psi]
    type = TensorMechanicsHardeningConstant
    value = 2
    convert_to_radians = true
  []

  # Drucker-Prager objects
  [dp]
    type = TensorMechanicsPlasticDruckerPragerHyperbolic
    mc_cohesion = mc_coh
    mc_friction_angle = mc_phi
    mc_dilation_angle = mc_psi
    yield_function_tolerance = 1E-3
    internal_constraint_tolerance = 1E-6
  []

  # Tensile strength
  [tens]
    type = TensorMechanicsHardeningConstant
    value = 3.0E6
  []

  # Compressive strength (cap on yield envelope)
  [compr_all]
    type = TensorMechanicsHardeningConstant
    value = 1E10
  []
[]

[Materials]
  [strain]
    type = ComputeIncrementalSmallStrain
    eigenstrain_names = eigenstrain_all
  []

  [eigenstrain_all]
    type = ComputeEigenstrainFromInitialStress
    initial_stress = 'ini_stress 0 0  0 ini_stress 0  0 0 ini_stress'
    eigenstrain_name = eigenstrain_all
  []

  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    bulk_modulus = 3.3333E9
    shear_modulus = 2.5E9
  []

  [dp_mat]
    type = CappedDruckerPragerStressUpdate
    DP_model = dp
    tensile_strength = tens
    compressive_strength = compr_all
    smoothing_tol = 1E5
    yield_function_tol = 1E-3
    tip_smoother = 0
  []

  [stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = dp_mat
  []

  # Permeability
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-13 0 0  0 1E-13 0  0 0 1E-13'
  []

  # Porosity
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = ${porosity0}
    biot_coefficient = 1.0
    solid_bulk = 1.0 # Required but irrelevant when biot_coefficient is unity
    mechanical = true
    fluid = true
  []

  # Density of saturated rock
  [density]
    type = PorousFlowTotalGravitationalDensityFullySaturatedFromPorosity
    rho_s = ${solid_density}
  []
[]

[DiracKernels]
  [pls]
    type = PorousFlowPolyLineSink
    variable = pp
    SumQuantityUO = pls_total_outflow_mass
    point_file = two_nodes.bh
    function_of = pressure
    fluid_phase = 0
    p_or_t_vals = '0 1E7'
    fluxes = '-1.59 -1.59'
  []
[]

[Preconditioning]
  [usual]
    type = SMP
    full = true
  []
[]

[Executioner]
  solve_type = Newton
  type = Transient
  dt = 1E6
  end_time = 1E6
  nl_rel_tol = 1E-7
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/image_function/flip.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    flip_x = true
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/user_objects/uo1.i)

# Relative-permeability User objects give the correct value
# (note that here p is x, where x runs between 0.01 and 0.99
# and that seff is p in the aux vars)
#
# If you want to add another test for another UserObject
# then add the UserObject, add a Function defining the expected result,
# add an AuxVariable and AuxKernel that will record the UserObjects value
# and finally add a NodalL2Error that compares this with the Function.

[UserObjects]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermPower5]
    type = RichardsRelPermPower
    simm = 0.0
    n = 5
  [../]
  [./RelPermVG]
    type = RichardsRelPermVG
    simm = 0.0
    m = 0.8
  [../]
  [./RelPermVG1]
    type = RichardsRelPermVG1
    simm = 0.0
    m = 0.8
    scut = 1E-6 # then we get a cubic
  [../]
  [./RelPermBW]
    type = RichardsRelPermBW
    Sn = 0.05
    Ss = 0.95
    Kn = 0.0
    Ks = 1.0
    C = 1.5
  [../]
  [./RelPermMonomial]
    type = RichardsRelPermMonomial
    simm = 0.0
    n = 3
  [../]
  [./RelPermPowerGas]
    type = RichardsRelPermPowerGas
    simm = 0.0
    n = 5
  [../]
  [./Q2PRelPermPowerGas]
    type = Q2PRelPermPowerGas
    simm = 0.0
    n = 5
  [../]
  [./RelPermMonomial_zero]
    type = RichardsRelPermMonomial
    simm = 0.1
    n = 0
    zero_to_the_zero = 0
  [../]

  # following are unimportant in this test
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-6
  [../]
  [./RelPermPower_unimportant]
    type = RichardsRelPermPower
    simm = 0.10101
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.054321
    sum_s_res = 0.054321
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E5
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = x
  [../]

  [./answer_RelPermPower]
    type = ParsedFunction
    value = ((n+1)*(x^n))-(n*(x^(n+1)))
    vars = 'n'
    vals = '2'
  [../]
  [./answer_dRelPermPower]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = ((n+1)*(x^n))-(n*(x^(n+1)))
    vars = 'n'
    vals = '2'
  [../]
  [./answer_d2RelPermPower]
    type = Grad2ParsedFunction
    direction = '1E-3 0 0'
    value = ((n+1)*(x^n))-(n*(x^(n+1)))
    vars = 'n'
    vals = '2'
  [../]

  [./answer_RelPermPower5]
    type = ParsedFunction
    value = ((n+1)*(x^n))-(n*(x^(n+1)))
    vars = 'n'
    vals = '5'
  [../]
  [./answer_dRelPermPower5]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = ((n+1)*(x^n))-(n*(x^(n+1)))
    vars = 'n'
    vals = '5'
  [../]
  [./answer_d2RelPermPower5]
    type = Grad2ParsedFunction
    direction = '1E-5 0 0'
    value = ((n+1)*(x^n))-(n*(x^(n+1)))
    vars = 'n'
    vals = '5'
  [../]

  [./answer_RelPermVG]
    type = ParsedFunction
    value = (x^(0.5))*(1-(1-(x^(1.0/m)))^m)^2
    vars = 'm'
    vals = '0.8'
  [../]
  [./answer_dRelPermVG]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = (x^(0.5))*(1-(1-(x^(1.0/m)))^m)^2
    vars = 'm'
    vals = '0.8'
  [../]
  [./answer_d2RelPermVG]
    type = Grad2ParsedFunction
    direction = '1E-5 0 0'
    value = (x^(0.5))*(1-(1-(x^(1.0/m)))^m)^2
    vars = 'm'
    vals = '0.8'
  [../]

  [./answer_RelPermVG1]
    type = ParsedFunction
    value = x^3
  [../]
  [./answer_dRelPermVG1]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = x^3
  [../]
  [./answer_d2RelPermVG1]
    type = Grad2ParsedFunction
    direction = '1E-5 0 0'
    value = x^3
  [../]

  [./answer_RelPermBW]
    type = ParsedFunction
    value = if(x>ss,1,if(x<sn,0,kn+(((x-sn)/(ss-sn))^2)*(c-1)*(ks-kn)/(c-((x-sn)/(ss-sn)))))
    vars = 'kn ks c sn ss'
    vals = '0 1 1.5 0.05 0.95'
  [../]
  [./answer_dRelPermBW]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = if(x>ss,1,if(x<sn,0,kn+(((x-sn)/(ss-sn))^2)*(c-1)*(ks-kn)/(c-((x-sn)/(ss-sn)))))
    vars = 'kn ks c sn ss'
    vals = '0 1 1.5 0.05 0.95'
  [../]
  [./answer_d2RelPermBW]
    type = Grad2ParsedFunction
    direction = '1E-5 0 0'
    value = if(x>ss,1,if(x<sn,0,kn+(((x-sn)/(ss-sn))^2)*(c-1)*(ks-kn)/(c-((x-sn)/(ss-sn)))))
    vars = 'kn ks c sn ss'
    vals = '0 1 1.5 0.05 0.95'
  [../]

  [./answer_RelPermMonomial]
    type = ParsedFunction
    value = x^n
    vars = 'n'
    vals = '3'
  [../]
  [./answer_dRelPermMonomial]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = x^n
    vars = 'n'
    vals = '3'
  [../]
  [./answer_d2RelPermMonomial]
    type = Grad2ParsedFunction
    direction = '1E-3 0 0'
    value = x^n
    vars = 'n'
    vals = '3'
  [../]

  [./answer_RelPermMonomial_zero]
    type = ParsedFunction
    value = if(x>simm,1,0)
    vars = 'simm'
    vals = '0.1'
  [../]
  [./answer_dRelPermMonomial_zero]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = if(x>simm,1,0)
    vars = 'simm'
    vals = '0.1'
  [../]
  [./answer_d2RelPermMonomial_zero]
    type = Grad2ParsedFunction
    direction = '1E-3 0 0'
    value = if(x>simm,1,0)
    vars = 'simm'
    vals = '0.1'
  [../]

  [./answer_RelPermPowerGas]
    type = ParsedFunction
    value = 1-((n+1)*((1-x)^n))+(n*((1-x)^(n+1)))
    vars = 'n'
    vals = '5'
  [../]
  [./answer_dRelPermPowerGas]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = 1-((n+1)*((1-x)^n))+(n*((1-x)^(n+1)))
    vars = 'n'
    vals = '5'
  [../]
  [./answer_d2RelPermPowerGas]
    type = Grad2ParsedFunction
    direction = '1E-5 0 0'
    value = 1-((n+1)*((1-x)^n))+(n*((1-x)^(n+1)))
    vars = 'n'
    vals = '5'
  [../]

  [./answer_Q2PRelPermPowerGas]
    type = ParsedFunction
    value = 1-((n+1)*(x^n))+(n*(x^(n+1)))
    vars = 'n'
    vals = '5'
  [../]
  [./answer_dQ2PRelPermPowerGas]
    type = GradParsedFunction
    direction = '1E-4 0 0'
    value = 1-((n+1)*(x^n))+(n*(x^(n+1)))
    vars = 'n'
    vals = '5'
  [../]
  [./answer_d2Q2PRelPermPowerGas]
    type = Grad2ParsedFunction
    direction = '1E-5 0 0'
    value = 1-((n+1)*(x^n))+(n*(x^(n+1)))
    vars = 'n'
    vals = '5'
  [../]
[]

[AuxVariables]
  [./RelPermPower_Aux]
  [../]
  [./dRelPermPower_Aux]
  [../]
  [./d2RelPermPower_Aux]
  [../]

  [./RelPermPower5_Aux]
  [../]
  [./dRelPermPower5_Aux]
  [../]
  [./d2RelPermPower5_Aux]
  [../]

  [./RelPermVG_Aux]
  [../]
  [./dRelPermVG_Aux]
  [../]
  [./d2RelPermVG_Aux]
  [../]

  [./RelPermVG1_Aux]
  [../]
  [./dRelPermVG1_Aux]
  [../]
  [./d2RelPermVG1_Aux]
  [../]

  [./RelPermBW_Aux]
  [../]
  [./dRelPermBW_Aux]
  [../]
  [./d2RelPermBW_Aux]
  [../]

  [./RelPermMonomial_Aux]
  [../]
  [./dRelPermMonomial_Aux]
  [../]
  [./d2RelPermMonomial_Aux]
  [../]

  [./RelPermPowerGas_Aux]
  [../]
  [./dRelPermPowerGas_Aux]
  [../]
  [./d2RelPermPowerGas_Aux]
  [../]

  [./Q2PRelPermPowerGas_Aux]
  [../]
  [./dQ2PRelPermPowerGas_Aux]
  [../]
  [./d2Q2PRelPermPowerGas_Aux]
  [../]

  [./RelPermMonomial_zero_Aux]
  [../]
  [./dRelPermMonomial_zero_Aux]
  [../]
  [./d2RelPermMonomial_zero_Aux]
  [../]

  [./check_Aux]
  [../]
[]

[AuxKernels]
  [./RelPermPower_AuxK]
    type = RichardsRelPermAux
    variable = RelPermPower_Aux
    relperm_UO = RelPermPower
    seff_var = pressure
  [../]
  [./dRelPermPower_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermPower_Aux
    relperm_UO = RelPermPower
    seff_var = pressure
  [../]
  [./d2RelPermPower_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermPower_Aux
    relperm_UO = RelPermPower
    seff_var = pressure
  [../]

  [./RelPermPower5_AuxK]
    type = RichardsRelPermAux
    variable = RelPermPower5_Aux
    relperm_UO = RelPermPower5
    seff_var = pressure
  [../]
  [./dRelPermPower5_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermPower5_Aux
    relperm_UO = RelPermPower5
    seff_var = pressure
  [../]
  [./d2RelPermPower5_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermPower5_Aux
    relperm_UO = RelPermPower5
    seff_var = pressure
  [../]

  [./RelPermVG_AuxK]
    type = RichardsRelPermAux
    variable = RelPermVG_Aux
    relperm_UO = RelPermVG
    seff_var = pressure
  [../]
  [./dRelPermVG_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermVG_Aux
    relperm_UO = RelPermVG
    seff_var = pressure
  [../]
  [./d2RelPermVG_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermVG_Aux
    relperm_UO = RelPermVG
    seff_var = pressure
  [../]

  [./RelPermVG1_AuxK]
    type = RichardsRelPermAux
    variable = RelPermVG1_Aux
    relperm_UO = RelPermVG1
    seff_var = pressure
  [../]
  [./dRelPermVG1_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermVG1_Aux
    relperm_UO = RelPermVG1
    seff_var = pressure
  [../]
  [./d2RelPermVG1_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermVG1_Aux
    relperm_UO = RelPermVG1
    seff_var = pressure
  [../]

  [./RelPermBW_AuxK]
    type = RichardsRelPermAux
    variable = RelPermBW_Aux
    relperm_UO = RelPermBW
    seff_var = pressure
  [../]
  [./dRelPermBW_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermBW_Aux
    relperm_UO = RelPermBW
    seff_var = pressure
  [../]
  [./d2RelPermBW_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermBW_Aux
    relperm_UO = RelPermBW
    seff_var = pressure
  [../]

  [./RelPermMonomial_AuxK]
    type = RichardsRelPermAux
    variable = RelPermMonomial_Aux
    relperm_UO = RelPermMonomial
    seff_var = pressure
  [../]
  [./dRelPermMonomial_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermMonomial_Aux
    relperm_UO = RelPermMonomial
    seff_var = pressure
  [../]
  [./d2RelPermMonomial_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermMonomial_Aux
    relperm_UO = RelPermMonomial
    seff_var = pressure
  [../]

  [./RelPermPowerGas_AuxK]
    type = RichardsRelPermAux
    variable = RelPermPowerGas_Aux
    relperm_UO = RelPermPowerGas
    seff_var = pressure
  [../]
  [./dRelPermPowerGas_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermPowerGas_Aux
    relperm_UO = RelPermPowerGas
    seff_var = pressure
  [../]
  [./d2RelPermPowerGas_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermPowerGas_Aux
    relperm_UO = RelPermPowerGas
    seff_var = pressure
  [../]

  [./Q2PRelPermPowerGas_AuxK]
    type = RichardsRelPermAux
    variable = Q2PRelPermPowerGas_Aux
    relperm_UO = Q2PRelPermPowerGas
    seff_var = pressure
  [../]
  [./dQ2PRelPermPowerGas_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dQ2PRelPermPowerGas_Aux
    relperm_UO = Q2PRelPermPowerGas
    seff_var = pressure
  [../]
  [./d2Q2PRelPermPowerGas_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2Q2PRelPermPowerGas_Aux
    relperm_UO = Q2PRelPermPowerGas
    seff_var = pressure
  [../]

  [./RelPermMonomial_zero_AuxK]
    type = RichardsRelPermAux
    variable = RelPermMonomial_zero_Aux
    relperm_UO = RelPermMonomial_zero
    seff_var = pressure
  [../]
  [./dRelPermMonomial_zero_AuxK]
    type = RichardsRelPermPrimeAux
    variable = dRelPermMonomial_zero_Aux
    relperm_UO = RelPermMonomial_zero
    seff_var = pressure
  [../]
  [./d2RelPermMonomial_zero_AuxK]
    type = RichardsRelPermPrimePrimeAux
    variable = d2RelPermMonomial_zero_Aux
    relperm_UO = RelPermMonomial_zero
    seff_var = pressure
  [../]

  [./check_AuxK]
    type = FunctionAux
    variable = check_Aux
    function = answer_RelPermBW
  [../]
[]

[Postprocessors]
  [./cf_RelPermPower]
    type = NodalL2Error
    function = answer_RelPermPower
    variable = RelPermPower_Aux
  [../]
  [./cf_dRelPermPower]
    type = NodalL2Error
    function = answer_dRelPermPower
    variable = dRelPermPower_Aux
  [../]
  [./cf_d2RelPermPower]
    type = NodalL2Error
    function = answer_d2RelPermPower
    variable = d2RelPermPower_Aux
  [../]

  [./cf_RelPermPower5]
    type = NodalL2Error
    function = answer_RelPermPower5
    variable = RelPermPower5_Aux
  [../]
  [./cf_dRelPermPower5]
    type = NodalL2Error
    function = answer_dRelPermPower5
    variable = dRelPermPower5_Aux
  [../]
  [./cf_d2RelPermPower5]
    type = NodalL2Error
    function = answer_d2RelPermPower5
    variable = d2RelPermPower5_Aux
  [../]

  [./cf_RelPermVG]
    type = NodalL2Error
    function = answer_RelPermVG
    variable = RelPermVG_Aux
  [../]
  [./cf_dRelPermVG]
    type = NodalL2Error
    function = answer_dRelPermVG
    variable = dRelPermVG_Aux
  [../]
  [./cf_d2RelPermVG]
    type = NodalL2Error
    function = answer_d2RelPermVG
    variable = d2RelPermVG_Aux
  [../]

  [./cf_RelPermVG1]
    type = NodalL2Error
    function = answer_RelPermVG1
    variable = RelPermVG1_Aux
  [../]
  [./cf_dRelPermVG1]
    type = NodalL2Error
    function = answer_dRelPermVG1
    variable = dRelPermVG1_Aux
  [../]
  [./cf_d2RelPermVG1]
    type = NodalL2Error
    function = answer_d2RelPermVG1
    variable = d2RelPermVG1_Aux
  [../]

  [./cf_RelPermBW]
    type = NodalL2Error
    function = answer_RelPermBW
    variable = RelPermBW_Aux
  [../]
  [./cf_dRelPermBW]
    type = NodalL2Error
    function = answer_dRelPermBW
    variable = dRelPermBW_Aux
  [../]
  [./cf_d2RelPermBW]
    type = NodalL2Error
    function = answer_d2RelPermBW
    variable = d2RelPermBW_Aux
  [../]

  [./cf_RelPermMonomial]
    type = NodalL2Error
    function = answer_RelPermMonomial
    variable = RelPermMonomial_Aux
  [../]
  [./cf_dRelPermMonomial]
    type = NodalL2Error
    function = answer_dRelPermMonomial
    variable = dRelPermMonomial_Aux
  [../]
  [./cf_d2RelPermMonomial]
    type = NodalL2Error
    function = answer_d2RelPermMonomial
    variable = d2RelPermMonomial_Aux
  [../]

  [./cf_RelPermPowerGas]
    type = NodalL2Error
    function = answer_RelPermPowerGas
    variable = RelPermPowerGas_Aux
  [../]
  [./cf_dRelPermPowerGas]
    type = NodalL2Error
    function = answer_dRelPermPowerGas
    variable = dRelPermPowerGas_Aux
  [../]
  [./cf_d2RelPermPowerGas]
    type = NodalL2Error
    function = answer_d2RelPermPowerGas
    variable = d2RelPermPowerGas_Aux
  [../]

  [./cf_Q2PRelPermPowerGas]
    type = NodalL2Error
    function = answer_Q2PRelPermPowerGas
    variable = Q2PRelPermPowerGas_Aux
  [../]
  [./cf_dQ2PRelPermPowerGas]
    type = NodalL2Error
    function = answer_dQ2PRelPermPowerGas
    variable = dQ2PRelPermPowerGas_Aux
  [../]
  [./cf_d2Q2PRelPermPowerGas]
    type = NodalL2Error
    function = answer_d2Q2PRelPermPowerGas
    variable = d2Q2PRelPermPowerGas_Aux
  [../]

  [./cf_RelPermMonomial_zero]
    type = NodalL2Error
    function = answer_RelPermMonomial_zero
    variable = RelPermMonomial_zero_Aux
  [../]
  [./cf_dRelPermMonomial_zero]
    type = NodalL2Error
    function = answer_dRelPermMonomial_zero
    variable = dRelPermMonomial_zero_Aux
  [../]
  [./cf_d2RelPermMonomial_zero]
    type = NodalL2Error
    function = answer_d2RelPermMonomial_zero
    variable = d2RelPermMonomial_zero_Aux
  [../]

[]



#############################################################################
#
# Following is largely unimportant as we are not running an actual similation
#
#############################################################################
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0.01
  xmax = 0.99
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    richardsVarNames_UO = PPNames
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    richardsVarNames_UO = PPNames
    variable = pressure
  [../]
[]

[Materials]
  [./unimportant_material]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-20 0 0  0 1E-20 0  0 0 1E-20'
    richardsVarNames_UO = PPNames
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower_unimportant
    sat_UO = Saturation
    seff_UO = SeffVG
    SUPG_UO = SUPGstandard
    viscosity = 1E-3
    gravity = '0 0 -10'
    linear_shape_fcns = true
  [../]
[]

[Preconditioning]
  [./does_nothing]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E50 1E50 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
  dt = 1E-100
[]

[Outputs]
  execute_on = 'timestep_end'
  active = 'csv'
  file_base = uo1
  [./csv]
    type = CSV
    [../]
  [./exodus]
    type = Exodus
    hide = pressure
  [../]
[]

(test/tests/ics/hermite_ic/hermite_ic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Functions]
  [./afunc]
    type = ParsedFunction
    value = x^2
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./func_ic]
    function = afunc
    variable = u
    type = FunctionIC
  [../]
[]

(tutorials/darcy_thermo_mech/step04_velocity_aux/tests/auxkernels/velocity_aux/velocity_aux.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [pressure]
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[Functions]
  [pressure_ic_func]
    type = ParsedFunction
    value = 2000*x*y*x*y
  []
[]

[ICs]
  [pressure_ic]
    type = FunctionIC
    variable = pressure
    function = pressure_ic_func
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
  solve = false
[]

[Materials]
  [pressure]
    type = ADGenericConstantMaterial
    prop_values = '0.8451e-9 7.98e-4'
    prop_names = 'permeability viscosity'
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(test/tests/userobjects/toggle_mesh_adaptivity/toggle_mesh_adaptivity_gaussian_ic_stop_time.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./gaussian_ic]
    type = FunctionIC
    variable = u
    function = gaussian_2d
  [../]
[]

[Functions]
  [./gaussian_2d]
    type = ParsedFunction
    value = exp(-((x-x0)*(x-x0)+(y-y0)*(y-y0))/2.0/sigma/sigma)
    vars = 'sigma x0 y0'
    vals = '0.05 0.35 0.25'
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = u
    coef = 0.02
  [../]
  [./time]
    type = TimeDerivative
    variable = u
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = u
      auto_direction = 'x y'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Adaptivity]
  initial_steps = 1
  initial_marker = marker
  cycles_per_step = 1
  marker = marker
  max_h_level = 2
  stop_time = 0.0
  [./Markers]
    [./marker]
      type = CircleMarker
      point = '0.35 0.25 0'
      radius = 0.2
      inside = refine
      outside = coarsen
    [../]
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    print_mesh_changed_info = true
  [../]
[]

(modules/combined/test/tests/CHSplitFlux/flux_gb.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.1*v'
    [../]
  [../]
  [./mu]
  [../]
  [./jx]
  [../]
  [./jy]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./mobility_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./mobility_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./diffusivity_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./diffusivity_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./aniso_tensor_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./aniso_tensor_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = mu_prop
    c = c
  [../]
  [./flux_x]
    type = CHSplitFlux
    variable = jx
    component = 0
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./flux_y]
    type = CHSplitFlux
    variable = jy
    component = 1
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./mobility_xx]
    type = MaterialRealTensorValueAux
    variable = mobility_xx
    property = mobility_prop
    row = 0
    column = 0
  [../]
  [./mobility_yy]
    type = MaterialRealTensorValueAux
    variable = mobility_yy
    property = mobility_prop
    row = 1
    column = 1
  [../]
  [./diffusivity_xx]
    type = MaterialRealTensorValueAux
    variable = diffusivity_xx
    property = diffusivity
    row = 0
    column = 0
  [../]
  [./diffusivity_yy]
    type = MaterialRealTensorValueAux
    variable = diffusivity_yy
    property = diffusivity
    row = 1
    column = 1
  [../]
  [./aniso_tensor_xx]
    type = MaterialRealTensorValueAux
    variable = aniso_tensor_xx
    property = aniso_tensor
    row = 0
    column = 0
  [../]
  [./aniso_tensor_yy]
    type = MaterialRealTensorValueAux
    variable = aniso_tensor_yy
    property = aniso_tensor
    row = 1
    column = 1
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  nl_max_its = 5
  dt = 20
  num_steps = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/solution_function/solution_function_rot3.i)

# checking rotation of points by 90 deg about z axis, then 45 deg about x axis in a SolutionUserObject
[Mesh]
  # this is chosen so when i rotate through 45deg i get a length of "1" along the x or y or z direction
  type = GeneratedMesh
  dim = 3
  xmin = -0.70710678
  xmax = 0.70710678
  nx = 3
  ymin = -0.70710678
  ymax = 0.70710678
  ny = 3
  zmin = -0.70710678
  zmax = 0.70710678
  nz = 3
[]

[UserObjects]
  [./solution_uo]
    type = SolutionUserObject
    mesh = cube_with_u_equals_x.e
    timestep = 1
    system_variables = u
    # the following takes:
    # (0.7, 0.7, +/-0.7) -> (-0.7, 0.7, +/-0.7)
    # (-0.7, 0.7, +/-0.7) -> (-0.7, -0.7, +/-0.7)
    # (0.7, -0.7, +/-0.7) -> (0.7, 0.7, +/-0.7)
    # (-0.7, -0.7, +/-0.7) -> (0.7, -0.7, +/-0.7)
    rotation0_vector = '0 0 1'
    rotation0_angle = 90
    # then the following takes:
    # (+/-0.7, 0.7, 0.7) -> (+/-0.7, 0, 1)
    # (+/-0.7, 0.7, -0.7) -> (+/-0.7, 1, 0)
    # (+/-0.7, -0.7, 0.7) -> (+/-0.7, -1, 0)
    # (+/-0.7, -0.7, -0.7) -> (+/-0.7, 0, -1)
    rotation1_vector = '1 0 0'
    rotation1_angle = 45
    # so, in total: a point y = +/-0.7 takes values from x = -/+0.7, so solution_function_rot3 should have u = -y
    transformation_order = 'rotation0 rotation1'
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = solution_fcn
  [../]
[]

[Functions]
  [./solution_fcn]
    type = SolutionFunction
    from_variable = u
    solution = solution_uo
  [../]
[]

[Kernels]
  [./diff]
    type = TimeDerivative
    variable = u
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  l_max_its = 800
  nl_rel_tol = 1e-10
  num_steps = 1
  end_time = 1
  dt = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = solution_function_rot3
  exodus = true
[]

(test/tests/functions/image_function/error/threshold_values.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [tif]
    type = ImageFunction
    file_base = ../stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    threshold = 30000
    upper_value = 1
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = tif
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/nodalkernels/constraint_enforcement/upper-bound.i)

l=10
nx=100
num_steps=10

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
  [lm]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = '${l} - x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = '1'
  []
[]

[NodalKernels]
  [positive_constraint]
    type = UpperBoundNodalKernel
    variable = lm
    v = u
    exclude_boundaries = 'left right'
    upper_bound = 10
  []
  [forces]
    type = CoupledForceNodalKernel
    variable = u
    v = lm
    coef = -1
  []
[]


[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = ${l}
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type'
  petsc_options_value = '0                           30          asm      16                    basic'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [active_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
  []
  [violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
[]

(test/tests/functions/image_function/image.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 10
  nz = 10
[]

[Adaptivity]
  max_h_level = 5
  initial_steps = 5
  initial_marker = marker
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = u
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      refine = 0.9
    []
  []
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file = stack/test_00.png
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/tensor_mechanics/test/tests/interface_stress/test.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 10
  nz = 10
  xmax = 1
  ymax = 1
  zmax = 1
  xmin = -1
  ymin = -1
  zmin = -1
[]

[GlobalParams]
  order = CONSTANT
  family = MONOMIAL
  rank_two_tensor = extra_stress
[]

[Functions]
  [./sphere]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2); if(r>1,0,1-3*r^2+2*r^3)'
  [../]
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[AuxVariables]
  [./eta]
    [./InitialCondition]
      type = FunctionIC
      function = sphere
    [../]
    order = FIRST
    family = LAGRANGE
  [../]
  [./s00]
  [../]
  [./s01]
  [../]
  [./s02]
  [../]
  [./s10]
  [../]
  [./s11]
  [../]
  [./s12]
  [../]
  [./s20]
  [../]
  [./s21]
  [../]
  [./s22]
  [../]
[]

[AuxKernels]
  [./s00]
    type = RankTwoAux
    variable = s00
    index_i = 0
    index_j = 0
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    index_i = 0
    index_j = 1
  [../]
  [./s02]
    type = RankTwoAux
    variable = s02
    index_i = 0
    index_j = 2
  [../]
  [./s10]
    type = RankTwoAux
    variable = s10
    index_i = 1
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    index_i = 1
    index_j = 1
  [../]
  [./s12]
    type = RankTwoAux
    variable = s12
    index_i = 1
    index_j = 2
  [../]
  [./s20]
    type = RankTwoAux
    variable = s20
    index_i = 2
    index_j = 0
  [../]
  [./s21]
    type = RankTwoAux
    variable = s21
    index_i = 2
    index_j = 1
  [../]
  [./s22]
    type = RankTwoAux
    variable = s22
    index_i = 2
    index_j = 2
  [../]
[]

[Materials]
  [./interface]
    type = ComputeInterfaceStress
    v = eta
    stress = 3.0
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  hide = 'dummy eta'
[]

(test/tests/interfacekernels/ik_displaced/different_jxw_displaced.i)

[Mesh]
  displacements = 'disp_x disp_y'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    xmax = 2
    ny = 1
    ymax = 1
  []
  [./subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 1 0'
    block_id = 1
  [../]
  [./break_boundary]
    input = subdomain1
    type = BreakMeshByBlockGenerator
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
    use_displaced_mesh = true
  [../]
[]

[InterfaceKernels]
  [./interface]
    type = InterfacialSource
    variable = u
    neighbor_var = u
    boundary = interface
    use_displaced_mesh = true
  [../]
[]

[BCs]
  [./u]
    type = DirichletBC
    variable = u
    boundary = 'left right'
    value = 0
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

[Functions]
  [./disp_x_func]
    type = ParsedFunction
    value = 1
  [../]
  [./disp_y_func]
    type = ParsedFunction
    value = y
  [../]
[]

[ICs]
  [./disp_x_ic]
    block = 0
    function = disp_x_func
    variable = disp_x
    type = FunctionIC
  [../]
  [./disp_y_ic]
    block = 0
    function = disp_y_func
    variable = disp_y
    type = FunctionIC
  [../]
[]

(modules/porous_flow/examples/multiapp_fracture_flow/3dFracture/matrix_app.i)

# 3D matrix app doing thermo-hydro PorousFlow and receiving heat energy via a VectorPostprocessor from the 2D fracture App
[Mesh]
  uniform_refine = 0
  [generate]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 11
    xmin = -10
    xmax = 210
    ny = 9
    ymin = -10
    ymax = 160
    nz = 11
    zmin = -10
    zmax = 210
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [matrix_P]
    scaling = 1E6
  []
  [matrix_T]
    initial_condition = 473
  []
[]

[ICs]
  [frac_P]
    type = FunctionIC
    variable = matrix_P
    function = insitu_pp
  []
[]

[Functions]
  [insitu_pp]
    type = ParsedFunction
    value = '10 - 0.847E-2 * z' # Approximate hydrostatic in MPa
  []
[]

[PorousFlowFullySaturated]
  coupling_type = ThermoHydro
  porepressure = matrix_P
  temperature = matrix_T
  fp = water
  gravity = '0 0 -9.81E-6' # Note the value, because of pressure_unit
  pressure_unit = MPa
[]

[DiracKernels]
  [heat_from_fracture]
    type = ReporterPointSource
    variable = matrix_T
    value_name = heat_transfer_rate/transferred_joules_per_s
    x_coord_name = heat_transfer_rate/x
    y_coord_name = heat_transfer_rate/y
    z_coord_name = heat_transfer_rate/z
  []
[]

[Modules]
  [FluidProperties]
    [water]
      type = SimpleFluidProperties # this is largely irrelevant here since we care about heat conduction only
      thermal_expansion = 0 # to prevent depressurization as the reservoir is cooled
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 1E-3 # small porosity of rock
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-18 0 0   0 1E-18 0   0 0 1E-18'
  []
  [internal_energy]
    type = PorousFlowMatrixInternalEnergy
    density = 2700 # kg/m^3
    specific_heat_capacity = 800 # rough guess at specific heat capacity
  []
  [aq_thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '5 0 0  0 5 0  0 0 5'
  []
[]

[VectorPostprocessors]
  [heat_transfer_rate]
    type = ConstantVectorPostprocessor
    vector_names = 'transferred_joules_per_s x y z'
    value = '0; 0; 0; 0'
    outputs = none
  []
[]

[AuxVariables]
  [normal_thermal_conductivity]
    family = MONOMIAL
    order = CONSTANT
  []
  [fracture_normal_x]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0
  []
  [fracture_normal_y]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 1
  []
  [fracture_normal_z]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0
  []
  [element_normal_length]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [normal_thermal_conductivity_auxk]
    type = ConstantAux
    variable = normal_thermal_conductivity
    value = 5 # very simple in this case
  []
  [element_normal_length_auxk]
    type = PorousFlowElementLength
    variable = element_normal_length
    direction = 'fracture_normal_x fracture_normal_y fracture_normal_z'
  []
[]

[Preconditioning]
  [entire_jacobian]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    growth_factor = 1.1
    optimal_iterations = 4
    timestep_limiting_postprocessor = 1E8
  []
  end_time = 1E8
  nl_abs_tol = 1E-2
[]

[Outputs]
  print_linear_residuals = false
  exodus = false
[]

[MultiApps]
  [fracture_app]
    type = TransientMultiApp
    input_files = fracture_only_aperture_changing.i
    cli_args = 'Outputs/ex/sync_only=false'
    execute_on = TIMESTEP_BEGIN
    sub_cycling = true
### catch_up = true
### max_catch_up_steps = 100
  []
[]

[Transfers]
  [element_normal_length_to_fracture]
    type = MultiAppNearestNodeTransfer
    to_multi_app = fracture_app
    source_variable = element_normal_length
    variable = enclosing_element_normal_length
  []
  [element_normal_thermal_cond_to_fracture]
    type = MultiAppNearestNodeTransfer
    to_multi_app = fracture_app
    source_variable = normal_thermal_conductivity
    variable = enclosing_element_normal_thermal_cond
  []
  [T_to_fracture]
    type = MultiAppInterpolationTransfer
    to_multi_app = fracture_app
    source_variable = matrix_T
    variable = transferred_matrix_T
  []
  [normal_x_from_fracture]
    type = MultiAppNearestNodeTransfer
    from_multi_app = fracture_app
    source_variable = normal_dirn_x
    variable = fracture_normal_x
  []
  [normal_y_from_fracture]
    type = MultiAppNearestNodeTransfer
    from_multi_app = fracture_app
    source_variable = normal_dirn_y
    variable = fracture_normal_y
  []
  [normal_z_from_fracture]
    type = MultiAppNearestNodeTransfer
    from_multi_app = fracture_app
    source_variable = normal_dirn_z
    variable = fracture_normal_z
  []
  [heat_from_fracture]
    type = MultiAppReporterTransfer
    from_multi_app = fracture_app
    from_reporters = 'heat_transfer_rate/joules_per_s heat_transfer_rate/x heat_transfer_rate/y heat_transfer_rate/z'
    to_reporters = 'heat_transfer_rate/transferred_joules_per_s heat_transfer_rate/x heat_transfer_rate/y heat_transfer_rate/z'
  []
[]

(modules/porous_flow/test/tests/numerical_diffusion/fltvd.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, with antidiffusion from superbee flux limiting
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  nl_max_its = 500
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/combined/examples/publications/rapid_dev/fig3.i)

#
# Fig. 3 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Comparison of an analytical (ca) and numerical (c) phase field interface
# profile. Supply the L parameter on the command line to gather the data for
# the inset plot.
#

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = ${L}
  xmin = -30
  xmax = 30
[]

[Functions]
  [./solution]
    type = ParsedFunction
    value = 0.5*(1+tanh(x/2^0.5))
  [../]
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = solution
      #type = FunctionIC
      #function = if(x>0,1,0)
    [../]
  [../]
  [./w]
  [../]
[]

[AuxVariables]
  [./diff]
  [../]
  [./ca]
    [./InitialCondition]
      type = FunctionIC
      function = '0.5*(1+tanh(x/2^0.5))'
    [../]
  [../]
[]

[AuxKernels]
  [./diff]
    type = ParsedAux
    variable = diff
    function = c-ca
    args = 'c ca'
  [../]
[]

[Materials]
  [./F]
    type = DerivativeParsedMaterial
    f_name = F
    function = 'c^2*(1-c)^2'
    args = c
  [../]
[]

[Kernels]
  # Split Cahn-Hilliard kernels
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = 1
    w = w
  [../]
  [./wres]
    type = SplitCHWRes
    variable = w
    mob_name = 1
  [../]
  [./time]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
[]

[Postprocessors]
  [./L2]
    type = ElementL2Error
    function = solution
    variable = c
  [../]
[]

[VectorPostprocessors]
  [./c]
    type = LineValueSampler
    variable = 'c ca diff'
    start_point = '-10 0 0'
    end_point = '10 0 0'
    num_points = 200
    sort_by = x
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12
  end_time = 1e+6

  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    optimal_iterations = 5
    iteration_window = 1
  [../]
[]

[Outputs]
  csv = true
  execute_on = final
[]

(test/tests/auxkernels/time_derivative/time_derivative_nl.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = -5.0
  xmax =  5.0
[]

[Variables]
  [./c]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./c_dot]
    order = FIRST
    family = LAGRANGE
  [../]
  [./c_dot_elem]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./coupled_dot]
    type = DotCouplingAux
    variable = c_dot
    v = c
  [../]
  [./coupled_dot_elem]
    type = DotCouplingAux
    variable = c_dot_elem
    v = c
  [../]
[]

[ICs]
  [./centered_gauss_func]
    type = FunctionIC
    variable = c
    function = gaussian_1d
  [../]
[]

[Functions]
  [./gaussian_1d]
    type = ParsedFunction
    value = exp(-x*x/2.0/1.0/1.0)
  [../]
[]

[Kernels]
  [./dot]
    type = TimeDerivative
    variable = c
  [../]
  [./diff]
    type = Diffusion
    variable = c
  [../]
[]

[BCs]
  [./Periodic]
    [./auto]
      variable = c
      auto_direction = 'x'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  dt = 0.1
  num_steps = 5
[]


[Outputs]
  exodus = true
  #
[]

(test/tests/materials/coupled_value_function/order.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 4
    nz = 4
  []
[]

[Functions]
  [test]
    type = ParsedFunction
    value = 't + x^2 + y^3 + sin(5*z)'
  []
[]

[AuxVariables]
  [a]
  []
  [b]
  []
  [c]
  []
  [d]
  []
[]

[ICs]
  [a]
    type = FunctionIC
    variable = a
    function = x
  []
  [b]
    type = FunctionIC
    variable = b
    function = y
  []
  [c]
    type = FunctionIC
    variable = c
    function = z
  []
  [d]
    type = FunctionIC
    variable = d
    function = t
  []
[]

[Variables]
  [u]
  []
[]

[Materials]
  [cvf]
    type = CoupledValueFunctionMaterial
    function = test
    v = 'a b c d'
    prop_name = p
    outputs = exodus
  []
[]

[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Executioner]
  type = Transient
  dt = 0.25
  num_steps = 4
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/jacobian/fflux02.i)

# 1phase, 3components, constant viscosity, constant insitu permeability
# density with constant bulk, Corey relative perm, nonzero gravity, unsaturated with vanGenuchten
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  xmin = 0
  xmax = 1
  ny = 1
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [massfrac0]
  []
  [massfrac1]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = -0.7+x+y
  []
  [massfrac0]
    type = RandomIC
    variable = massfrac0
    min = 0
    max = 0.3
  []
  [massfrac1]
    type = RandomIC
    variable = massfrac1
    min = 0
    max = 0.4
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
    gravity = '-1 -0.1 0'
  []
  [flux2]
    type = PorousFlowAdvectiveFlux
    fluid_component = 2
    variable = massfrac1
    gravity = '-1 -0.1 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0 massfrac1'
    number_fluid_phases = 1
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      density0 = 1
      thermal_expansion = 0
      viscosity = 1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac0 massfrac1'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0 0 2 0 0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Preconditioning]
  active = check
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000'
  []
  [check]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  exodus = false
[]

(modules/navier_stokes/test/tests/finite_element/ins/bcs/advection_bc/advection_bc.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 10.0
  nx = 100
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./vx]
  [../]

  [./force]
  [../]
[]

[ICs]
  [./vx]
    type = FunctionIC
    variable = vx
    function = vx_function
  [../]

  [./force]
    type = FunctionIC
    variable = force
    function = forcing
  [../]
[]

[Kernels]
  [./advection]
    type = MassConvectiveFlux
    variable = phi
    vel_x = vx
  [../]

  [./rhs]
    type = CoupledForce
    variable = phi
    v = force
  [../]
[]

[BCs]
  [./inflow_enthalpy]
    type = DirichletBC
    variable = phi
    boundary = 'left'
    value = 1
  [../]

  [./outflow_term]
    type = AdvectionBC
    variable = phi
    velocity_vector = 'vx'
    boundary = 'right'
  [../]
[]

[Functions]
  [./vx_function]
    type = ParsedFunction
    value = '1 + x * x'
  [../]

  [./forcing]
    type = ParsedFunction
    value = 'x'
  [../]

  [./analytical]
    type = ParsedFunction
    value = '(1 + 0.5 * x * x) / (1 + x * x)'
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = analytical
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/richards/test/tests/buckley_leverett/bl20_lumped.i)

# two-phase version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 30
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '0.1 0.5 0.5 1 2  4'
    x = '0   0.1 1   5 40 42'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./w_aux_seff]
  [../]
[]



[Kernels]
  [./richardstwater]
    type = RichardsLumpedMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsLumpedMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]

[AuxKernels]
  [./w_aux_seff_auxk]
    type = RichardsSeffAux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
    variable = w_aux_seff
  [../]
[]


[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_water
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_gas
  [../]
[]

[BCs]
  [./left_w]
    type = DirichletBC
    variable = pwater
    boundary = left
    value = 1E6
  [../]
  [./left_g]
    type = DirichletBC
    variable = pgas
    boundary = left
    value = 1000
  [../]
  [./right_w]
    type = DirichletBC
    variable = pwater
    boundary = right
    value = -300000
  [../]
  [./right_g]
    type = DirichletBC
    variable = pgas
    boundary = right
    value = 0
  [../]
[]


[Functions]
  [./initial_water]
    type = ParsedFunction
    value = 1000000*(1-min(x/5,1))-if(x<5,0,300000)
  [../]
  [./initial_gas]
    type = ParsedFunction
    value = 1000
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    viscosity = '1E-3 1E-6'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'standard'

  [./bounded]
  # must use --use-petsc-dm command line argument
    type = SMP
    full = true
    petsc_options_iname = '-snes_type   -pc_factor_shift_type'
    petsc_options_value = 'vinewtonssls nonzero'
  [../]

  [./standard]
    type = SMP
    full = true
    petsc_options_iname = '-pc_factor_shift_type'
    petsc_options_value = 'nonzero'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 50

  nl_rel_tol = 1.e-9
  nl_max_its = 10

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  file_base = bl20_lumped
  execute_on = 'initial timestep_end final'
  interval = 100000
  exodus = true
  hide = pgas
  [./console_out]
    type = Console
    interval = 1
  [../]
[]

(modules/navier_stokes/test/tests/finite_element/ins/bcs/advection_bc/2d_advection_bc.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10.0
  ymax = 10
  nx = 10
  ny = 10
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./vx]
  [../]

  [./force]
  [../]
[]

[ICs]
  [./vx]
    type = FunctionIC
    variable = vx
    function = vx_function
  [../]

  [./force]
    type = FunctionIC
    variable = force
    function = forcing
  [../]
[]

[Kernels]
  [./advection]
    type = MassConvectiveFlux
    variable = phi
    vel_x = vx
  [../]

  [./rhs]
    type = CoupledForce
    variable = phi
    v = force
  [../]
[]

[BCs]
  [./inflow_enthalpy]
    type = DirichletBC
    variable = phi
    boundary = 'left'
    value = 1
  [../]

  [./outflow_term]
    type = AdvectionBC
    variable = phi
    velocity_vector = 'vx'
    boundary = 'right'
  [../]
[]

[Functions]
  [./vx_function]
    type = ParsedFunction
    value = '1 + x * x'
  [../]

  [./forcing]
    type = ParsedFunction
    value = 'x'
  [../]

  [./analytical]
    type = ParsedFunction
    value = '(1 + 0.5 * x * x) / (1 + x * x)'
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = analytical
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/porous_flow/test/tests/sinks/s02.i)

# apply a sink flux with use_mobility=true and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = y+1
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '0.2 0 0 0 0.1 0 0 0 0.1'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[AuxVariables]
  [flux_out]
  []
  [xval]
  []
  [yval]
  []
[]

[ICs]
  [xval]
    type = FunctionIC
    variable = xval
    function = x
  []
  [yval]
    type = FunctionIC
    variable = yval
    function = y
  []
[]

[Functions]
  [mass00]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)'
    vars = 'vol por dens0 pp bulk'
    vals = '0.25 0.1 1.1 p00 1.3'
  []
  [mass01]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)'
    vars = 'vol por dens0 pp bulk'
    vals = '0.25 0.1 1.1 p01 1.3'
  []
  [expected_mass_change00]
    type = ParsedFunction
    value = 'fcn*perm*dens0*exp(pp/bulk)/visc*area*dt'
    vars = 'fcn perm dens0 pp bulk visc area dt'
    vals = '6   0.2  1.1  p00 1.3  1.1  0.5  1E-3'
  []
  [expected_mass_change01]
    type = ParsedFunction
    value = 'fcn*perm*dens0*exp(pp/bulk)/visc*area*dt'
    vars = 'fcn perm dens0 pp bulk visc area dt'
    vals = '6   0.2  1.1  p01 1.3  1.1  0.5  1E-3'
  []
  [mass00_expect]
    type = ParsedFunction
    value = 'mass_prev-mass_change'
    vars = 'mass_prev mass_change'
    vals = 'm00_prev  del_m00'
  []
  [mass01_expect]
    type = ParsedFunction
    value = 'mass_prev-mass_change'
    vars = 'mass_prev mass_change'
    vals = 'm01_prev  del_m01'
  []
[]

[Postprocessors]
  [p00]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m00]
    type = FunctionValuePostprocessor
    function = mass00
    execute_on = 'initial timestep_end'
  []
  [m00_prev]
    type = FunctionValuePostprocessor
    function = mass00
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [del_m00]
    type = FunctionValuePostprocessor
    function = expected_mass_change00
    execute_on = 'timestep_end'
    outputs = 'console'
  []
  [m00_expect]
    type = FunctionValuePostprocessor
    function = mass00_expect
    execute_on = 'timestep_end'
  []
  [p10]
    type = PointValue
    point = '1 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p01]
    type = PointValue
    point = '0 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m01]
    type = FunctionValuePostprocessor
    function = mass01
    execute_on = 'initial timestep_end'
  []
  [m01_prev]
    type = FunctionValuePostprocessor
    function = mass01
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [del_m01]
    type = FunctionValuePostprocessor
    function = expected_mass_change01
    execute_on = 'timestep_end'
    outputs = 'console'
  []
  [m01_expect]
    type = FunctionValuePostprocessor
    function = mass01_expect
    execute_on = 'timestep_end'
  []
  [p11]
    type = PointValue
    point = '1 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [flux]
    type = PorousFlowSink
    boundary = 'left'
    variable = pp
    use_mobility = true
    use_relperm = true
    fluid_phase = 0
    flux_function = 6
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10000 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-3
  end_time = 0.03
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s02
  [console]
    type = Console
    execute_on = 'nonlinear linear'
    interval = 30
  []
  [csv]
    type = CSV
    execute_on = 'timestep_end'
    interval = 3
  []
[]

(modules/combined/examples/phase_field-mechanics/interface_stress.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 50
  ny = 50
  nz = 50
  xmax = 10
  ymax = 10
  zmax = 10
  xmin = -10
  ymin = -10
  zmin = -10
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Functions]
  [./sphere]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2+z^2); R:=(4.0-r)/2.0; if(R>1,1,if(R<0,0,3*R^2-2*R^3))'
  [../]
[]

[AuxVariables]
  [./eta]
    [./InitialCondition]
      type = FunctionIC
      function = sphere
    [../]
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    add_variables = true
    generate_output = 'hydrostatic_stress stress_xx'
  [../]
[]

[Materials]
  [./ym]
    type = DerivativeParsedMaterial
    f_name = ym
    function = (1-eta)*7+0.5
    args = eta
  [../]
  [./elasticity]
    type = ComputeVariableIsotropicElasticityTensor
    poissons_ratio = 0.45
    youngs_modulus = ym
    args = eta
  [../]

  [./stress]
    type = ComputeLinearElasticStress
  [../]
  [./interface]
    type = ComputeInterfaceStress
    v = eta
    stress = 1.0
  [../]
[]

[VectorPostprocessors]
  [./line]
    type = SphericalAverage
    variable = 'hydrostatic_stress'
    radius = 10
    bin_number = 40
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/heat_conduction/test/tests/verify_against_analytical/1D_transient.i)

# This test solves a 1D transient heat equation
# The error is caclulated by comparing to the analytical solution
# The problem setup and analytical solution are taken from "Advanced Engineering
# Mathematics, 10th edition" by Erwin Kreyszig.
# http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364
# It is Example 1 in section 12.6 on page 561

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 160
  xmax = 80
[]

[Variables]
  [./T]
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '100*sin(pi*x/80)'
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = HeatConduction
    variable = T
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = T
  [../]
[]

[BCs]
  [./sides]
    type = DirichletBC
    variable = T
    boundary = 'left right'
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '0.95' #copper in cal/(cm sec C)
  [../]
  [./cp]
    type = GenericConstantMaterial
    prop_names = 'specific_heat'
    prop_values = '0.092' #copper in cal/(g C)
  [../]
  [./rho]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = '8.92' #copper in g/(cm^3)
  [../]
[]

[Postprocessors]
  [./error]
    type = NodalL2Error
    function = '100*sin(pi*x/80)*exp(-0.95/(0.092*8.92)*pi^2/80^2*t)'
    variable = T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  l_tol = 1e-6
  dt = 2
  end_time = 100
[]

[Outputs]
  exodus = true
[]

(test/tests/userobjects/shape_element_user_object/shape_side_uo_physics_test.i)

u_left = 0.5

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pot]
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./adv_u]
    type = PotentialAdvection
    variable = u
    potential = pot
  [../]
  [./diff_pot]
    type = Diffusion
    variable = pot
  [../]
[]

[BCs]
  [./left]
    boundary = left
    type = DirichletBC
    value = ${u_left}
    variable = u
  [../]
  [./right]
    boundary = right
    type = DirichletBC
    variable = u
    value = 0
  [../]

  [./left_pot]
    boundary = left
    type = ExampleShapeSideIntegratedBC
    variable = pot
    num_user_object = num_user_object
    denom_user_object = denom_user_object
    v = u
    Vb = 1
  [../]
  [./right_pot]
    boundary = right
    type = DirichletBC
    variable = pot
    value = 0
  [../]
[]

[UserObjects]
  [./num_user_object]
    type = NumShapeSideUserObject
    u = u
    boundary = left
    execute_on = 'linear nonlinear'
  [../]
  [./denom_user_object]
    type = DenomShapeSideUserObject
    u = u
    boundary = left
    execute_on = 'linear nonlinear'
  [../]
[]

[AuxVariables]
  [./u_flux]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./u_flux]
    type = DriftDiffusionFluxAux
    variable = u_flux
    u = u
    potential = pot
    component = 0
  [../]
[]

[Problem]
  type = FEProblem
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady

  solve_type = NEWTON
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_linesearch_monitor'
  petsc_options_iname = '-pc_type -sub_pc_type -sub_ksp_type'
  petsc_options_value = 'asm      lu           preonly'
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

[ICs]
  [./u]
    type = FunctionIC
    variable = u
    function = ic_u
  [../]
  [./pot]
    type = FunctionIC
    variable = pot
    function = ic_pot
  [../]
[]

[Functions]
  [./ic_u]
    type = ParsedFunction
    value = '${u_left} * (1 - x)'
  [../]
  [./ic_pot]
    type = ParsedFunction
    value = '1 - x'
  [../]
[]

(modules/phase_field/examples/interfacekernels/interface_fluxbc.i)

#
# This test demonstrates an InterfaceKernel (InterfaceDiffusionFlux) that can
# replace a pair of integrated DiffusionFluxBC boundary conditions.
#
# The AuxVariable 'diff' shows the difference between the BC and the InterfaceKernel
# approach.
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
  []
  [./box1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.51 1 0'
  [../]
  [./box2]
    input = box1
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.49 0 0'
    top_right = '1 1 0'
  [../]
  [./iface_u]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = 10
    input = box2
  [../]
  [./iface_v]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 1
    new_boundary = 11
    input = iface_u
  [../]
[]

[Variables]
  [./u1]
    block = 1
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.4)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
  [./v1]
    block = 2
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.7)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
  [./u2]
    block = 1
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.4)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
  [./v2]
    block = 2
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.7)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
[]

[Kernels]
  [./u1_diff]
    type = Diffusion
    variable = u1
    block = 1
  [../]
  [./u1_dt]
    type = TimeDerivative
    variable = u1
    block = 1
  [../]
  [./v1_diff]
    type = Diffusion
    variable = v1
    block = 2
  [../]
  [./v1_dt]
    type = TimeDerivative
    variable = v1
    block = 2
  [../]

  [./u2_diff]
    type = Diffusion
    variable = u2
    block = 1
  [../]
  [./u2_dt]
    type = TimeDerivative
    variable = u2
    block = 1
  [../]
  [./v2_diff]
    type = Diffusion
    variable = v2
    block = 2
  [../]
  [./v2_dt]
    type = TimeDerivative
    variable = v2
    block = 2
  [../]
[]

[AuxVariables]
  [./diff]
  [../]
[]

[AuxKernels]
  [./u_side]
    type = ParsedAux
    variable = diff
    block = 1
    args = 'u1 u2'
    function = 'u1 - u2'
  [../]
  [./v_side]
    type = ParsedAux
    variable = diff
    block = 2
    args = 'v1 v2'
    function = 'v1 - v2'
  [../]
[]

[InterfaceKernels]
  [./iface]
    type = InterfaceDiffusionBoundaryTerm
    boundary = 10
    variable = u2
    neighbor_var = v2
  [../]
[]

[BCs]
  [./u_boundary_term]
    type = DiffusionFluxBC
    variable = u1
    boundary = 10
  [../]
  [./v_boundary_term]
    type = DiffusionFluxBC
    variable = v1
    boundary = 11
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.001
  num_steps = 20
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/phase_field/examples/fourier_noise.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 100
[]

[Variables]
  [./c]
  [../]
[]

[Functions]
  [./fn]
    type = FourierNoise
    lambda = 0.1
  [../]
[]

[ICs]
  [./c]
    type = FunctionIC
    variable = c
    function = fn
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/relperm/vangenuchten2.i)

# Test van Genuchten relative permeability curve by varying saturation over the mesh
# van Genuchten exponent m = 0.4 for both phases
# Phase 0 residual saturation s0r = 0.1
# Phase 1 residual saturation s1r = 0.2

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.4
    s_res = 0.1
    sum_s_res = 0.3
  []
  [kr1]
    type = PorousFlowRelativePermeabilityVG
    phase = 1
    m = 0.4
    s_res = 0.2
    sum_s_res = 0.3
    wetting = false
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-7
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/jacobian/basic_advection1.i)

# Basic advection with no PorousFlow variables
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = RandomIC
    variable = u
  []
[]

[Kernels]
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 4
      thermal_expansion = 0
      viscosity = 150.0
    []
  []
[]

[Materials]
  [temperature_qp]
    type = PorousFlowTemperature
  []
  [ppss_qp]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid_qp]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm_qp]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity_qp]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[Preconditioning]
  [check]
    type = SMP
    full = true
    #petsc_options = '-snes_test_display'
    petsc_options_iname = '-snes_type'
    petsc_options_value = ' test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
[]

(modules/phase_field/test/tests/MultiPhase/crosstermbarrierfunction.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 200
  xmin = 0
  xmax = 9
[]

[Functions]
  [./func1]
    type = ParsedFunction
    value = 'il:=x-7; ir:=2-x; if(x<1, 1,
                               if(x<2, 0.5-0.5*cos(ir*pi),
                               if(x<7, 0,
                               if(x<8, 0.5-0.5*cos(il*pi),
                               1))))'
  [../]
  [./func2]
    type = ParsedFunction
    value = 'il:=x-1; ir:=5-x; if(x<1, 0,
                               if(x<2, 0.5-0.5*cos(il*pi),
                               if(x<4, 1,
                               if(x<5, 0.5-0.5*cos(ir*pi),
                               0))))'
  [../]
  [./func3]
    type = ParsedFunction
    value = 'il:=x-4; ir:=8-x; if(x<4, 0,
                               if(x<5, 0.5-0.5*cos(il*pi),
                               if(x<7, 1,
                               if(x<8, 0.5-0.5*cos(ir*pi),
                               0))))'
  [../]
[]

[AuxVariables]
  [./eta1]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = func1
    [../]
  [../]
  [./eta2]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = func2
    [../]
  [../]
  [./eta3]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = func3
    [../]
  [../]
[]

[Materials]
  [./crosstermbarrier_simple]
    type = CrossTermBarrierFunctionMaterial
    etas = 'eta1 eta2 eta3'
    W_ij = '0   1   2.2
            1   0   3.1
            2.2 3.1 0'
    function_name = gsimple
    g_order = SIMPLE
    outputs = exodus
  [../]
  [./crosstermbarrier_low]
    type = CrossTermBarrierFunctionMaterial
    etas = 'eta1 eta2 eta3'
    W_ij = '0   1   2.2
            1   0   3.1
            2.2 3.1 0'
    function_name = glow
    g_order = LOW
    outputs = exodus
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  num_steps = 1
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

[Outputs]
  exodus = true
  execute_on = final
[]

(test/tests/variables/side_hierarchic/side_hierarchic.i)

[Problem]
  solve = false
[]

[Mesh]
  type = GeneratedMesh
  elem_type = QUAD9
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [./side_var]
    order = CONSTANT
    family = SIDE_HIERARCHIC
  [../]
[]

[AuxVariables]
  [./aux_side_var]
    order = FIRST
    family = SIDE_HIERARCHIC
  [../]
[]


[Functions]
  [./nl_var]
    type = ParsedFunction
    value = 'x+y+1'
  [../]
  [./aux_var]
    type = ParsedFunction
    value = 'x-y+10'
  [../]
[]

[ICs]
  [./side_nl]
    type = FunctionIC
    variable = side_var
    function = nl_var
  [../]
  [./side_aux]
    type = FunctionIC
    variable = aux_side_var
    function = aux_var
  [../]
[]

[Outputs]
  exodus = true
[]

[Executioner]
  type = Steady
[]

(test/tests/bcs/sin_bc/sin_dirichlet_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  nz = 0
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Functions]
  [./initial_value]
    type = ParsedFunction
    value = 'x'
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = initial_value
    [../]
  [../]
[]

[Kernels]
  active = 'diff ie'

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ie]
    type = TimeDerivative
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = SinDirichletBC
    variable = u
    boundary = 3
    initial = 0.0
    final = 1.0
    duration = 10.0
  [../]

  [./right]
    type = SinDirichletBC
    variable = u
    boundary = 1
    initial = 1.0
    final = 0.0
    duration = 10.0
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  num_steps = 10
  dt = 1.0
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/sinks/s03.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[AuxVariables]
  [./seff]
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 2
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-lfout-rfout-mf)/2/(mi+mf))
    vars = 'mi mf lfout rfout'
    vals = 'mass_init mass_fin left_flux_out right_flux_out'
  [../]
[]

[Postprocessors]
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]
  [./mass_fin]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]
  [./left_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = left
    variable = pressure
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    use_mobility = true
    use_relperm = true
  [../]
  [./right_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = right
    variable = pressure
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    use_mobility = true
    use_relperm = true
  [../]
  [./p0]
    type = PointValue
    point = '0 0 0'
    variable = pressure
  [../]
  [./s0]
    type = PointValue
    point = '0 0 0'
    variable = seff
  [../]
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]

[BCs]
  [./left_flux]
    type = RichardsPiecewiseLinearSink
    boundary = left
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    variable = pressure
    use_mobility = true
    use_relperm = true
  [../]
  [./right_flux]
    type = RichardsPiecewiseLinearSink
    boundary = right
    pressures = '-1 1'
    bare_fluxes = '1E2 2E2'
    variable = pressure
    use_mobility = true
    use_relperm = true
  [../]
[]

[Kernels]
  active = 'richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
[]

[AuxKernels]
  [./seff_auxk]
    type = RichardsSeffAux
    variable = seff
    seff_UO = SeffVG
    pressure_vars = 'pressure'
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 2.1E-5 2.2E-5  2.1E-5 0.1E-5 3.3E-5  2.2E-5 3.3E-5 2E-5'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2E-3
  end_time = 0.2
[]

[Outputs]
  file_base = s03
  csv = true
  execute_on = timestep_end
[]

(modules/chemical_reactions/test/tests/aqueous_equilibrium/2species_eqaux.i)

# In this example, two primary species a and b are transported by diffusion and convection
# from the left of the porous medium, reacting to form two equilibrium species pa2 and pab
# according to the equilibrium reaction specified in the AqueousEquilibriumReactions block as:
#
#      reactions = '2a = pa2     2
#                   a + b = pab -2'
#
# where the 2 is the weight of the equilibrium species, the 2 on the RHS of the first reaction
# refers to the equilibrium constant (log10(Keq) = 2), and the -2 on the RHS of the second
# reaction equates to log10(Keq) = -2.
#
# This example is identical to 2species.i, except that it explicitly includes all AuxKernels
# and Kernels that are set up by the action in 2species.i, and that the equilbrium constants
# are provided by AuxVariables

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
[]

[Variables]
  [./a]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    [../]
  [../]
  [./b]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    [../]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pa2]
  [../]
  [./pab]
  [../]
  [./pa2_logk]
    initial_condition = 2
  [../]
  [./pab_logk]
    initial_condition = -2
  [../]
[]

[AuxKernels]
  [./pa2eq]
    type = AqueousEquilibriumRxnAux
    variable = pa2
    v = a
    sto_v = 2
    log_k = pa2_logk
  [../]
  [./pabeq]
    type = AqueousEquilibriumRxnAux
    variable = pab
    v = 'a b'
    sto_v = '1 1'
    log_k = pab_logk
  [../]
[]

[ICs]
  [./pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  [../]
[]

[Kernels]
  [./a_ie]
    type = PrimaryTimeDerivative
    variable = a
  [../]
  [./a_diff]
    type = PrimaryDiffusion
    variable = a
  [../]
  [./a_conv]
    type = PrimaryConvection
    variable = a
    p = pressure
  [../]
  [./b_ie]
    type = PrimaryTimeDerivative
    variable = b
  [../]
  [./b_diff]
    type = PrimaryDiffusion
    variable = b
  [../]
  [./b_conv]
    type = PrimaryConvection
    variable = b
    p = pressure
  [../]
  [./a1eq]
    type = CoupledBEEquilibriumSub
    variable = a
    log_k = pa2_logk
    weight = 2
    sto_u = 2
  [../]
  [./a1diff]
    type = CoupledDiffusionReactionSub
    variable = a
    log_k = pa2_logk
    weight = 2
    sto_u = 2
  [../]
  [./a1conv]
    type = CoupledConvectionReactionSub
    variable = a
    log_k = pa2_logk
    weight = 2
    sto_u = 2
    p = pressure
  [../]
  [./a2eq]
    type = CoupledBEEquilibriumSub
    variable = a
    v = b
    log_k = pab_logk
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./a2diff]
    type = CoupledDiffusionReactionSub
    variable = a
    v = b
    log_k = pab_logk
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./a2conv]
    type = CoupledConvectionReactionSub
    variable = a
    v = b
    log_k = pab_logk
    weight = 1
    sto_v = 1
    sto_u = 1
    p = pressure
  [../]
  [./b2eq]
    type = CoupledBEEquilibriumSub
    variable = b
    v = a
    log_k = pab_logk
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./b2diff]
    type = CoupledDiffusionReactionSub
    variable = b
    v = a
    log_k = pab_logk
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./b2conv]
    type = CoupledConvectionReactionSub
    variable = b
    v = a
    log_k = pab_logk
    weight = 1
    sto_v = 1
    sto_u = 1
    p = pressure
  [../]
[]

[BCs]
  [./a_left]
    type = DirichletBC
    variable = a
    boundary = left
    value = 1.0e-2
  [../]
  [./a_right]
    type = ChemicalOutFlowBC
    variable = a
    boundary = right
  [../]
  [./b_left]
    type = DirichletBC
    variable = b
    boundary = left
    value = 1.0e-2
  [../]
  [./b_right]
    type = ChemicalOutFlowBC
    variable = b
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-4 1e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-12
  start_time = 0.0
  end_time = 100
  dt = 10.0
[]

[Outputs]
  file_base = 2species_out
  exodus = true
  perf_graph = true
  print_linear_residuals = true
  hide = 'pa2_logk pab_logk'
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

(modules/thermal_hydraulics/test/tests/utils/smooth_transition/ad_smooth_transition.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -2
  xmax = 2
[]

[Variables]
  [u]
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    variable = u
    function = u_ic_fn
  []
[]

[Functions]
  [u_ic_fn]
    type = ParsedFunction
    value = 'x'
  []
[]

[Materials]
  [test_mat]
    type = ADSmoothTransitionTestMaterial
    transition_type = weighted
    var = u
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[VectorPostprocessors]
  [test_vpp]
    type = ADSampler1DReal
    block = 0
    property = myadmatprop
    sort_by = x
    execute_on = 'INITIAL'
  []
[]

[Outputs]
  csv = true
  file_base = 'ad_weighted'
  execute_on = 'INITIAL'
[]

(test/tests/scaling/residual-based/residual-based.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = '1000 * (1 - x)'
  []
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [rxn]
    type = PReaction
    power = 2
    variable = u
  []
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 1000
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 0
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  verbose = true
  automatic_scaling = true
  resid_vs_jac_scaling_param = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/time_integrators/explicit-euler/ee-1d-quadratic.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 20
  elem_type = EDGE3
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x*x-2*t
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x*x
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
#    lumping = true
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[BCs]
  active = 'all'

  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1'
    function = exact_fn
    implicit = true
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'explicit-euler'
  solve_type = 'LINEAR'

  l_tol = 1e-12
  start_time = 0.0
  num_steps = 20
  dt = 0.00005
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(test/tests/fvkernels/fv_burgers/fv_burgers.i)

[Mesh]
  [./gen_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 10
    nx = 50
  [../]
[]

[Variables]
  [./v]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  [../]
[]

[ICs]
  [./v_ic]
    type = FunctionIC
    variable = v
    function = 'if (x > 2 & x < 3, 0.5, 0)'
  [../]
[]

[FVKernels]
  [./burgers]
    type = FVBurgers1D
    variable = v
  [../]
  [./time]
    type = FVTimeKernel
    variable = v
  [../]
[]

[FVBCs]
  [./fv_burgers_outflow]
    type = FVBurgersOutflowBC
    variable = v
    boundary = 'left right'
  [../]
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  petsc_options = '-snes_converged_reason'
  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-8
  num_steps = 5
  dt = 0.05
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_pflow/pffltvd_2D.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, employing PorousFlow Kernels and UserObjects, with superbee flux-limiter
# 3D version
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  xmin = 0
  xmax = 1
  ny = 4
  ymin = 0
  ymax = 0.5
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0.5 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/phase_field/examples/multiphase/GrandPotential3Phase.i)

# This is an example of implementation of the multi-phase, multi-order parameter
# grand potential based phase-field model described in Phys. Rev. E, 98, 023309
# (2019). It includes 3 phases with 1 grain of each phase. This example was used
# to generate the results shown in Fig. 3 of the paper.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 60
  xmin = -15
  xmax = 15
[]

[Variables]
  [./w]
  [../]
  [./etaa0]
  [../]
  [./etab0]
  [../]
  [./etad0]
  [../]
[]

[ICs]
  [./IC_etaa0]
    type = FunctionIC
    variable = etaa0
    function = ic_func_etaa0
  [../]
  [./IC_etab0]
    type = FunctionIC
    variable = etab0
    function = ic_func_etab0
  [../]
  [./IC_etad0]
    type = ConstantIC
    variable = etad0
    value = 0.1
  [../]
  [./IC_w]
    type = FunctionIC
    variable = w
    function = ic_func_w
  [../]
[]

[Functions]
  [./ic_func_etaa0]
    type = ParsedFunction
    value = '0.9*0.5*(1.0-tanh((x)/sqrt(2.0)))'
  [../]
  [./ic_func_etab0]
    type = ParsedFunction
    value = '0.9*0.5*(1.0+tanh((x)/sqrt(2.0)))'
  [../]
  [./ic_func_w]
    type = ParsedFunction
    value = 0
  [../]
[]

[Kernels]
# Order parameter eta_alpha0
  [./ACa0_bulk]
    type = ACGrGrMulti
    variable = etaa0
    v =           'etab0 etad0'
    gamma_names = 'gab   gad'
  [../]
  [./ACa0_sw]
    type = ACSwitching
    variable = etaa0
    Fj_names  = 'omegaa omegab omegad'
    hj_names  = 'ha     hb     hd'
    args = 'etab0 etad0 w'
  [../]
  [./ACa0_int]
    type = ACInterface
    variable = etaa0
    kappa_name = kappa
  [../]
  [./ea0_dot]
    type = TimeDerivative
    variable = etaa0
  [../]
# Order parameter eta_beta0
  [./ACb0_bulk]
    type = ACGrGrMulti
    variable = etab0
    v =           'etaa0 etad0'
    gamma_names = 'gab   gbd'
  [../]
  [./ACb0_sw]
    type = ACSwitching
    variable = etab0
    Fj_names  = 'omegaa omegab omegad'
    hj_names  = 'ha     hb     hd'
    args = 'etaa0 etad0 w'
  [../]
  [./ACb0_int]
    type = ACInterface
    variable = etab0
    kappa_name = kappa
  [../]
  [./eb0_dot]
    type = TimeDerivative
    variable = etab0
  [../]
# Order parameter eta_delta0
  [./ACd0_bulk]
    type = ACGrGrMulti
    variable = etad0
    v =           'etaa0 etab0'
    gamma_names = 'gad   gbd'
  [../]
  [./ACd0_sw]
    type = ACSwitching
    variable = etad0
    Fj_names  = 'omegaa omegab omegad'
    hj_names  = 'ha     hb     hd'
    args = 'etaa0 etab0 w'
  [../]
  [./ACd0_int]
    type = ACInterface
    variable = etad0
    kappa_name = kappa
  [../]
  [./ed0_dot]
    type = TimeDerivative
    variable = etad0
  [../]
#Chemical potential
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
    args = 'etaa0 etab0 etad0'
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = Dchi
    args = ''
  [../]
  [./coupled_etaa0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etaa0
    Fj_names = 'rhoa rhob rhod'
    hj_names = 'ha   hb   hd'
    args = 'etaa0 etab0 etad0'
  [../]
  [./coupled_etab0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab0
    Fj_names = 'rhoa rhob rhod'
    hj_names = 'ha   hb   hd'
    args = 'etaa0 etab0 etad0'
  [../]
  [./coupled_etad0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etad0
    Fj_names = 'rhoa rhob rhod'
    hj_names = 'ha   hb   hd'
    args = 'etaa0 etab0 etad0'
  [../]
[]

[Materials]
  [./ha_test]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = ha
    all_etas = 'etaa0 etab0 etad0'
    phase_etas = 'etaa0'
  [../]
  [./hb_test]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hb
    all_etas = 'etaa0 etab0 etad0'
    phase_etas = 'etab0'
  [../]
  [./hd_test]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hd
    all_etas = 'etaa0 etab0 etad0'
    phase_etas = 'etad0'
  [../]
  [./omegaa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegaa
    material_property_names = 'Vm ka caeq'
    function = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
    derivative_order = 2
  [../]
  [./omegab]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegab
    material_property_names = 'Vm kb cbeq'
    function = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
    derivative_order = 2
  [../]
  [./omegad]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegad
    material_property_names = 'Vm kd cdeq'
    function = '-0.5*w^2/Vm^2/kd-w/Vm*cdeq'
    derivative_order = 2
  [../]
  [./rhoa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhoa
    material_property_names = 'Vm ka caeq'
    function = 'w/Vm^2/ka + caeq/Vm'
    derivative_order = 2
  [../]
  [./rhob]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhob
    material_property_names = 'Vm kb cbeq'
    function = 'w/Vm^2/kb + cbeq/Vm'
    derivative_order = 2
  [../]
  [./rhod]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhod
    material_property_names = 'Vm kd cdeq'
    function = 'w/Vm^2/kd + cdeq/Vm'
    derivative_order = 2
  [../]
  [./c]
    type = ParsedMaterial
    material_property_names = 'Vm rhoa rhob rhod ha hb hd'
    function = 'Vm * (ha * rhoa + hb * rhob + hd * rhod)'
    f_name = c
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'kappa_c  kappa   L   D    Vm   ka    caeq kb    cbeq  kd    cdeq  gab gad gbd  mu  tgrad_corr_mult'
    prop_values = '0        1       1.0 1.0  1.0  10.0  0.1  10.0  0.9   10.0  0.5   1.5 1.5 1.5  1.0 0.0'
  [../]
  [./Mobility]
    type = DerivativeParsedMaterial
    f_name = Dchi
    material_property_names = 'D chi'
    function = 'D*chi'
    derivative_order = 2
  [../]
  [./chi]
    type = DerivativeParsedMaterial
    f_name = chi
    material_property_names = 'Vm ha(etaa0,etab0,etad0) ka hb(etaa0,etab0,etad0) kb hd(etaa0,etab0,etad0) kd'
    function = '(ha/ka + hb/kb + hd/kd) / Vm^2'
    args = 'etaa0 etab0 etad0'
    derivative_order = 2
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[VectorPostprocessors]
  [./etaa0]
    type = LineValueSampler
    variable = etaa0
    start_point = '-15 0 0'
    end_point = '15 0 0'
    num_points = 61
    sort_by = x
    execute_on = 'initial timestep_end final'
  [../]
  [./etab0]
    type = LineValueSampler
    variable = etab0
    start_point = '-15 0 0'
    end_point = '15 0 0'
    num_points = 61
    sort_by = x
    execute_on = 'initial timestep_end final'
  [../]
  [./etad0]
    type = LineValueSampler
    variable = etad0
    start_point = '-15 0 0'
    end_point = '15 0 0'
    num_points = 61
    sort_by = x
    execute_on = 'initial timestep_end final'
  [../]
[]

[Executioner]
  type = Transient
  nl_max_its = 15
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = -pc_type
  petsc_options_value = asm
  l_max_its = 15
  l_tol = 1.0e-3
  nl_rel_tol = 1.0e-8
  start_time = 0.0
  num_steps = 20
  nl_abs_tol = 1e-10
  dt = 1.0
[]

[Outputs]
  [./exodus]
    type = Exodus
    execute_on = 'initial timestep_end final'
    interval = 1
  [../]
  [./csv]
    type = CSV
    execute_on = 'initial timestep_end final'
    interval = 1
  [../]
[]

(modules/phase_field/test/tests/GBAnisotropy/testwidth1.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 30
  ny = 2
  nz = 0
  xmin = -500
  xmax = 1000
  ymin = 0
  ymax = 100
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[GlobalParams]
  op_num = 3
  var_name_base = gr
  length_scale = 1.0e-9
  time_scale = 1.0e-9
[]

[Variables]
  [./PolycrystalVariables]
  [../]
[]

[Functions]
  [./ic_func_eta1]
    type = ParsedFunction
    value = '0.5*(1.0-tanh((x)*sqrt(m/kappa/2.0)))'
    vars = 'm kappa'
    vals = '0.26514 331.414'
  [../]
  [./ic_func_eta2]
    type = ParsedFunction
    value = '0.5*(1.0+tanh((x)*sqrt(m/kappa/2.0)))*0.5*(1.0-tanh((x-500)*sqrt(m/kappa/2.0)))'
    vars = 'm kappa'
    vals = '0.26514 331.414'
  [../]
  [./ic_func_eta3]
    type = ParsedFunction
    value = '0.5*(1.0+tanh((x-500)*sqrt(m/kappa/2.0)))'
    vars = 'm kappa'
    vals = '0.26514 331.414'
  [../]
[]

[ICs]
  [./eta1_ic]
    variable = gr0
    type = FunctionIC
    function = ic_func_eta1
  [../]
  [./eta2_ic]
    variable = gr1
    type = FunctionIC
    function = ic_func_eta2
  [../]
  [./eta3_ic]
    variable = gr2
    type = FunctionIC
    function = ic_func_eta3
  [../]
[]

[AuxVariables]
  [./bnds]
    order = FIRST
    family = LAGRANGE
  [../]
  [./unique_grains]
    order = FIRST
    family = LAGRANGE
  [../]
  [./var_indices]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./PolycrystalKernel]
  [../]
[]

[AuxKernels]
  [./bnds_aux]
    type = BndsCalcAux
    variable = bnds
    execute_on = timestep_end
  [../]
[]

[Materials]
  [./CuGrGranisotropic]
    type = GBWidthAnisotropy
    kappa = 331.414
    mu = 0.26514
    T = 600 # K

    # molar_volume_value = 7.11e-6 #Units:m^3/mol
    Anisotropic_GB_file_name = anisotropy_energy.txt
    inclination_anisotropy = false # true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 31'

  l_max_its = 30
  l_tol = 1e-4
  nl_max_its = 40
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-11

  num_steps = 2

  dt = 10
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(modules/richards/test/tests/buckley_leverett/bl21.i)

# two-phase version
# sharp front version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1E-3 1E-2 3E-2 4E-2 0.5 0.5 1'
    x = '0    1E-2 1E-1 1    5   40  41'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 3E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 3E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
  [./bounds_dummy]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
  [./richardsppenalty]
    type = RichardsPPenalty
    variable = pgas
    a = 1E-18
    lower_var = pwater
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[Bounds]
  [./pwater_upper_bounds]
    type = ConstantBoundsAux
    variable = bounds_dummy
    bounded_variable = pwater
    bound_type = upper
    bound_value = 1E7
  [../]
  [./pwater_lower_bounds]
    type = ConstantBoundsAux
    variable = bounds_dummy
    bounded_variable = pwater
    bound_type = lower
    bound_value = -110000
  [../]
[]


[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_water
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_gas
  [../]
[]

[BCs]
  [./left_w]
    type = DirichletBC
    variable = pwater
    boundary = left
    value = 1E6
  [../]
  [./left_g]
    type = DirichletBC
    variable = pgas
    boundary = left
    value = 1E6+1000
  [../]
  [./right_w]
    type = DirichletBC
    variable = pwater
    boundary = right
    value = -100000
  [../]
  [./right_g]
    type = DirichletBC
    variable = pgas
    boundary = right
    value = 0+1000
  [../]
[]


[Functions]
  [./initial_water]
    type = ParsedFunction
    value = 1000000*(1-min(x/5,1))-100000*(max(x-5,0)/max(abs(x-5),1E-10))
  [../]
  [./initial_gas]
    type = ParsedFunction
    value = max(1000000*(1-x/5),0)+1000
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 1E-6'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'standard'

  [./bounded]
  # must use --use-petsc-dm command line argument
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type -ksp_rtol -ksp_atol'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 50 vinewtonssls 1E-20 1E-20'
  [../]

  [./standard]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 20 1E-20 1E-20'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 50

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  file_base = bl21
  interval = 10000
  exodus = true
[]

(test/tests/functions/image_function/error/check_error.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [tif]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = tif
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/chemical_reactions/examples/calcium_bicarbonate/calcium_bicarbonate.i)

# Example of reactive transport model with precipitation and dissolution.
# Calcium (ca2) and bicarbonate (hco3) reaction to form calcite (CaCO3).
# Models bicarbonate injection following calcium injection, so that a
# moving reaction front forms a calcite precipitation zone. As the front moves,
# the upstream side of the front continues to form calcite via precipitation,
# while at the downstream side, dissolution of the solid calcite occurs.
#
# The reaction network considered is as follows:
# Aqueous equilibrium reactions:
# a)  h+ + hco3- = CO2(aq),             Keq = 10^(6.341)
# b)  hco3- = h+ + CO23-,               Keq = 10^(-10.325)
# c)  ca2+ + hco3- = h+ + CaCO3(aq),    Keq = 10^(-7.009)
# d)  ca2+ + hco3- = cahco3+,           Keq = 10^(-0.653)
# e)  ca2+ = h+ + CaOh+,                Keq = 10^(-12.85)
# f)  - h+ = oh-,                       Keq = 10^(-13.991)
#
# Kinetic reactions
# g)  ca2+ + hco3- = h+ + CaCO3(s),     A = 0.461 m^2/L, k = 6.456542e-2 mol/m^2 s,
#                                       Keq = 10^(1.8487)
#
# The primary chemical species are h+, hco3- and ca2+. The pressure gradient is fixed,
# and a conservative tracer is also included.
#
# This example is taken from:
# Guo et al, A parallel, fully coupled, fully implicit solution to reactive
# transport in porous media using the preconditioned Jacobian-Free Newton-Krylov
# Method, Advances in Water Resources, 53, 101-108 (2013).

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  xmax = 1
  ymax = 0.25
[]

[Variables]
  [./tracer]
  [../]
  [./ca2+]
  [../]
  [./h+]
    initial_condition = 1.0e-7
    scaling = 1e6
  [../]
  [./hco3-]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./pressure_ic]
    type = FunctionIC
    variable = pressure
    function = pic
  [../]
  [./hco3_ic]
    type = BoundingBoxIC
    variable = hco3-
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 5.0e-2
    outside = 1.0e-6
  [../]
  [./ca2_ic]
    type = BoundingBoxIC
    variable = ca2+
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 1.0e-6
    outside = 5.0e-2
  [../]
  [./tracer_ic]
    type = BoundingBoxIC
    variable = tracer
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 1.0
    outside = 0.0
  [../]
[]

[Functions]
  [./pic]
    type = ParsedFunction
    value = 60-50*x
  [../]
[]

[ReactionNetwork]
  [./AqueousEquilibriumReactions]
    primary_species = 'ca2+ hco3- h+'
    secondary_species = 'co2_aq co32- caco3_aq cahco3+ caoh+ oh-'
    pressure = pressure
    reactions = 'h+ + hco3- = co2_aq 6.341,
                 hco3- - h+ = co32- -10.325,
                 ca2+ + hco3- - h+ = caco3_aq -7.009,
                 ca2+ + hco3- = cahco3+ -0.653,
                 ca2+ - h+ = caoh+ -12.85,
                 - h+ = oh- -13.991'
  [../]
  [./SolidKineticReactions]
    primary_species = 'ca2+ hco3- h+'
    kin_reactions = 'ca2+ + hco3- - h+ = caco3_s'
    secondary_species = caco3_s
    log10_keq = 1.8487
    reference_temperature = 298.15
    system_temperature = 298.15
    gas_constant = 8.314
    specific_reactive_surface_area = 4.61e-4
    kinetic_rate_constant = 6.456542e-7
    activation_energy = 1.5e4
  [../]
[]

[Kernels]
  [./tracer_ie]
    type = PrimaryTimeDerivative
    variable = tracer
  [../]
  [./tracer_pd]
    type = PrimaryDiffusion
    variable = tracer
  [../]
  [./tracer_conv]
    type = PrimaryConvection
    variable = tracer
    p = pressure
  [../]
  [./ca2+_ie]
    type = PrimaryTimeDerivative
    variable = ca2+
  [../]
  [./ca2+_pd]
    type = PrimaryDiffusion
    variable = ca2+
  [../]
  [./ca2+_conv]
    type = PrimaryConvection
    variable = ca2+
    p = pressure
  [../]
  [./h+_ie]
    type = PrimaryTimeDerivative
    variable = h+
  [../]
  [./h+_pd]
    type = PrimaryDiffusion
    variable = h+
  [../]
  [./h+_conv]
    type = PrimaryConvection
    variable = h+
    p = pressure
  [../]
  [./hco3-_ie]
    type = PrimaryTimeDerivative
    variable = hco3-
  [../]
  [./hco3-_pd]
    type = PrimaryDiffusion
    variable = hco3-
  [../]
  [./hco3-_conv]
    type = PrimaryConvection
    variable = hco3-
    p = pressure
  [../]
[]

[BCs]
  [./tracer_left]
    type = DirichletBC
    variable = tracer
    boundary = left
    value = 1.0
  [../]
  [./tracer_right]
    type = ChemicalOutFlowBC
    variable = tracer
    boundary = right
  [../]
  [./ca2+_left]
    type = SinDirichletBC
    variable = ca2+
    boundary = left
    initial = 5.0e-2
    final = 1.0e-6
    duration = 1
  [../]
  [./ca2+_right]
    type = ChemicalOutFlowBC
    variable = ca2+
    boundary = right
  [../]
  [./hco3-_left]
    type = SinDirichletBC
    variable = hco3-
    boundary = left
    initial = 1.0e-6
    final = 5.0e-2
    duration = 1
  [../]
  [./hco3-_right]
    type = ChemicalOutFlowBC
    variable = hco3-
    boundary = right
  [../]
  [./h+_left]
    type = DirichletBC
    variable = h+
    boundary = left
    value = 1.0e-7
  [../]
  [./h+_right]
    type = ChemicalOutFlowBC
    variable = h+
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-7 2e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  l_max_its = 50
  l_tol = 1e-5
  nl_max_its = 10
  nl_rel_tol = 1e-5
  end_time = 10
  [./TimeStepper]
    type = ConstantDT
    dt = 0.1
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Outputs]
  perf_graph = true
  exodus = true
[]

(modules/porous_flow/test/tests/aux_kernels/darcy_velocity_lower_2D.i)

# checking that the PorousFlowDarcyVelocityComponentLowerDimensional AuxKernel works as expected in 1D+2D situation
# for the fully-saturated case (relative-permeability = 1)
# The 1_frac_in_2D_example.e has size 0.3x0.2x0, and a fracture running through its
# centre, with normal = (0, 1, 0)
# Porepressure is initialised to grad(P) = (1, 2, 0)
# Fluid_density = 2
# viscosity = 10
# relative_permeability = 1
# permeability = (5, 5, 5)  (in the bulk, measured in m^2)
# permeability = (10, 10, 10)   (in the fracture, measured in m^3)
# aperture = 0.01
# gravity = (1, 0.5, 0)
# So Darcy velocity in the bulk = (0.5, -0.5, 0)
# in the fracture grad(P) = (1, 0, 0)
# In the fracture the projected gravity vector is
# tangential_gravity = (1, 0, 0)
# So the Darcy velocity in the fracture = (100, 0, 0)

[Mesh]
  type = FileMesh
  file = 1_frac_in_2D_example.e
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '1 0.5 0'
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = 'x+2*y'
    variable = pp
  []
[]

[Kernels]
  [dummy]
    type = TimeDerivative
    variable = pp
  []
[]

[AuxVariables]
  [bulk_vel_x]
    order = CONSTANT
    family = MONOMIAL
    block = '2 3'
  []
  [bulk_vel_y]
    order = CONSTANT
    family = MONOMIAL
    block = '2 3'
  []
  [bulk_vel_z]
    order = CONSTANT
    family = MONOMIAL
    block = '2 3'
  []
  [fracture_vel_x]
    order = CONSTANT
    family = MONOMIAL
    block = 1
  []
  [fracture_vel_y]
    order = CONSTANT
    family = MONOMIAL
    block = 1
  []
  [fracture_vel_z]
    order = CONSTANT
    family = MONOMIAL
    block = 1
  []
[]

[AuxKernels]
  [bulk_vel_x]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_x
    component = x
    fluid_phase = 0
  []
  [bulk_vel_y]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_y
    component = y
    fluid_phase = 0
  []
  [bulk_vel_z]
    type = PorousFlowDarcyVelocityComponent
    variable = bulk_vel_z
    component = z
    fluid_phase = 0
  []
  [fracture_vel_x]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_x
    component = x
    fluid_phase = 0
    aperture = 0.01
  []
  [fracture_vel_y]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_y
    component = y
    fluid_phase = 0
    aperture = 0.01
  []
  [fracture_vel_z]
    type = PorousFlowDarcyVelocityComponentLowerDimensional
    variable = fracture_vel_z
    component = z
    fluid_phase = 0
    aperture = 0.01
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1E16
      viscosity = 10
      density0 = 2
      thermal_expansion = 0
    []
  []
[]

[Postprocessors]
  [bulk_vel_x]
    type = PointValue
    variable = bulk_vel_x
    point = '0 -0.05 0'
  []
  [bulk_vel_y]
    type = PointValue
    variable = bulk_vel_y
    point = '0 -0.05 0'
  []
  [bulk_vel_z]
    type = PointValue
    variable = bulk_vel_z
    point = '0 -0.05 0'
  []
  [fracture_vel_x]
    type = PointValue
    point = '0 0 0'
    variable = fracture_vel_x
  []
  [fracture_vel_y]
    type = PointValue
    point = '0 0 0'
    variable = fracture_vel_y
  []
  [fracture_vel_z]
    type = PointValue
    point = '0 0 0'
    variable = fracture_vel_z
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
    block = '2 3'
  []
  [permeability_fracture]
    type = PorousFlowPermeabilityConst
    permeability = '10 0 0 0 10 0 0 0 10'
    block = 1
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-basic-kt-mixed.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_mom_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_mom_x]
    type = FunctionIC
    variable = sup_mom_x
    function = 'exact_rho_ud'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = sup_mom_x
    momentum_component = x
    eqn = "momentum"
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_mom_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_mom_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [pressure_right]
    type = FVFunctionDirichletBC
    variable = pressure
    function = exact_p
    boundary = 'right'
  []
  [sup_mom_x_left]
    type = FVFunctionDirichletBC
    variable = sup_mom_x
    function = exact_rho_ud
    boundary = 'left'
  []
  [T_fluid_left]
    type = FVFunctionDirichletBC
    variable = T_fluid
    function = exact_T
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousMixedVarMaterial
    pressure = pressure
    superficial_rhou = sup_mom_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  value = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  value = '-3.83667087618017*sin(1.1*x)*cos(1.3*x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  value = '3.48788261470924*cos(1.1*x)*cos(1.3*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  value = '(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x))*cos(1.3*x) + 3.48788261470924*sin(x)*cos(1.1*x)^2*cos(1.3*x)/cos(x)^2 - 7.67334175236034*sin(1.1*x)*cos(1.1*x)*cos(1.3*x)/cos(x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)^2/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  value = '26.7439413073546*cos(1.5*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  value = '1.0*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(x)*cos(1.1*x)*cos(1.3*x)/cos(x)^2 - 1.1*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.1*x)*cos(1.3*x)/cos(x) - 1.3*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.3*x)*cos(1.1*x)/cos(x) + 1.0*(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x) - 40.1159119610319*sin(1.5*x))*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  value = '0.0106975765229418*cos(1.5*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)*cos(1.3*x)'
[]
[exact_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  value = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  value = 'cos(1.3*x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  value_x = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_mom_x]
    variable = sup_mom_x
    function = exact_rho_ud
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/functions/constant_function/constant_function_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 4
  ny = 4
  elem_type = QUAD4
[]

[Functions]
  [./bc_fn]
    type = ParsedFunction
    value = 'x*x+y*y'
  [../]

  [./icfn]
    type = ConstantFunction
    value = 1
  [../]

  [./ffn]
    type = ConstantFunction
    value = -4
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = icfn
    [../]
  [../]
[]

[Kernels]
  # Coupling of nonlinear to Aux
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./force]
    type = BodyForce
    variable = u
    function = ffn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = bc_fn
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'

[]

[Outputs]
  exodus = true
[]

(modules/chemical_reactions/test/tests/aqueous_equilibrium/2species_without_action.i)

# Simple equilibrium reaction example to illustrate the use of the AqueousEquilibriumReactions
# action.
# In this example, two primary species a and b are transported by diffusion and convection
# from the left of the porous medium, reacting to form two equilibrium species pa2 and pab
# according to the equilibrium reaction specified in the AqueousEquilibriumReactions block as:
#
#      reactions = '2a = pa2     2
#                   a + b = pab -2'
#
# where the 2 is the weight of the equilibrium species, the 2 on the RHS of the first reaction
# refers to the equilibrium constant (log10(Keq) = 2), and the -2 on the RHS of the second
# reaction equates to log10(Keq) = -2.
#
# This example is identical to 2species.i, except that it explicitly includes all AuxKernels
# and Kernels that are set up by the action in 2species.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
[]

[Variables]
  [./a]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    [../]
  [../]
  [./b]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    [../]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pa2]
  [../]
  [./pab]
  [../]
[]

[AuxKernels]
  [./pa2eq]
    type = AqueousEquilibriumRxnAux
    variable = pa2
    v = a
    sto_v = 2
    log_k = 2
  [../]
  [./pabeq]
    type = AqueousEquilibriumRxnAux
    variable = pab
    v = 'a b'
    sto_v = '1 1'
    log_k = -2
  [../]
[]

[ICs]
  [./pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  [../]
[]

[Kernels]
  [./a_ie]
    type = PrimaryTimeDerivative
    variable = a
  [../]
  [./a_diff]
    type = PrimaryDiffusion
    variable = a
  [../]
  [./a_conv]
    type = PrimaryConvection
    variable = a
    p = pressure
  [../]
  [./b_ie]
    type = PrimaryTimeDerivative
    variable = b
  [../]
  [./b_diff]
    type = PrimaryDiffusion
    variable = b
  [../]
  [./b_conv]
    type = PrimaryConvection
    variable = b
    p = pressure
  [../]
  [./a1eq]
    type = CoupledBEEquilibriumSub
    variable = a
    log_k = 2
    weight = 2
    sto_u = 2
  [../]
  [./a1diff]
    type = CoupledDiffusionReactionSub
    variable = a
    log_k = 2
    weight = 2
    sto_u = 2
  [../]
  [./a1conv]
    type = CoupledConvectionReactionSub
    variable = a
    log_k = 2
    weight = 2
    sto_u = 2
    p = pressure
  [../]
  [./a2eq]
    type = CoupledBEEquilibriumSub
    variable = a
    v = b
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./a2diff]
    type = CoupledDiffusionReactionSub
    variable = a
    v = b
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./a2conv]
    type = CoupledConvectionReactionSub
    variable = a
    v = b
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
    p = pressure
  [../]
  [./b2eq]
    type = CoupledBEEquilibriumSub
    variable = b
    v = a
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./b2diff]
    type = CoupledDiffusionReactionSub
    variable = b
    v = a
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
  [../]
  [./b2conv]
    type = CoupledConvectionReactionSub
    variable = b
    v = a
    log_k = -2
    weight = 1
    sto_v = 1
    sto_u = 1
    p = pressure
  [../]
[]

[BCs]
  [./a_left]
    type = DirichletBC
    variable = a
    boundary = left
    value = 1.0e-2
  [../]
  [./a_right]
    type = ChemicalOutFlowBC
    variable = a
    boundary = right
  [../]
  [./b_left]
    type = DirichletBC
    variable = b
    boundary = left
    value = 1.0e-2
  [../]
  [./b_right]
    type = ChemicalOutFlowBC
    variable = b
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-4 1e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-12
  start_time = 0.0
  end_time = 100
  dt = 10.0
[]

[Outputs]
  file_base = 2species_out
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

(modules/porous_flow/test/tests/flux_limited_TVD_pflow/pffltvd_1D.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, mploying PorousFlow Kernels and UserObjects, with superbee flux-limiter
# 1D version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/phase_field/test/tests/phase_field_kernels/SplitCHWRes.i)

#
# Test the split parsed function free enery Cahn-Hilliard Bulk kernel
# with two concentration variables and coupling through off-diagonal Onsager
# matrix coefficients
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmin = 0
  xmax = 60
  ymin = 0
  ymax = 60
  elem_type = QUAD4
[]

[Variables]
  [./c1]
    [./InitialCondition]
      type = FunctionIC
      function = 'cos(x/60*pi)'
    [../]
  [../]
  [./c2]
    [./InitialCondition]
      type = FunctionIC
      function = 'cos(y/60*pi)'
    [../]
  [../]
  [./w1]
  [../]
  [./w2]
  [../]
[]

[Kernels]
  [./c1_res]
    type = SplitCHParsed
    variable = c1
    f_name = F
    kappa_name = kappa_c
    w = w1
  [../]
  [./w11_res]
    type = SplitCHWRes
    variable = w1
    mob_name = M11
  [../]
  [./w12_res]
    type = SplitCHWRes
    variable = w1
    w = w2
    mob_name = M12
  [../]

  [./c2_res]
    type = SplitCHParsed
    variable = c2
    f_name = F
    kappa_name = kappa_c
    w = w2
  [../]
  [./w22_res]
    type = SplitCHWRes
    variable = w2
    mob_name = M22
  [../]
  [./w21_res]
    type = SplitCHWRes
    variable = w2
    w = w1
    mob_name = M21
  [../]

  [./time1]
    type = CoupledTimeDerivative
    variable = w1
    v = c1
  [../]
  [./time2]
    type = CoupledTimeDerivative
    variable = w2
    v = c2
  [../]
[]

[Materials]
  [./pfmobility]
    type = GenericConstantMaterial
    prop_names  = 'M11 M12 M21 M22 kappa_c'
    prop_values = '10  2.5 20  5   40'
  [../]

  [./free_energy]
    # equivalent to `MathFreeEnergy`
    type = DerivativeParsedMaterial
    f_name = F
    args = 'c1 c2'
    function = '0.25*(1+c1)^2*(1-c1)^2 + 0.25*(1+c2)^2*(1-c2)^2'
    derivative_order = 2
  [../]
[]

[Preconditioning]
  # active = ' '
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2

  solve_type = 'NEWTON'
  petsc_options_iname = -pc_type
  petsc_options_value = lu

  l_max_its = 30
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-10
  start_time = 0.0
  num_steps = 2

  dt = 10
[]

[Outputs]
  exodus = true
[]

(test/tests/executioners/nullspace/singular.i)

[Mesh]
 type = GeneratedMesh
 dim = 1
 xmin = 0
 xmax = 10
 nx = 8
[]

[Problem]
  null_space_dimension = 1
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./eig]
    type = MassEigenKernel
    variable = u
    eigen_postprocessor = 1.0002920196258376e+01
    eigen = false
  [../]

  [./force]
    type = CoupledForce
    variable = u
    v = aux_v
  [../]
[]

[AuxVariables]
  [./aux_v]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = eigen_mode
    [../]
  [../]
[]

[AuxKernels]
  [./set_source]
    type = FunctionAux
    variable = aux_v
    function = second_harmonic
    execute_on = timestep_begin
  [../]
[]

[Functions]
  [./eigen_mode]
    type = ParsedFunction
    value = 'sqrt(2.0 / L) * sin(mode * pi  * x / L)'
    vars = 'L  mode'
    vals = '10 1'
  [../]

  [./second_harmonic]
    type = ParsedFunction
    value = 'sqrt(2.0 / L) * sin(mode * pi  * x / L)'
    vars = 'L  mode'
    vals = '10 2'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1'
    value = 0
  [../]
[]

[VectorPostprocessors]
  [./sample_solution]
    type = LineValueSampler
    variable = u
    start_point = '0 0 0'
    end_point = '10 0 0'
    sort_by = x
    num_points = 9
    execute_on = timestep_end
  [../]
[]

[Preconditioning]
  [./prec]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = SteadyWithNull
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_pc_side -snes_type -ksp_norm_type'
  petsc_options_value = 'hypre boomeramg  left ksponly preconditioned'
  nl_rel_tol = 1.0e-14
  nl_abs_tol = 1.0e-14
[]

[Outputs]
  execute_on = 'timestep_end'
  csv = true
[]

(test/tests/postprocessors/variable_inner_product/variable_inner_product.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  xmin = -1
  xmax = 1
  ymin = 0
  ymax = 1
  elem_type = QUAD9
[]

[AuxVariables]
  [./f]
    order = SECOND
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = leg2
    [../]
  [../]
  [./g]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = leg1
    [../]
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[Functions]
  [./leg1]
    type = ParsedFunction
    value = 'x'
  [../]

  [./leg2]
    type = ParsedFunction
    value = '0.5*(3.0*x*x-1.0)'
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'

  [./Quadrature]
    order = fourth
  []
[]

[Postprocessors]
  [./f_dot_g]
    type = VariableInnerProduct
    variable = f
    second_variable = g
  [../]

  [./f_dot_f]
    type = VariableInnerProduct
    variable = f
    second_variable = f
  [../]

  [./norm_f]
    type = ElementL2Norm
    variable = f
  [../]
[]

[Outputs]
  file_base = variable_inner_product
  csv = true
[]

(modules/chemical_reactions/test/tests/aqueous_equilibrium/2species.i)

# Simple equilibrium reaction example to illustrate the use of the AqueousEquilibriumReactions
# action.
# In this example, two primary species a and b are transported by diffusion and convection
# from the left of the porous medium, reacting to form two equilibrium species pa2 and pab
# according to the equilibrium reaction specified in the AqueousEquilibriumReactions block as:
#
#      reactions = '2a = pa2     2
#                   a + b = pab -2'
#
# where the 2 is the weight of the equilibrium species, the 2 on the RHS of the first reaction
# refers to the equilibrium constant (log10(Keq) = 2), and the -2 on the RHS of the second
# reaction equates to log10(Keq) = -2.
#
# The AqueousEquilibriumReactions action creates all the required kernels and auxkernels
# to compute the reaction given by the above equilibrium reaction equation.
#
# Specifically, it adds to following:
# * An AuxVariable named 'pa2' (given in the reactions equations)
# * An AuxVariable named 'pab' (given in the reactions equations)
# * A AqueousEquilibriumRxnAux AuxKernel for each AuxVariable with all parameters
# * A CoupledBEEquilibriumSub Kernel for each primary species with all parameters
# * A CoupledDiffusionReactionSub Kernel for each primary species with all parameters
# * A CoupledConvectionReactionSub Kernel for each primary species with all parameters if
# pressure is a coupled variable

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
[]

[Variables]
  [./a]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    [../]
  [../]
  [./b]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    [../]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  [../]
[]

[ReactionNetwork]
  [./AqueousEquilibriumReactions]
    primary_species = 'a b'
    reactions = '2a = pa2     2,
                 a + b = pab -2'
    secondary_species = 'pa2 pab'
    pressure = pressure
  [../]
[]

[Kernels]
  [./a_ie]
    type = PrimaryTimeDerivative
    variable = a
  [../]
  [./a_diff]
    type = PrimaryDiffusion
    variable = a
  [../]
  [./a_conv]
    type = PrimaryConvection
    variable = a
    p = pressure
  [../]
  [./b_ie]
    type = PrimaryTimeDerivative
    variable = b
  [../]
  [./b_diff]
    type = PrimaryDiffusion
    variable = b
  [../]
  [./b_conv]
    type = PrimaryConvection
    variable = b
    p = pressure
  [../]
[]

[BCs]
  [./a_left]
    type = DirichletBC
    variable = a
    boundary = left
    value = 1.0e-2
  [../]
  [./a_right]
    type = ChemicalOutFlowBC
    variable = a
    boundary = right
  [../]
  [./b_left]
    type = DirichletBC
    variable = b
    boundary = left
    value = 1.0e-2
  [../]
  [./b_right]
    type = ChemicalOutFlowBC
    variable = b
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-4 1e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-12
  start_time = 0.0
  end_time = 100
  dt = 10.0
[]

[Outputs]
  file_base = 2species_out
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

(modules/richards/test/tests/dirac/bh_fu_08.i)

#fullyupwind
[Mesh]
  type = FileMesh
  file = bh07_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1000 10000'
    x = '100 1000'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[BCs]
  [./fix_outer]
    type = DirichletBC
    boundary = perimeter
    variable = pressure
    value = 1E7
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFullyUpwindFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh08.bh
    borehole_length = 1
    borehole_direction = '0 0 1'
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    re_constant = 0.1594
    character = 2
    fully_upwind = true
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
    execute_on = 'initial timestep_end'
  [../]

  [./fluid_mass]
    type = RichardsMass
    variable = pressure
    execute_on = 'initial timestep_end'
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-11 0 0  0 1E-11 0  0 0 1E-11'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1000
  solve_type = NEWTON

  [./TimeStepper]
    # get only marginally better results for smaller time steps
    type = FunctionDT
    function = dts
  [../]

[]

[Outputs]
  file_base = bh_fu_08
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
[]

(modules/combined/test/tests/DiffuseCreep/stress_flux_n_gb_relax.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.1*v'
    [../]
  [../]
  [./mu]
  [../]
  [./jx]
  [../]
  [./jy]
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./creep_strain_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./creep_strain_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./creep_strain_xy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_xy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = mu_prop
    c = c
  [../]
  [./flux_x]
    type = CHSplitFlux
    variable = jx
    component = 0
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./flux_y]
    type = CHSplitFlux
    variable = jy
    component = 1
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./creep_strain_xx]
    type = RankTwoAux
    variable = creep_strain_xx
    rank_two_tensor = creep_strain
    index_i = 0
    index_j = 0
  [../]
  [./creep_strain_yy]
    type = RankTwoAux
    variable = creep_strain_yy
    rank_two_tensor = creep_strain
    index_i = 1
    index_j = 1
  [../]
  [./creep_strain_xy]
    type = RankTwoAux
    variable = creep_strain_xy
    rank_two_tensor = creep_strain
    index_i = 0
    index_j = 1
  [../]
  [./stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    variable = stress_yy
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./stress_xy]
    type = RankTwoAux
    variable = stress_xy
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
  [./diffuse_strain_increment]
    type = FluxBasedStrainIncrement
    xflux = jx
    yflux = jy
    gb = gb
    property_name = diffuse
  [../]
  [./gb_relax_prefactor]
    type = DerivativeParsedMaterial
    block = 0
    function = '0.01*(c-0.15)*gb'
    args = 'c gb'
    f_name = gb_relax_prefactor
    derivative_order = 1
  [../]
  [./gb_relax]
    type = GBRelaxationStrainIncrement
    property_name = gb_relax
    prefactor_name = gb_relax_prefactor
    gb_normal_name = gb_normal
  [../]
  [./creep_strain]
    type = SumTensorIncrements
    tensor_name = creep_strain
    coupled_tensor_increment_names = 'diffuse gb_relax'
  [../]
  [./strain]
   type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y'
  [../]
  [./stress]
    type = ComputeStrainIncrementBasedStress
    inelastic_strain_names = creep_strain
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '120.0 80.0'
    fill_method = symmetric_isotropic
  [../]
[]

[BCs]
  [./Periodic]
    [./cbc]
      auto_direction = 'x y'
      variable = c
    [../]
  [../]
  [./fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  nl_rel_tol = 1e-10
  nl_max_its = 5

  l_tol = 1e-4
  l_max_its = 20

  dt = 1
  num_steps = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/misc/interface_flux.i)

#
# This test demonstrates an InterfaceKernel (InterfaceDiffusionFlux) that can
# replace a pair of integrated DiffusionFluxBC boundary conditions.
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    ymax = 0.5
  []
  [./box1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.51 1 0'
    input = gen
  [../]
  [./box2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.49 0 0'
    top_right = '1 1 0'
    input = box1
  [../]
  [./iface_u]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = 10
    input = box2
  [../]
[]

[Variables]
  [./u2]
    block = 1
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.4)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
  [./v2]
    block = 2
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.7)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
[]

[Kernels]
  [./u2_diff]
    type = Diffusion
    variable = u2
    block = 1
  [../]
  [./u2_dt]
    type = TimeDerivative
    variable = u2
    block = 1
  [../]
  [./v2_diff]
    type = Diffusion
    variable = v2
    block = 2
  [../]
  [./v2_dt]
    type = TimeDerivative
    variable = v2
    block = 2
  [../]
[]

[InterfaceKernels]
  [./iface]
    type = InterfaceDiffusionBoundaryTerm
    boundary = 10
    variable = u2
    neighbor_var = v2
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.002
  num_steps = 6
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/level_set/examples/vortex/vortex_reinit.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 1
  ymax = 1
  nx = 16
  ny = 16
  uniform_refine = 2
  elem_type = QUAD9
  second_order = true
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[AuxKernels]
  [./vec]
    type = VectorFunctionAux
    variable = velocity
    function = velocity_func
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Variables]
  [phi]
    family = LAGRANGE
  []
[]

[Functions]
  [phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0.5 0.75 0'
    radius = 0.15
  []
  [./velocity_func]
    type = LevelSetOlssonVortex
    reverse_time = 2
  [../]
[]

[ICs]
  [phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = phi
  []
  [advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  []
  [advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = phi
  []
  [time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = phi
  []
[]

[Postprocessors]
  [area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  []
  [cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  []
[]

[Problem]
  type = LevelSetProblem
[]

[Preconditioning/smp]
    type = SMP
    full = true
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  start_time = 0
  end_time = 2
  scheme = crank-nicolson
  [TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  []
[]

[MultiApps]
  [reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'vortex_reinit_sub.i'
    execute_on = TIMESTEP_END
  []
[]

[Transfers]
  [to_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [to_sub_init]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi_0
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [from_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    from_multi_app = reinit
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/geochemistry/test/tests/kernels/time_deriv_1.i)

# An initial concentration field in a material with constant porosity is subjected to a constant source
# porosity * d(concentration)/dt = source
# The result is checked vs the expected solution, which is conc = conc_old + dt * source / porosity
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 2
  ny = 4
  nz = 2
[]

[Variables]
  [conc]
  []
[]

[Kernels]
  [dot]
    type = GeochemistryTimeDerivative
    porosity = porosity
    variable = conc
  []
  [source]
    type = BodyForce
    function = 3.0
    variable = conc
  []
[]

[ICs]
  [conc]
    type = FunctionIC
    function = 'z * z + 4 * x * x * x + y'
    variable = conc
  []
[]

[AuxVariables]
  [porosity]
  []
  [expected]
  []
  [should_be_zero]
  []
[]

[AuxKernels]
  [porosity]
    type = FunctionAux
    function = '6.0'
    variable = porosity
  []
  [expected]
    type = FunctionAux
    function = 'z * z + 4 * x * x * x + y + 2.0 * 3.0 / 6.0'
    variable = expected
  []
  [should_be_zero]
    type = ParsedAux
    args = 'expected conc'
    function = 'expected - conc'
    variable = should_be_zero
  []
[]

[Postprocessors]
  [error]
    type = NodalL2Norm
    variable = should_be_zero
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2
  end_time = 2
[]

[Outputs]
  csv = true
[]

(modules/richards/test/tests/jacobian_2/jn_lumped_17.i)

# two phase
# water saturated

# gravity = true
# supg = true
# transient = true


[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
  viscosity = '1E-3 0.5E-3'
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1.0 # notice small quantity, so the PETSc constant state works
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 0.5
    bulk_mod = 0.5 # notice small quantity, so the PETSc constant state works
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1 # notice small quantity, so the PETSc constant state works
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1 # notice small quantity, so the PETSc constant state works
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.2
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.1
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.15
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.05
    sum_s_res = 0.15
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 0.01
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      block = 0
      function = init_p
    [../]
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      block = 0
      function = init_p
    [../]
  [../]
[]

[Functions]
  [./init_p]
    type = ParsedFunction
    value = x+0.6*y+0.3*z
  [../]
[]

[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsLumpedMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsLumpedMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    gravity = '1 2 3'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-10
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = jn17
  exodus = false
[]

(test/tests/time_integrators/actually_explicit_euler_verification/ee-1d-quadratic.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 20
  elem_type = EDGE3
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x*x-2*t
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x*x
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    preset = false
    boundary = '0 1'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  l_tol = 1e-12
  start_time = 0.0
  num_steps = 20
  dt = 0.00005

  [./TimeIntegrator]
    type = ActuallyExplicitEuler
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/porous_flow/test/tests/relperm/corey1.i)

# Test Corey relative permeability curve by varying saturation over the mesh
# Corey exponent n = 1 for both phases (linear residual saturation)
# No residual saturation in either phase

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityCorey
    phase = 0
    n = 1
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 1
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(test/tests/kernels/ad_mat_diffusion/ad_1D_transient.i)

# This test solves a 1D transient heat equation
# The error is caclulated by comparing to the analytical solution
# The problem setup and analytical solution are taken from "Advanced Engineering
# Mathematics, 10th edition" by Erwin Kreyszig.
# http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364
# It is Example 1 in section 12.6 on page 561

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 160
  xmax = 80
[]

[Variables]
  [./T]
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '100*sin(pi*x/80)'
  [../]
[]

[Kernels]
  [./diff]
    type = ADMatDiffusion
    variable = T
    diffusivity = diffusivity
  [../]
  [./dt]
    type = CoefTimeDerivative
    variable = T
    Coefficient = 0.82064
  [../]
[]

[BCs]
  [./sides]
    type = DirichletBC
    variable = T
    boundary = 'left right'
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = ADGenericConstantMaterial
    prop_names = 'diffusivity'
    prop_values = '0.95'
  [../]
[]

[Executioner]
  type = Transient
  dt = 1e-2
  end_time = 1
[]

[Postprocessors]
  [./error]
    type = NodalL2Error
    function = '100*sin(pi*x/80)*exp(-0.95/(0.092*8.92)*pi^2/80^2*t)'
    variable = T
    outputs = console
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/parsed/mms_transient_coupled.i)

###########################################################
# This is a simple test of the Function System. This
# test uses forcing terms produced from analytical
# functions of space and time to verify a solution
# using MMS.
#
# @Requirement F6.20
###########################################################


[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 1.0
  nx = 10
  ymin = 0.0
  ymax = 1.0
  ny = 10
  uniform_refine = 2
  elem_type = QUAD4
[]

[Variables]
  [./u]
  [../]
  [./v]
  [../]
[]

[Functions]
  [./v_left_bc]
    # Left-side boundary condition for v equation, v(0,y,t) = u(0.5,y,t). This is accomplished using a PointValue postprocessor, which is what this input file was designed to test.
    type = ParsedFunction
    value = a
    vals = u_midpoint
    vars = a
  [../]
  [./u_mms_func]
    # MMS Forcing function for the u equation.
    type = ParsedFunction
    value = ' 20*exp(20*t)*x*x*x-6*exp(20*t)*x-(2-0.125*exp(20*t))*sin(5/2*x*pi)-0.125*exp(20*t)-1
'
  [../]
  [./v_mms_func]
    # MMS forcing function for the v equation.
    type = ParsedFunction
    value = -2.5*exp(20*t)*sin(5/2*x*pi)+2.5*exp(20*t)+25/4*(2-0.125*exp(20*t))*sin(5/2*x*pi)*pi*pi
  [../]
  [./u_right_bc]
    type = ParsedFunction
    value = 3*exp(20*t) # \nabla{u}|_{x=1} = 3\exp(20*t)
  [../]
  [./u_exact]
    # Exact solution for the MMS function for the u variable.
    type = ParsedFunction
    value = exp(20*t)*pow(x,3)+1
  [../]
  [./v_exact]
    # Exact MMS solution for v.
    type = ParsedFunction
    value = (2-0.125*exp(20*t))*sin(5/2*pi*x)+0.125*exp(20*t)+1
  [../]
[]

[Kernels]
  # Strong Form:
  # \frac{\partial u}{\partial t} - \nabla \cdot 0.5 \nabla u - v = 0
  # \frac{\partial u}{\partial t} - \nabla \cdot \nabla v = 0
  #
  # BCs:
  # u(0,y,t) = 1
  # \nabla u |_{x=1} = 3\exp(20*t)
  # v(0,y,t) = u(0.5,y,t)
  # v(1,y,t) = 3
  # \nabla u |_{y=0,1} = 0
  # \nabla v |_{y=0,1} = 0
  #
  [./u_time]
    type = TimeDerivative
    variable = u
  [../]
  [./u_diff]
    type = Diffusion
    variable = u
  [../]
  [./u_source]
    type = CoupledForce
    variable = u
    v = v
  [../]
  [./v_diff]
    type = Diffusion
    variable = v
  [../]
  [./u_mms]
    type = BodyForce
    variable = u
    function = u_mms_func
  [../]
  [./v_mms]
    type = BodyForce
    variable = v
    function = v_mms_func
  [../]
  [./v_time]
    type = TimeDerivative
    variable = v
  [../]
[]

[BCs]
  [./u_left]
    type = DirichletBC
    variable = u
    boundary = left # x=0
    value = 1 # u(0,y,t)=1
  [../]
  [./u_right]
    type = FunctionNeumannBC
    variable = u
    boundary = right # x=1
    function = u_right_bc # \nabla{u}|_{x=1}=3\exp(20t)
  [../]
  [./v_left]
    type = FunctionDirichletBC
    variable = v
    boundary = left # x=0
    function = v_left_bc # v(0,y,t) = u(0.5,y,t)
  [../]
  [./v_right]
    type = DirichletBC
    variable = v
    boundary = right # x=1
    value = 3 # v(1,y,t) = 3
  [../]
[]

[Postprocessors]
  [./u_midpoint]
    type = PointValue
    variable = u
    point = '0.5 0.5 0'
    execute_on = 'initial timestep_end'
  [../]
  [./u_midpoint_exact]
    type = FunctionValuePostprocessor
    function = u_exact
    point = '0.5 0.5 0.0'
    execute_on = 'initial timestep_end'
  [../]
  [./u_error]
    type = ElementL2Error
    variable = u
    function = u_exact
    execute_on = 'initial timestep_end'
  [../]
  [./v_error]
    type = ElementL2Error
    variable = v
    function = v_exact
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.01

  solve_type = NEWTON

  end_time = 0.1
  scheme = crank-nicolson
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./u_initial]
    # Use the MMS exact solution to compute the initial conditions.
    function = u_exact
    variable = u
    type = FunctionIC
  [../]
  [./v_exact]
    # Use the MMS exact solution to compute the initial condition.
    function = v_exact
    variable = v
    type = FunctionIC
  [../]
[]

(test/tests/kernels/conservative_advection/none_in_none_out.i)

# Using ConservativeAdvection with full upwinding
# This demonstrates BCs (no BCs) that allow no mass to
# enter or exit the domain.
# Total mass remains constant and the pulse advects
# with the correct velocity
[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 10
  nx = 10
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u]
    type = FunctionIC
    variable = u
    function = 'if(x<5,x,10-x)'
  [../]
[]

[Kernels]
  [./dot]
    type = MassLumpedTimeDerivative
    variable = u
  [../]
  [./advection]
    type = ConservativeAdvection
    variable = u
    upwinding_type = full
    velocity = '1 0 0'
  [../]
[]

[Postprocessors]
  [./total_mass]
    type = VariableInnerProduct
    variable = u
    second_variable = 1
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 10
  l_tol = 1E-14
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/examples/tidal/atm_tides.i)

# A 10m x 10m "column" of height 100m is subjected to cyclic pressure at its top
# Assumptions:
# the boundaries are impermeable, except the top boundary
# only vertical displacement is allowed
# the atmospheric pressure sets the total stress at the top of the model
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 10
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  zmin = -100
  zmax = 0
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  PorousFlowDictator = dictator
  block = 0
  biot_coefficient = 0.6
  multiply_by_density = false
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [porepressure]
    scaling = 1E11
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '-10000*z'  # approximately correct
  []
[]

[Functions]
  [ini_stress_zz]
    type = ParsedFunction
    value = '(25000 - 0.6*10000)*z' # remember this is effective stress
  []
  [cyclic_porepressure]
    type = ParsedFunction
    value = 'if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
  [neg_cyclic_porepressure]
    type = ParsedFunction
    value = '-if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
[]

[BCs]
  # zmin is called 'back'
  # zmax is called 'front'
  # ymin is called 'bottom'
  # ymax is called 'top'
  # xmin is called 'left'
  # xmax is called 'right'
  [no_x_disp]
    type = DirichletBC
    variable = disp_x
    value = 0
    boundary = 'bottom top' # because of 1-element meshing, this fixes u_x=0 everywhere
  []
  [no_y_disp]
    type = DirichletBC
    variable = disp_y
    value = 0
    boundary = 'bottom top' # because of 1-element meshing, this fixes u_y=0 everywhere
  []
  [no_z_disp_at_bottom]
    type = DirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
  [pp]
    type = FunctionDirichletBC
    variable = porepressure
    function = cyclic_porepressure
    boundary = front
  []
  [total_stress_at_top]
    type = FunctionNeumannBC
    variable = disp_z
    function = neg_cyclic_porepressure
    boundary = front
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      thermal_expansion = 0.0
      bulk_modulus = 2E9
      viscosity = 1E-3
      density0 = 1000.0
    []
  []
[]

[PorousFlowBasicTHM]
  coupling_type = HydroMechanical
  displacements = 'disp_x disp_y disp_z'
  porepressure = porepressure
  gravity = '0 0 -10'
  fp = the_simple_fluid
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    bulk_modulus = 10.0E9 # drained bulk modulus
    poissons_ratio = 0.25
  []
  [strain]
    type = ComputeSmallStrain
    eigenstrain_names = ini_stress
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [ini_stress]
    type = ComputeEigenstrainFromInitialStress
    initial_stress = '0 0 0  0 0 0  0 0 ini_stress_zz'
    eigenstrain_name = ini_stress
  []
  [porosity]
    type = PorousFlowPorosityConst # only the initial value of this is ever used
    porosity = 0.1
  []
  [biot_modulus]
    type = PorousFlowConstantBiotModulus
    solid_bulk_compliance = 1E-10
    fluid_bulk_modulus = 2E9
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-12 0 0   0 1E-12 0   0 0 1E-14'
  []
  [density]
    type = GenericConstantMaterial
    prop_names = density
    prop_values = 2500.0
  []
[]

[Postprocessors]
  [p0]
    type = PointValue
    outputs = csv
    point = '0 0 0'
    variable = porepressure
  []
  [uz0]
    type = PointValue
    outputs = csv
    point = '0 0 0'
    variable = disp_z
  []
  [p100]
    type = PointValue
    outputs = csv
    point = '0 0 -100'
    variable = porepressure
  []
[]


[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  start_time = -3600 # so postprocessors get recorded correctly at t=0
  dt = 3600
  end_time = 360000
  nl_abs_tol = 5E-7
  nl_rel_tol = 1E-10
[]

[Outputs]
  csv = true
[]

(modules/combined/examples/phase_field-mechanics/kks_mechanics_VTS.i)

# KKS phase-field model coupled with elasticity using the Voigt-Taylor scheme as
# described in L.K. Aagesen et al., Computational Materials Science, 140, 10-21 (2017)
# Original run #170329e

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 640
  ny = 1
  nz = 1
  xmin = -10
  xmax = 10
  ymin = 0
  ymax = 0.03125
  zmin = 0
  zmax = 0.03125
  elem_type = HEX8
[]


[Variables]
  # order parameter
  [./eta]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute concentration
  [./c]
    order = FIRST
    family = LAGRANGE
  [../]

  # chemical potential
  [./w]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute phase concentration (matrix)
  [./cm]
    order = FIRST
    family = LAGRANGE
  [../]
  # solute phase concentration (precipitate)
  [./cp]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./eta_ic]
    variable = eta
    type = FunctionIC
    function = ic_func_eta
    block = 0
  [../]
  [./c_ic]
    variable = c
    type = FunctionIC
    function = ic_func_c
    block = 0
  [../]
  [./w_ic]
    variable = w
    type = ConstantIC
    value = 0.00991
    block = 0
  [../]
  [./cm_ic]
    variable = cm
    type = ConstantIC
    value = 0.131
    block = 0
  [../]
  [./cp_ic]
    variable = cp
    type = ConstantIC
    value = 0.236
    block = 0
  [../]
[]

[Functions]
  [./ic_func_eta]
    type = ParsedFunction
    value = '0.5*(1.0+tanh((x)/delta_eta/sqrt(2.0)))'
    vars = 'delta_eta'
    vals = '0.8034'
  [../]
  [./ic_func_c]
    type = ParsedFunction
    value = '0.2388*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10)+0.1338*(1-(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10))'
    vars = 'delta'
    vals = '0.8034'
  [../]
  [./psi_eq_int]
    type = ParsedFunction
    value = 'volume*psi_alpha'
    vars = 'volume psi_alpha'
    vals = 'volume psi_alpha'
  [../]
  [./gamma]
    type = ParsedFunction
    value = '(psi_int - psi_eq_int) / dy / dz'
    vars = 'psi_int psi_eq_int dy       dz'
    vals = 'psi_int psi_eq_int 0.03125  0.03125'
  [../]
[]

[AuxVariables]
  [./sigma11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./sigma22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./sigma33]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e12]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e33]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_el11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_el12]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_el22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./f_el]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./eigen_strain00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./Fglobal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./psi]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_sigma11]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = sigma11
  [../]
  [./matl_sigma22]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = sigma22
  [../]
  [./matl_sigma33]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    variable = sigma33
  [../]
  [./matl_e11]
    type = RankTwoAux
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
    variable = e11
  [../]
  [./matl_e12]
    type = RankTwoAux
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 1
    variable = e12
  [../]
  [./matl_e22]
    type = RankTwoAux
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
    variable = e22
  [../]
  [./matl_e33]
    type = RankTwoAux
    rank_two_tensor = total_strain
    index_i = 2
    index_j = 2
    variable = e33
  [../]
  [./f_el]
    type = MaterialRealAux
    variable = f_el
    property = f_el_mat
    execute_on = timestep_end
  [../]
  [./GlobalFreeEnergy]
    variable = Fglobal
    type = KKSGlobalFreeEnergy
    fa_name = fm
    fb_name = fp
    w = 0.0264
    kappa_names = kappa
    interfacial_vars = eta
  [../]
  [./psi_potential]
    variable = psi
    type = ParsedAux
    args = 'Fglobal w c f_el sigma11 e11'
    function = 'Fglobal - w*c + f_el - sigma11*e11'
  [../]
[]


[BCs]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./right_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0
  [../]
  [./front_y]
    type = DirichletBC
    variable = disp_y
    boundary = front
    value = 0
  [../]
  [./back_y]
    type = DirichletBC
    variable = disp_y
    boundary = back
    value = 0
  [../]
  [./top_z]
    type = DirichletBC
    variable = disp_z
    boundary = top
    value = 0
  [../]
  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  [../]
[]

[Materials]
  # Chemical free energy of the matrix
  [./fm]
    type = DerivativeParsedMaterial
    f_name = fm
    args = 'cm'
    function = '6.55*(cm-0.13)^2'
  [../]
# Elastic energy of the matrix
  [./elastic_free_energy_m]
    type = ElasticEnergyMaterial
    base_name = matrix
    f_name = fe_m
    args = ' '
    outputs = exodus
  [../]
# Total free energy of the matrix
  [./Total_energy_matrix]
    type = DerivativeSumMaterial
    f_name = f_total_matrix
    sum_materials = 'fm fe_m'
    args = 'cm'
  [../]

  # Free energy of the precipitate phase
  [./fp]
    type = DerivativeParsedMaterial
    f_name = fp
    args = 'cp'
    function = '6.55*(cp-0.235)^2'
  [../]

# Elastic energy of the precipitate
  [./elastic_free_energy_p]
    type = ElasticEnergyMaterial
    base_name = ppt
    f_name = fe_p
    args = ' '
    outputs = exodus
  [../]

# Total free energy of the precipitate
  [./Total_energy_ppt]
    type = DerivativeSumMaterial
    f_name = f_total_ppt
    sum_materials = 'fp fe_p'
    args = 'cp'
  [../]

  # Total elastic energy
    [./Total_elastic_energy]
      type = DerivativeTwoPhaseMaterial
      eta = eta
      f_name = f_el_mat
      fa_name = fe_m
      fb_name = fe_p
      outputs = exodus
      W = 0
    [../]

  # h(eta)
  [./h_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta
  [../]

  # g(eta)
  [./g_eta]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'M   L   kappa     misfit'
    prop_values = '0.7 0.7 0.01704   0.00377'
  [../]

  #Mechanical properties
  [./Stiffness_matrix]
    type = ComputeElasticityTensor
    C_ijkl = '103.3 74.25 74.25 103.3 74.25 103.3 46.75 46.75 46.75'
    base_name = matrix
    fill_method = symmetric9
  [../]
  [./Stiffness_ppt]
    type = ComputeElasticityTensor
    C_ijkl = '100.7 71.45 71.45 100.7 71.45 100.7 50.10 50.10 50.10'
    base_name = ppt
    fill_method = symmetric9
  [../]
  [./stress_matrix]
    type = ComputeLinearElasticStress
    base_name = matrix
  [../]
  [./stress_ppt]
    type = ComputeLinearElasticStress
    base_name = ppt
  [../]
  [./strain_matrix]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y disp_z'
    base_name = matrix
  [../]
  [./strain_ppt]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y disp_z'
    base_name = ppt
    eigenstrain_names = 'eigenstrain_ppt'
  [../]
  [./eigen_strain]
    type = ComputeEigenstrain
    base_name = ppt
    eigen_base = '1 1 1 0 0 0'
    prefactor = misfit
    eigenstrain_name = 'eigenstrain_ppt'
  [../]
  [./global_stress]
    type = TwoPhaseStressMaterial
    base_A = matrix
    base_B = ppt
  [../]
  [./global_strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y disp_z'
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y disp_z'
  [../]

  # enforce c = (1-h(eta))*cm + h(eta)*cp
  [./PhaseConc]
    type = KKSPhaseConcentration
    ca       = cm
    variable = cp
    c        = c
    eta      = eta
  [../]

  # enforce pointwise equality of chemical potentials
  [./ChemPotVacancies]
    type = KKSPhaseChemicalPotential
    variable = cm
    cb       = cp
    fa_name  = f_total_matrix
    fb_name  = f_total_ppt
  [../]

  #
  # Cahn-Hilliard Equation
  #
  [./CHBulk]
    type = KKSSplitCHCRes
    variable = c
    ca       = cm
    fa_name  = f_total_matrix
    w        = w
  [../]

  [./dcdt]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
  [./ckernel]
    type = SplitCHWRes
    mob_name = M
    variable = w
  [../]

  #
  # Allen-Cahn Equation
  #
  [./ACBulkF]
    type = KKSACBulkF
    variable = eta
    fa_name  = f_total_matrix
    fb_name  = f_total_ppt
    w        = 0.0264
    args = 'cp cm'
  [../]
  [./ACBulkC]
    type = KKSACBulkC
    variable = eta
    ca       = cm
    cb       = cp
    fa_name  = f_total_matrix
  [../]
  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = kappa
  [../]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -sub_pc_type   -sub_pc_factor_shift_type'
  petsc_options_value = 'asm       ilu            nonzero'

  l_max_its = 30
  nl_max_its = 10
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-11
  num_steps = 200

  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.5
  [../]
[]

[VectorPostprocessors]
  #[./eta]
  #  type =  LineValueSampler
  #  start_point = '-10 0 0'
  #  end_point = '10 0 0'
  #  variable = eta
  #  num_points = 321
  #  sort_by =  id
  #[../]
  #[./eta_position]
  #  type = FindValueOnLineSample
  #  vectorpostprocessor = eta
  #  variable_name = eta
  #  search_value = 0.5
  #[../]
#  [./f_el]
#    type =  LineMaterialRealSampler
#    start = '-20 0 0'
#    end   = '20 0 0'
#    sort_by = id
#    property = f_el
#  [../]
#  [./f_el_a]
#    type =  LineMaterialRealSampler
#    start = '-20 0 0'
#    end   = '20 0 0'
#    sort_by = id
#    property = fe_m
#  [../]
#  [./f_el_b]
#    type =  LineMaterialRealSampler
#    start = '-20 0 0'
#    end   = '20 0 0'
#    sort_by = id
#    property = fe_p
#  [../]
#  [./h_out]
#    type =  LineMaterialRealSampler
#    start = '-20 0 0'
#    end   = '20 0 0'
#    sort_by = id
#    property = h
#  [../]
#  [./fm_out]
#    type =  LineMaterialRealSampler
#    start = '-20 0 0'
#    end   = '20 0 0'
#    sort_by = id
#    property = fm
#  [../]
[]

[Postprocessors]
  [./f_el_int]
    type = ElementIntegralMaterialProperty
    mat_prop = f_el_mat
  [../]
  [./c_alpha]
    type =  SideAverageValue
    boundary = left
    variable = c
  [../]
  [./c_beta]
    type =  SideAverageValue
    boundary = right
    variable = c
  [../]
  [./e11_alpha]
    type =  SideAverageValue
    boundary = left
    variable = e11
  [../]
  [./e11_beta]
    type =  SideAverageValue
    boundary = right
    variable = e11
  [../]
  [./s11_alpha]
    type =  SideAverageValue
    boundary = left
    variable = sigma11
  [../]
  [./s22_alpha]
    type =  SideAverageValue
    boundary = left
    variable = sigma22
  [../]
  [./s33_alpha]
    type =  SideAverageValue
    boundary = left
    variable = sigma33
  [../]
  [./s11_beta]
    type =  SideAverageValue
    boundary = right
    variable = sigma11
  [../]
  [./s22_beta]
    type =  SideAverageValue
    boundary = right
    variable = sigma22
  [../]
  [./s33_beta]
    type =  SideAverageValue
    boundary = right
    variable = sigma33
  [../]
  [./f_el_alpha]
    type =  SideAverageValue
    boundary = left
    variable = f_el
  [../]
  [./f_el_beta]
    type =  SideAverageValue
    boundary = right
    variable = f_el
  [../]
  [./f_c_alpha]
    type =  SideAverageValue
    boundary = left
    variable = Fglobal
  [../]
  [./f_c_beta]
    type =  SideAverageValue
    boundary = right
    variable = Fglobal
  [../]
  [./chem_pot_alpha]
    type =  SideAverageValue
    boundary = left
    variable = w
  [../]
  [./chem_pot_beta]
    type =  SideAverageValue
    boundary = right
    variable = w
  [../]
  [./psi_alpha]
    type =  SideAverageValue
    boundary = left
    variable = psi
  [../]
  [./psi_beta]
    type =  SideAverageValue
    boundary = right
    variable = psi
  [../]
  [./total_energy]
    type = ElementIntegralVariablePostprocessor
    variable = Fglobal
  [../]
  # Get simulation cell size from postprocessor
  [./volume]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
  [../]
  [./psi_eq_int]
    type = FunctionValuePostprocessor
    function = psi_eq_int
  [../]
  [./psi_int]
    type = ElementIntegralVariablePostprocessor
    variable = psi
  [../]
  [./gamma]
    type = FunctionValuePostprocessor
    function = gamma
  [../]
[]

#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
  [./full]
    type = SMP
    full = true
  [../]
[]


[Outputs]
  [./exodus]
    type = Exodus
    interval = 20
  [../]
  [./csv]
    type = CSV
    execute_on = 'final'
  [../]
#[./console]
#    type = Console
#    output_file = true
#  [../]
[]

(modules/phase_field/test/tests/misc/coupled_value_function_ic.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []
[]

# Here we sum up the inverses of the ICs above. This should add up to 2.0 everywhere
[Functions]
  [map]
    type = ParsedFunction
    value = 'x^2+y^3+log(z)+acos(t)'
  []
[]

[Variables]
  [out]
    [InitialCondition]
      type = CoupledValueFunctionIC
      function = map
      v = 'v1 v2 a3 a4'
    []
  []
  [v1]
    [InitialCondition]
      type = FunctionIC
      function = x^(1/2)
    []
  []
  [v2]
    [InitialCondition]
      type = FunctionIC
      function = y^(1/3)
    []
  []
[]

[AuxVariables]
  [a3]
    [InitialCondition]
      type = FunctionIC
      function = exp(1-x)
    []
  []
  [a4]
    [InitialCondition]
      type = FunctionIC
      function = cos(1-y)
    []
  []
[]

[Postprocessors]
  [out_min]
    type = ElementExtremeValue
    variable = out
    value_type = min
  []
  [out_max]
    type = ElementExtremeValue
    variable = out
    value_type = max
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  execute_on = 'FINAL'
  csv = true
[]

(modules/porous_flow/examples/coal_mining/fine_with_fluid.i)

#################################################################
#
#  NOTE:
#  The mesh for this model is too large for the MOOSE repository
#  so is kept in the the large_media submodule
#
#################################################################
#
# Strata deformation and fluid flow aaround a coal mine - 3D model
#
# A "half model" is used.  The mine is 400m deep and
# just the roof is studied (-400<=z<=0).  The mining panel
# sits between 0<=x<=150, and 0<=y<=1000, so this simulates
# a coal panel that is 300m wide and 1000m long.  The outer boundaries
# are 1km from the excavation boundaries.
#
# The excavation takes 0.5 years.
#
# The boundary conditions for this simulation are:
#  - disp_x = 0 at x=0 and x=1150
#  - disp_y = 0 at y=-1000 and y=1000
#  - disp_z = 0 at z=-400, but there is a time-dependent
#               Young modulus that simulates excavation
#  - wc_x = 0 at y=-1000 and y=1000
#  - wc_y = 0 at x=0 and x=1150
#  - no flow at x=0, z=-400 and z=0
#  - fixed porepressure at y=-1000, y=1000 and x=1150
# That is, rollers on the sides, free at top,
# and prescribed at bottom in the unexcavated portion.
#
# A single-phase unsaturated fluid is used.
#
# The small strain formulation is used.
#
# All stresses are measured in MPa, and time units are measured in years.
#
# The initial porepressure is hydrostatic with P=0 at z=0, so
# Porepressure ~ - 0.01*z MPa, where the fluid has density 1E3 kg/m^3 and
# gravity = = 10 m.s^-2 = 1E-5 MPa m^2/kg.
# To be more accurate, i use
# Porepressure = -bulk * log(1 + g*rho0*z/bulk)
# where bulk=2E3 MPa and rho0=1Ee kg/m^3.
# The initial stress is consistent with the weight force from undrained
# density 2500 kg/m^3, and fluid porepressure, and a Biot coefficient of 0.7, ie,
# stress_zz^effective = 0.025*z + 0.7 * initial_porepressure
# The maximum and minimum principal horizontal effective stresses are
# assumed to be equal to 0.8*stress_zz.
#
# Material properties:
# Young's modulus = 8 GPa
# Poisson's ratio = 0.25
# Cosserat layer thickness = 1 m
# Cosserat-joint normal stiffness = large
# Cosserat-joint shear stiffness = 1 GPa
# MC cohesion = 2 MPa
# MC friction angle = 35 deg
# MC dilation angle = 8 deg
# MC tensile strength = 1 MPa
# MC compressive strength = 100 MPa
# WeakPlane cohesion = 0.1 MPa
# WeakPlane friction angle = 30 deg
# WeakPlane dilation angle = 10 deg
# WeakPlane tensile strength = 0.1 MPa
# WeakPlane compressive strength = 100 MPa softening to 1 MPa at strain = 1
# Fluid density at zero porepressure = 1E3 kg/m^3
# Fluid bulk modulus = 2E3 MPa
# Fluid viscosity = 1.1E-3 Pa.s = 1.1E-9 MPa.s = 3.5E-17 MPa.year
#
[GlobalParams]
  perform_finite_strain_rotations = false
  displacements = 'disp_x disp_y disp_z'
  Cosserat_rotations = 'wc_x wc_y wc_z'
  PorousFlowDictator = dictator
  biot_coefficient = 0.7
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = fine.e
  []
  [xmin]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    new_boundary = xmin
    normal = '-1 0 0'
    input = file
  []
  [xmax]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    new_boundary = xmax
    normal = '1 0 0'
    input = xmin
  []
  [ymin]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    new_boundary = ymin
    normal = '0 -1 0'
    input = xmax
  []
  [ymax]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    new_boundary = ymax
    normal = '0 1 0'
    input = ymin
  []
  [zmax]
    type = SideSetsAroundSubdomainGenerator
    block = 30
    new_boundary = zmax
    normal = '0 0 1'
    input = ymax
  []
  [zmin]
    type = SideSetsAroundSubdomainGenerator
    block = 2
    new_boundary = zmin
    normal = '0 0 -1'
    input = zmax
  []
  [excav]
    type = SubdomainBoundingBoxGenerator
    input = zmin
    block_id = 1
    bottom_left = '0 0 -400'
    top_right = '150 1000 -397'
  []
  [roof]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 3
    paired_block = 1
    input = excav
    new_boundary = roof
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [wc_x]
  []
  [wc_y]
  []
  [porepressure]
    scaling = 1E-5
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = ini_pp
  []
[]

[Kernels]
  [cx_elastic]
    type = CosseratStressDivergenceTensors
    use_displaced_mesh = false
    variable = disp_x
    component = 0
  []
  [cy_elastic]
    type = CosseratStressDivergenceTensors
    use_displaced_mesh = false
    variable = disp_y
    component = 1
  []
  [cz_elastic]
    type = CosseratStressDivergenceTensors
    use_displaced_mesh = false
    variable = disp_z
    component = 2
  []
  [x_couple]
    type = StressDivergenceTensors
    use_displaced_mesh = false
    variable = wc_x
    displacements = 'wc_x wc_y wc_z'
    component = 0
    base_name = couple
  []
  [y_couple]
    type = StressDivergenceTensors
    use_displaced_mesh = false
    variable = wc_y
    displacements = 'wc_x wc_y wc_z'
    component = 1
    base_name = couple
  []
  [x_moment]
    type = MomentBalancing
    use_displaced_mesh = false
    variable = wc_x
    component = 0
  []
  [y_moment]
    type = MomentBalancing
    use_displaced_mesh = false
    variable = wc_y
    component = 1
  []
  [gravity]
    type = Gravity
    use_displaced_mesh = false
    variable = disp_z
    value = -10E-6 # remember this is in MPa
  []
  [poro_x]
    type = PorousFlowEffectiveStressCoupling
    use_displaced_mesh = false
    variable = disp_x
    component = 0
  []
  [poro_y]
    type = PorousFlowEffectiveStressCoupling
    use_displaced_mesh = false
    variable = disp_y
    component = 1
  []
  [poro_z]
    type = PorousFlowEffectiveStressCoupling
    use_displaced_mesh = false
    component = 2
    variable = disp_z
  []
  [poro_vol_exp]
    type = PorousFlowMassVolumetricExpansion
    use_displaced_mesh = false
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    variable = porepressure
    fluid_component = 0
  []
  [mass0]
    type = PorousFlowMassTimeDerivative
    use_displaced_mesh = false
    fluid_component = 0
    variable = porepressure
  []
  [flux]
    type = PorousFlowAdvectiveFlux
    use_displaced_mesh = false
    variable = porepressure
    gravity = '0 0 -10E-6'
    fluid_component = 0
  []
[]


[AuxVariables]
  [saturation]
    order = CONSTANT
    family = MONOMIAL
  []
  [darcy_x]
    order = CONSTANT
    family = MONOMIAL
  []
  [darcy_y]
    order = CONSTANT
    family = MONOMIAL
  []
  [darcy_z]
    order = CONSTANT
    family = MONOMIAL
  []
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
  [wc_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [perm_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [perm_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [perm_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_shear]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_tensile]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_shear]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_tensile]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_shear_f]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_tensile_f]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_shear_f]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_tensile_f]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_water]
    type = PorousFlowPropertyAux
    variable = saturation
    property = saturation
    phase = 0
    execute_on = timestep_end
  []
  [darcy_x]
    type = PorousFlowDarcyVelocityComponent
    variable = darcy_x
    gravity = '0 0 -10E-6'
    component = x
  []
  [darcy_y]
    type = PorousFlowDarcyVelocityComponent
    variable = darcy_y
    gravity = '0 0 -10E-6'
    component = y
  []
  [darcy_z]
    type = PorousFlowDarcyVelocityComponent
    variable = darcy_z
    gravity = '0 0 -10E-6'
    component = z
  []
  [porosity]
    type = PorousFlowPropertyAux
    property = porosity
    variable = porosity
    execute_on = timestep_end
  []
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  []
  [stress_xz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xz
    index_i = 0
    index_j = 2
    execute_on = timestep_end
  []
  [stress_yx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yx
    index_i = 1
    index_j = 0
    execute_on = timestep_end
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yz
    index_i = 1
    index_j = 2
    execute_on = timestep_end
  []
  [stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
    execute_on = timestep_end
  []
  [stress_zy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zy
    index_i = 2
    index_j = 1
    execute_on = timestep_end
  []
  [stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_xz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xz
    index_i = 0
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_yx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yx
    index_i = 1
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_yz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yz
    index_i = 1
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_zx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zx
    index_i = 2
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_zy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zy
    index_i = 2
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [perm_xx]
    type = PorousFlowPropertyAux
    property = permeability
    variable = perm_xx
    row = 0
    column = 0
    execute_on = timestep_end
  []
  [perm_yy]
    type = PorousFlowPropertyAux
    property = permeability
    variable = perm_yy
    row = 1
    column = 1
    execute_on = timestep_end
  []
  [perm_zz]
    type = PorousFlowPropertyAux
    property = permeability
    variable = perm_zz
    row = 2
    column = 2
    execute_on = timestep_end
  []
  [mc_shear]
    type = MaterialStdVectorAux
    index = 0
    property = mc_plastic_internal_parameter
    variable = mc_shear
    execute_on = timestep_end
  []
  [mc_tensile]
    type = MaterialStdVectorAux
    index = 1
    property = mc_plastic_internal_parameter
    variable = mc_tensile
    execute_on = timestep_end
  []
  [wp_shear]
    type = MaterialStdVectorAux
    index = 0
    property = wp_plastic_internal_parameter
    variable = wp_shear
    execute_on = timestep_end
  []
  [wp_tensile]
    type = MaterialStdVectorAux
    index = 1
    property = wp_plastic_internal_parameter
    variable = wp_tensile
    execute_on = timestep_end
  []
  [mc_shear_f]
    type = MaterialStdVectorAux
    index = 6
    property = mc_plastic_yield_function
    variable = mc_shear_f
    execute_on = timestep_end
  []
  [mc_tensile_f]
    type = MaterialStdVectorAux
    index = 0
    property = mc_plastic_yield_function
    variable = mc_tensile_f
    execute_on = timestep_end
  []
  [wp_shear_f]
    type = MaterialStdVectorAux
    index = 0
    property = wp_plastic_yield_function
    variable = wp_shear_f
    execute_on = timestep_end
  []
  [wp_tensile_f]
    type = MaterialStdVectorAux
    index = 1
    property = wp_plastic_yield_function
    variable = wp_tensile_f
    execute_on = timestep_end
  []
[]



[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'xmin xmax'
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'ymin ymax'
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = zmin
    value = 0.0
  []
  [no_wc_x]
    type = DirichletBC
    variable = wc_x
    boundary = 'ymin ymax'
    value = 0.0
  []
  [no_wc_y]
    type = DirichletBC
    variable = wc_y
    boundary = 'xmin xmax'
    value = 0.0
  []
  [fix_porepressure]
    type = FunctionDirichletBC
    variable = porepressure
    boundary = 'ymin ymax xmax'
    function = ini_pp
  []
  [roof_porepressure]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    pt_vals = '-1E3 1E3'
    multipliers = '-1 1'
    fluid_phase = 0
    flux_function = roof_conductance
    boundary = roof
  []
  [roof]
    type = StickyBC
    variable = disp_z
    min_value = -3.0
    boundary = roof
  []
[]

[Functions]
  [ini_pp]
    type = ParsedFunction
    vars = 'bulk p0 g    rho0'
    vals = '2E3 0.0 1E-5 1E3'
    value = '-bulk*log(exp(-p0/bulk)+g*rho0*z/bulk)'
  []
  [ini_xx]
    type = ParsedFunction
    vars = 'bulk p0 g    rho0 biot'
    vals = '2E3 0.0 1E-5 1E3  0.7'
    value = '0.8*(2500*10E-6*z+biot*(-bulk*log(exp(-p0/bulk)+g*rho0*z/bulk)))'
  []
  [ini_zz]
    type = ParsedFunction
    vars = 'bulk p0 g    rho0 biot'
    vals = '2E3 0.0 1E-5 1E3  0.7'
    value = '2500*10E-6*z+biot*(-bulk*log(exp(-p0/bulk)+g*rho0*z/bulk))'
  []
  [excav_sideways]
    type = ParsedFunction
    vars = 'end_t ymin ymax  minval maxval slope'
    vals = '0.5   0    1000.0 1E-9 1 10'
    # excavation face at ymin+(ymax-ymin)*min(t/end_t,1)
    # slope is the distance over which the modulus reduces from maxval to minval
    value = 'if(y<ymin+(ymax-ymin)*min(t/end_t,1),minval,if(y<ymin+(ymax-ymin)*min(t/end_t,1)+slope,minval+(maxval-minval)*(y-(ymin+(ymax-ymin)*min(t/end_t,1)))/slope,maxval))'
  []
  [density_sideways]
    type = ParsedFunction
    vars = 'end_t ymin ymax  minval maxval'
    vals = '0.5   0    1000.0 0 2500'
    value = 'if(y<ymin+(ymax-ymin)*min(t/end_t,1),minval,maxval)'
  []
  [roof_conductance]
    type = ParsedFunction
    vars = 'end_t ymin ymax   maxval minval'
    vals = '0.5   0    1000.0 1E7      0'
    value = 'if(y<ymin+(ymax-ymin)*min(t/end_t,1),maxval,minval)'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure disp_x disp_y disp_z'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1 # MPa^-1
  []

  [mc_coh_strong_harden]
    type = TensorMechanicsHardeningExponential
    value_0 = 1.99 # MPa
    value_residual = 2.01 # MPa
    rate = 1.0
  []
  [mc_fric]
    type = TensorMechanicsHardeningConstant
    value = 0.61 # 35deg
  []
  [mc_dil]
    type = TensorMechanicsHardeningConstant
    value = 0.15 # 8deg
  []

  [mc_tensile_str_strong_harden]
    type = TensorMechanicsHardeningExponential
    value_0 = 1.0 # MPa
    value_residual = 1.0 # MPa
    rate = 1.0
  []
  [mc_compressive_str]
    type = TensorMechanicsHardeningCubic
    value_0 = 100 # Large!
    value_residual = 100
    internal_limit = 0.1
  []

  [wp_coh_harden]
    type = TensorMechanicsHardeningCubic
    value_0 = 0.05
    value_residual = 0.05
    internal_limit = 10
  []
  [wp_tan_fric]
    type = TensorMechanicsHardeningConstant
    value = 0.26 # 15deg
  []
  [wp_tan_dil]
    type = TensorMechanicsHardeningConstant
    value = 0.18 # 10deg
  []

  [wp_tensile_str_harden]
    type = TensorMechanicsHardeningCubic
    value_0 = 0.05
    value_residual = 0.05
    internal_limit = 10
  []
  [wp_compressive_str_soften]
    type = TensorMechanicsHardeningCubic
    value_0 = 100
    value_residual = 1
    internal_limit = 1.0
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E3
      density0 = 1000
      thermal_expansion = 0
      viscosity = 3.5E-17
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [eff_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [vol_strain]
    type = PorousFlowVolumetricStrain
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity_for_aux]
    type = PorousFlowPorosity
    at_nodes = false
    fluid = true
    mechanical = true
    ensure_positive = true
    porosity_zero = 0.02
    solid_bulk = 5.3333E3
  []
  [porosity_bulk]
    type = PorousFlowPorosity
    fluid = true
    mechanical = true
    block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    ensure_positive = true
    porosity_zero = 0.02
    solid_bulk = 5.3333E3
  []
  [porosity_excav]
    type = PorousFlowPorosityConst
    block = 1
    porosity = 1.0
  []
  [permeability_bulk]
    type = PorousFlowPermeabilityKozenyCarman
    block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    poroperm_function = kozeny_carman_phi0
    k0 = 1E-15
    phi0 = 0.02
    n = 2
    m = 2
  []
  [permeability_excav]
    type = PorousFlowPermeabilityConst
    block = 1
    permeability = '0 0 0   0 0 0   0 0 0'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 4
    s_res = 0.4
    sum_s_res = 0.4
    phase = 0
  []

  [elasticity_tensor_0]
    type = ComputeLayeredCosseratElasticityTensor
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    young = 8E3 # MPa
    poisson = 0.25
    layer_thickness = 1.0
    joint_normal_stiffness = 1E9 # huge
    joint_shear_stiffness = 1E3 # MPa
  []
  [elasticity_tensor_1]
    type = ComputeLayeredCosseratElasticityTensor
    block = 1
    young = 8E3 # MPa
    poisson = 0.25
    layer_thickness = 1.0
    joint_normal_stiffness = 1E9 # huge
    joint_shear_stiffness = 1E3 # MPa
    elasticity_tensor_prefactor = excav_sideways
  []
  [strain]
    type = ComputeCosseratIncrementalSmallStrain
    eigenstrain_names = ini_stress
  []
  [ini_stress]
    type = ComputeEigenstrainFromInitialStress
    eigenstrain_name = ini_stress
    initial_stress = 'ini_xx 0 0  0 ini_xx 0  0 0 ini_zz'
  []

  [stress_0]
    type = ComputeMultipleInelasticCosseratStress
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    inelastic_models = 'mc wp'
    cycle_models = true
    relative_tolerance = 2.0
    absolute_tolerance = 1E6
    max_iterations = 1
    tangent_operator = nonlinear
    perform_finite_strain_rotations = false
  []
  [stress_1]
    type = ComputeMultipleInelasticCosseratStress
    block = 1
    inelastic_models = ''
    relative_tolerance = 2.0
    absolute_tolerance = 1E6
    max_iterations = 1
    tangent_operator = nonlinear
    perform_finite_strain_rotations = false
  []
  [mc]
    type = CappedMohrCoulombCosseratStressUpdate
    warn_about_precision_loss = false
    host_youngs_modulus = 8E3
    host_poissons_ratio = 0.25
    base_name = mc
    tensile_strength = mc_tensile_str_strong_harden
    compressive_strength = mc_compressive_str
    cohesion = mc_coh_strong_harden
    friction_angle = mc_fric
    dilation_angle = mc_dil
    max_NR_iterations = 100000
    smoothing_tol = 0.1 # MPa  # Must be linked to cohesion
    yield_function_tol = 1E-9 # MPa.  this is essentially the lowest possible without lots of precision loss
    perfect_guess = true
    min_step_size = 1.0
  []
  [wp]
    type = CappedWeakPlaneCosseratStressUpdate
    warn_about_precision_loss = false
    base_name = wp
    cohesion = wp_coh_harden
    tan_friction_angle = wp_tan_fric
    tan_dilation_angle = wp_tan_dil
    tensile_strength = wp_tensile_str_harden
    compressive_strength = wp_compressive_str_soften
    max_NR_iterations = 10000
    tip_smoother = 0.05
    smoothing_tol = 0.05 # MPa  # Note, this must be tied to cohesion, otherwise get no possible return at cone apex
    yield_function_tol = 1E-11 # MPa.  this is essentially the lowest possible without lots of precision loss
    perfect_guess = true
    min_step_size = 1.0E-3
  []


  [undrained_density_0]
    type = GenericConstantMaterial
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    prop_names = density
    prop_values = 2500
  []
  [undrained_density_1]
    type = GenericFunctionMaterial
    block = 1
    prop_names = density
    prop_values = density_sideways
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[Postprocessors]
  [min_roof_disp]
    type = NodalExtremeValue
    boundary = roof
    value_type = min
    variable = disp_z
  []
  [min_roof_pp]
    type = NodalExtremeValue
    boundary = roof
    value_type = min
    variable = porepressure
  []
  [min_surface_disp]
    type = NodalExtremeValue
    boundary = zmax
    value_type = min
    variable = disp_z
  []
  [min_surface_pp]
    type = NodalExtremeValue
    boundary = zmax
    value_type = min
    variable = porepressure
  []
  [max_perm_zz]
    type = ElementExtremeValue
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30'
    variable = perm_zz
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  petsc_options = '-snes_converged_reason'

  # best overall
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = ' lu       mumps'

  # best if you don't have mumps:
  #petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -ksp_type -ksp_gmres_restart'
  #petsc_options_value = ' asm      2              lu            gmres     200'

  # very basic:
  #petsc_options_iname = '-pc_type -ksp_type -ksp_gmres_restart'
  #petsc_options_value = ' bjacobi  gmres     200'

  line_search = bt

  nl_abs_tol = 1e-3
  nl_rel_tol = 1e-5

  l_max_its = 200
  nl_max_its = 30

  start_time = 0.0
  dt = 0.0025
  end_time = 0.5
[]

[Outputs]
  interval = 1
  print_linear_residuals = true
  exodus = true
  csv = true
  console = true
[]

(test/tests/auxkernels/solution_aux/aux_nonlinear_solution_xda.i)

[Mesh]
  # This test uses SolutionUserObject which doesn't work with DistributedMesh.
  type = GeneratedMesh
  parallel_type = replicated
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./u_aux]
  [../]
[]

[Functions]
  [./u_xda_func]
    type = SolutionFunction
    solution = xda_u
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[AuxKernels]
  [./aux_xda_kernel]
    type = SolutionAux
    variable = u_aux
    solution = xda_u_aux
    execute_on = initial
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 2
  [../]
[]

[UserObjects]
  [./xda_u_aux]
    type = SolutionUserObject
    system = aux0
    mesh = aux_nonlinear_solution_out_0001_mesh.xda
    es = aux_nonlinear_solution_out_0001.xda
    system_variables = u_aux
    execute_on = initial
  [../]
  [./xda_u]
    type = SolutionUserObject
    system = nl0
    mesh = aux_nonlinear_solution_out_0001_mesh.xda
    es = aux_nonlinear_solution_out_0001.xda
    system_variables = u
    execute_on = initial
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_rel_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./u_func_ic]
    function = u_xda_func
    variable = u
    type = FunctionIC
  [../]
[]

(modules/combined/test/tests/DiffuseCreep/strain_gb_relax.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.1*v'
    [../]
  [../]
  [./mu]
  [../]
  [./jx]
  [../]
  [./jy]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./strain_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./strain_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./strain_xy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = mu_prop
    c = c
  [../]
  [./flux_x]
    type = CHSplitFlux
    variable = jx
    component = 0
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./flux_y]
    type = CHSplitFlux
    variable = jy
    component = 1
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./strain_xx]
    type = RankTwoAux
    variable = strain_xx
    rank_two_tensor = strain
    index_i = 0
    index_j = 0
  [../]
  [./strain_yy]
    type = RankTwoAux
    variable = strain_yy
    rank_two_tensor = strain
    index_i = 1
    index_j = 1
  [../]
  [./strain_xy]
    type = RankTwoAux
    variable = strain_xy
    rank_two_tensor = strain
    index_i = 0
    index_j = 1
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
  [./gb_relax_prefactor]
    type = DerivativeParsedMaterial
    block = 0
    function = '0.01*(c-0.15)*gb'
    args = 'c gb'
    f_name = gb_relax_prefactor
    derivative_order = 1
  [../]
  [./gb_relax]
    type = GBRelaxationStrainIncrement
    property_name = gb_relax
    prefactor_name = gb_relax_prefactor
    gb_normal_name = gb_normal
  [../]
  [./strain]
    type = SumTensorIncrements
    tensor_name = strain
    coupled_tensor_increment_names = gb_relax
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  nl_max_its = 5
  dt = 20
  num_steps = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/function_file_test15.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_rows_more_data.csv
    xy_in_file_only = false
    x_index_in_file = 3 # will generate an error because no forth row of data
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/combined/test/tests/GBDependentTensors/gb_property.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.1*v'
    [../]
  [../]
  [./mu]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./mobility_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./mobility_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./diffusivity_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./diffusivity_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./aniso_tensor_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./aniso_tensor_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = mu_prop
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./mobility_xx]
    type = MaterialRealTensorValueAux
    variable = mobility_xx
    property = mobility_prop
    row = 0
    column = 0
  [../]
  [./mobility_yy]
    type = MaterialRealTensorValueAux
    variable = mobility_yy
    property = mobility_prop
    row = 1
    column = 1
  [../]
  [./diffusivity_xx]
    type = MaterialRealTensorValueAux
    variable = diffusivity_xx
    property = diffusivity
    row = 0
    column = 0
  [../]
  [./diffusivity_yy]
    type = MaterialRealTensorValueAux
    variable = diffusivity_yy
    property = diffusivity
    row = 1
    column = 1
  [../]
  [./aniso_tensor_xx]
    type = MaterialRealTensorValueAux
    variable = aniso_tensor_xx
    property = aniso_tensor
    row = 0
    column = 0
  [../]
  [./aniso_tensor_yy]
    type = MaterialRealTensorValueAux
    variable = aniso_tensor_yy
    property = aniso_tensor
    row = 1
    column = 1
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 20
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  l_tol = 1e-3
  l_max_its = 20
  nl_max_its = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/hysteresis/hys_pc_3.i)

# Capillary-pressure calculation.  Third-order curve
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0.4
    xmax = 0.9
    nx = 50
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = ''
  []
[]

[Variables]
  [sat]
  []
[]

[ICs]
  [sat]
    type = FunctionIC
    variable = sat
    function = 'x'
  []
[]

[BCs]
  [sat]
    type = FunctionDirichletBC
    variable = sat
    function = 'x'
    boundary = 'left right'
  []
[]


[Kernels]
  [dummy]
    type = Diffusion
    variable = sat
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
    initial_order = 3
    previous_turning_points = '0.1 0.9 0.4'
  []
  [pc_calculator]
    type = PorousFlowHystereticInfo
    alpha_d = 10.0
    alpha_w = 7.0
    n_d = 1.5
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 12.0
    high_ratio = 0.9
    low_extension_type = none
    high_extension_type = none
    sat_var = sat
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [pc]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [pc]
    type = PorousFlowPropertyAux
    variable = pc
    property = hysteretic_info
  []
[]

[VectorPostprocessors]
  [pc]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0.4 0 0'
    end_point = '0.9 0 0'
    num_points = 8
    sort_by = x
    variable = 'sat pc'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/hysteresis/hys_pc_2.i)

# Capillary-pressure calculation.  Second-order drying curve
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0.1
    xmax = 0.9
    nx = 80
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = ''
  []
[]

[Variables]
  [sat]
  []
[]

[ICs]
  [sat]
    type = FunctionIC
    variable = sat
    function = 'x'
  []
[]

[BCs]
  [sat]
    type = FunctionDirichletBC
    variable = sat
    function = 'x'
    boundary = 'left right'
  []
[]


[Kernels]
  [dummy]
    type = Diffusion
    variable = sat
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
    initial_order = 2
    previous_turning_points = '0.1 0.9'
  []
  [pc_calculator]
    type = PorousFlowHystereticInfo
    alpha_d = 10.0
    alpha_w = 7.0
    n_d = 1.5
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 12.0
    high_ratio = 0.9
    low_extension_type = none
    high_extension_type = none
    sat_var = sat
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [pc]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [pc]
    type = PorousFlowPropertyAux
    variable = pc
    property = hysteretic_info
  []
[]

[VectorPostprocessors]
  [pc]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0.1 0 0'
    end_point = '0.9 0 0'
    num_points = 8
    sort_by = x
    variable = 'sat pc'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/capillary_pressure/vangenuchten1.i)

# Test van Genuchten relative permeability curve by varying saturation over the mesh
# van Genuchten exponent m = 0.5 for both phases
# No residual saturation in either phase

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [p0]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 0
    variable = p0aux
  []
  [p1]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = p1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1e-5
    m = 0.5
    sat_lr = 0.1
    log_extension = false
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    variable = 's0aux s1aux p0aux p1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 500
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-6
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/level_set/test/tests/transfers/copy_solution/master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    function = 'x*x*y'
    variable = u
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[MultiApps]
  [./sub]
    type = FullSolveMultiApp
    input_files = 'sub.i'
    execute_on = timestep_end
  [../]
[]

[Transfers]
  [./to_sub]
    type = MultiAppCopyTransfer
    variable = u
    source_variable = u
    to_multi_app = sub
    execute_on = timestep_end
    check_multiapp_execute_on = false
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/excav/ex01.i)

###########################################
#                                         #
#   THIS EXAMPLE CONTAINS AN EXCAVATION   #
#                                         #
###########################################


# Easiest way of figuring out what's happening:
# Run this example, load into paraview, take
# a slice through (0,0,0) with normal (0,0,1),
# colour by pressure and play the animation.


# This mesh has an interior sideset called excav_bdy
[Mesh]
  type = FileMesh
  file = ex01_input.e
[]



# This is a boundary condition acting on excav_bdy
# All it does is to set the pressure to p_excav=0
# at places on excav_bdy wherever excav_fcn tells it to.
[BCs]
  [./excav_bdy]
    type = RichardsExcav
    boundary = excav_bdy
    p_excav = 0.0
    variable = pressure
    excav_geom_function = excav_fcn
  [../]
[]



[Functions]
# excav_fcn controls where to set pressure=p_excav
# You supply start and end positions and times and
# by a linear interpolation these define the position
# of the coal face at all times
  [./excav_fcn]
    type = RichardsExcavGeom
    start_posn = '0 -500 0'
    start_time = 0
    end_posn = '0 -300 0'
    end_time = 6E6
    active_length = 1E4
  [../]

# mass_bal_fcn calculates the mass balance
  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-fout-mf)/2/(mi+mf))
    vars = 'mi mf fout'
    vals = 'mass_init mass_final flux_out'
  [../]

# initial pressure - unimportant in this example
  [./initial_pressure]
    type = ParsedFunction
    value = -10000*(z-100)
  [../]
[]




# following is needed by postprocessors, kernels, etc
# unimportant in this example
[GlobalParams]
  richardsVarNames_UO = PPNames
[]




# following does the calculation of relevant
# masses and mass-flux to the excavation
[Postprocessors]

# note that this is calculated at beginning of timestep
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = 'initial timestep_begin'
  [../]

# note this is calculated at end of timestep
  [./mass_final]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

# this is what calculates the mass flux to the excavation
# it is calculating it for boundary=excav_bdy, and the
# excavation time-dependence is set through the excav_fcn
  [./flux_out]
    type = RichardsExcavFlow
    boundary = excav_bdy
    variable = pressure
    excav_geom_function = excav_fcn
  [../]

# mass_bal just outputs the result to screen
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]




######################################
#                                    #
#  THE FOLLOWING STUFF IS STANDARD   #
#                                    #
######################################


[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E+2
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = '1 2 3 4'
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-15 0 0  0 1E-15 0  0 0 1E-15'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 -10'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-13 1E-14 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 6E6
  dt = 3E6
  solve_type = NEWTON
[]

[Outputs]
  file_base = ex01
  exodus = true
  csv = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/jacobian_02.i)

# Checking the Jacobian of Flux-Limited TVD Advection, using flux_limiter_type = superbee
# Here we use snes_check_jacobian instead of snes_type=test.  The former just checks the Jacobian for the
# random initial conditions, while the latter checks for u=1 and u=-1
#
# The Jacobian is correct for u=1 and u=-1, but the finite-difference scheme used by snes_type=test gives the
# wrong answer.
# For u=1, the Kuzmin-Turek scheme adds as much antidiffusion as possible, resulting in a central-difference
# version of advection (flux_limiter = 1).  This is correct, and the Jacobian is calculated correctly.
# However, when computing the Jacobian using finite differences, u is increased or decreased at a node.
# This results in that node being at a maximum or minimum, which means no antidiffusion should be added
# (flux_limiter = 0).  This corresponds to a full-upwind scheme.  So the finite-difference computes the
# Jacobian in the full-upwind scenario, which is incorrect (the original residual = 0, after finite-differencing
# the residual comes from the full-upwind scenario).
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 2
  xmin = 0
  xmax = 1
  ny = 2
  ymin = -1
  ymax = 2
  bias_y = 1.5
  nz = 2
  zmin = 1
  zmax = 2
  bias_z = 0.8
[]

[Variables]
  [u]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x + 0.5 * y - 0.4 * z - 0.1 * sin(x) - 0.1 * cos(y) + 0.2 * exp(-z)'
  []
[]

[Kernels]
  [flux]
    type = FluxLimitedTVDAdvection
    variable = u
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = u
    velocity = '1 -2 1.5'
  []
[]


[Preconditioning]
  active = smp
  [smp]
    type = SMP
    full = true
    petsc_options = '-snes_check_jacobian'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear # this is to force convergence even though the nonlinear residual is high: we just care about the Jacobian in this test
  end_time = 1
  num_steps = 1
  dt = 1
[]

(modules/porous_flow/test/tests/poroperm/except1.i)

# Exception test: thermal=true but no thermal_expansion_coeff provided
[Mesh]
  type = GeneratedMesh
  dim = 3
[]

[GlobalParams]
  PorousFlowDictator = dictator
  displacements = 'disp_x disp_y disp_z'
  biot_coefficient = 0.7
[]

[Variables]
  [porepressure]
    initial_condition = 2
  []
  [temperature]
    initial_condition = 4
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[ICs]
  [disp_x]
    type = FunctionIC
    function = '0.5 * x'
    variable = disp_x
  []
[]

[Kernels]
  [dummy_p]
    type = TimeDerivative
    variable = porepressure
  []
  [dummy_t]
    type = TimeDerivative
    variable = temperature
  []
  [dummy_x]
    type = TimeDerivative
    variable = disp_x
  []
  [dummy_y]
    type = TimeDerivative
    variable = disp_y
  []
  [dummy_z]
    type = TimeDerivative
    variable = disp_z
  []
[]

[AuxVariables]
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [porosity]
    type = PorousFlowPropertyAux
    property = porosity
    variable = porosity
  []
[]

[Postprocessors]
  [porosity]
    type = PointValue
    variable = porosity
    point = '0 0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure temperature'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [eff_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [vol_strain]
    type = PorousFlowVolumetricStrain
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [porosity]
    type = PorousFlowPorosity
    mechanical = true
    fluid = true
    thermal = true
    ensure_positive = false
    porosity_zero = 0.5
    solid_bulk = 0.3
    reference_porepressure = 3
    reference_temperature = 3.5
  []
[]

[Executioner]
  solve_type = Newton
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
[]

(test/tests/bcs/periodic/no_add_scalar.i)

# Test to make sure that periodic boundaries
# are not applied to scalar variables.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
  [./scalar]
    family = SCALAR
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = x
    [../]
  [../]
[]

[Kernels]
  [./dt]
    type = TimeDerivative
    variable = c
  [../]
  [./diff]
    type = Diffusion
    variable = c
  [../]
[]

[ScalarKernels]
  [./scalar]
    type = ODETimeDerivative
    variable = scalar
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.1
  num_steps = 3
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/newton_cooling/nc06.i)

# Newton cooling from a bar.  1-phase and heat, steady
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 1
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pressure temp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.8
    alpha = 1e-5
  []
[]

[Variables]
  [pressure]
  []
  [temp]
  []
[]

[ICs]
  # have to start these reasonably close to their steady-state values
  [pressure]
    type = FunctionIC
    variable = pressure
    function = '(2-x/100)*1E6'
  []
  [temperature]
    type = FunctionIC
    variable = temp
    function = 100+0.1*x
  []
[]

[Kernels]
  [flux]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    gravity = '0 0 0'
    variable = pressure
  []
  [heat_advection]
    type = PorousFlowHeatAdvection
    gravity = '0 0 0'
    variable = temp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1e6
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
      cv = 1e6
      porepressure_coefficient = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey # irrelevant in this fully-saturated situation
    n = 2
    phase = 0
  []
[]

[BCs]
  [leftp]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 2E6
  []
  [leftt]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 100
  []
  [newtonp]
    type = PorousFlowPiecewiseLinearSink
    variable = pressure
    boundary = right
    pt_vals = '0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000 1100000 1200000 1300000 1400000 1500000 1600000 1700000 1800000 1900000 2000000'
    multipliers = '0. 5.6677197748570516e-6 0.000011931518841831313 0.00001885408740732065 0.000026504708864284114 0.000034959953203725676 0.000044304443352900224 0.00005463170211001232 0.00006604508815181467 0.00007865883048198513 0.00009259917167338928 0.00010800563134618119 0.00012503240252705603 0.00014384989486488752 0.00016464644014777016 0.00018763017719085535 0.0002130311349595711 0.00024110353477682344 0.00027212833465544285 0.00030641604122040985 0.00034430981736352295'
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 1
  []
  [newton]
    type = PorousFlowPiecewiseLinearSink
    variable = temp
    boundary = right
    pt_vals = '0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000 1100000 1200000 1300000 1400000 1500000 1600000 1700000 1800000 1900000 2000000'
    multipliers = '0. 5.6677197748570516e-6 0.000011931518841831313 0.00001885408740732065 0.000026504708864284114 0.000034959953203725676 0.000044304443352900224 0.00005463170211001232 0.00006604508815181467 0.00007865883048198513 0.00009259917167338928 0.00010800563134618119 0.00012503240252705603 0.00014384989486488752 0.00016464644014777016 0.00018763017719085535 0.0002130311349595711 0.00024110353477682344 0.00027212833465544285 0.00030641604122040985 0.00034430981736352295'
    use_mobility = false
    use_relperm = false
    use_internal_energy = true
    fluid_phase = 0
    flux_function = 1
  []
[]

[VectorPostprocessors]
  [porepressure]
    type = LineValueSampler
    variable = pressure
    start_point = '0 0.5 0'
    end_point = '100 0.5 0'
    sort_by = x
    num_points = 11
    execute_on = timestep_end
  []
  [temperature]
    type = LineValueSampler
    variable = temp
    start_point = '0 0.5 0'
    end_point = '100 0.5 0'
    sort_by = x
    num_points = 11
    execute_on = timestep_end
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol '
    petsc_options_value = 'gmres asm lu 100 NONZERO 2 1E-8 1E-15'
  []
[]

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Outputs]
  file_base = nc06
  execute_on = timestep_end
  exodus = true
  [along_line]
    type = CSV
    execute_vector_postprocessors_on = timestep_end
  []
[]

(modules/porous_flow/test/tests/basic_advection/1phase.i)

# Basic advection of u in a 1-phase situation
#
# grad(P) = -2
# density * gravity = 4 * 0.25
# grad(P) - density * gravity = -3
# permeability = 5
# viscosity = 150
# so Darcy velocity = 0.1
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 4
      thermal_expansion = 0
      viscosity = 150.0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(test/tests/nodalkernels/constraint_enforcement/lower-bound.i)

l=10
nx=100
num_steps=10

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
  [lm]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = '${l} - x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = '-1'
  []
[]

[NodalKernels]
  [positive_constraint]
    type = LowerBoundNodalKernel
    variable = lm
    v = u
    exclude_boundaries = 'left right'
  []
  [forces]
    type = CoupledForceNodalKernel
    variable = u
    v = lm
  []
[]


[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = ${l}
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type'
  petsc_options_value = '0                           30          asm      16                    basic'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [active_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
  []
  [violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
[]

(modules/richards/test/tests/theis/th21.i)

# two-phase, fully-saturated
# production
[Mesh]
  type = FileMesh
  file = th01_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '0.5 1 2 10'
    x = '0 1 10 100'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]

  [./total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]


[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_pressure
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsPolyLineSink
    pressures = '-1E9 1E9'
    fluxes = '200 200'
    point_file = th01.points
    SumQuantityUO = total_outflow_mass
    variable = pwater
  [../]
[]


[Postprocessors]
  [./flow_report]
    type = RichardsPlotQuantity
    uo = total_outflow_mass
  [../]
  [./p50]
    type = PointValue
    variable = pwater
    point = '50 0 0'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E5
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    mat_porosity = 0.1
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 1E-5'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]



[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-6 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 100
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  file_base = th21
  csv = true
[]

(test/tests/kernels/mass_lumping/mass_lumping_jacobian.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 2
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = init_f
  [../]
[]

[Kernels]
  [./time_deriv]
    type = MassLumpedTimeDerivative
    variable = u
  [../]
  [./diff]
    type = FuncCoefDiffusion
    variable = u
    coef = diff_f
  [../]
[]

[Functions]
  [./init_f]
    type = ParsedFunction
    value = max(x,0) #(x>0)
  [../]
  [./diff_f]
    type = ParsedFunction
    value = max(x,0)
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1
  solve_type = 'NEWTON'
  petsc_options_iname = '-snes_type'
  petsc_options_value = 'test'
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/DiffuseCreep/stress.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.1*v'
    [../]
  [../]
  [./mu]
  [../]
  [./jx]
  [../]
  [./jy]
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./creep_strain_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./creep_strain_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./creep_strain_xy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_xy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = mu_prop
    c = c
  [../]
  [./flux_x]
    type = CHSplitFlux
    variable = jx
    component = 0
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./flux_y]
    type = CHSplitFlux
    variable = jy
    component = 1
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./creep_strain_xx]
    type = RankTwoAux
    variable = creep_strain_xx
    rank_two_tensor = creep_strain
    index_i = 0
    index_j = 0
  [../]
  [./creep_strain_yy]
    type = RankTwoAux
    variable = creep_strain_yy
    rank_two_tensor = creep_strain
    index_i = 1
    index_j = 1
  [../]
  [./creep_strain_xy]
    type = RankTwoAux
    variable = creep_strain_xy
    rank_two_tensor = creep_strain
    index_i = 0
    index_j = 1
  [../]
  [./stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    variable = stress_yy
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./stress_xy]
    type = RankTwoAux
    variable = stress_xy
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
  [./diffuse_strain_increment]
    type = FluxBasedStrainIncrement
    xflux = jx
    yflux = jy
    gb = gb
    property_name = diffuse
  [../]
  [./diffuse_creep_strain]
    type = SumTensorIncrements
    tensor_name = creep_strain
    coupled_tensor_increment_names = diffuse
  [../]
  [./strain]
   type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y'
  [../]
  [./stress]
    type = ComputeStrainIncrementBasedStress
    inelastic_strain_names = creep_strain
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '120.0 80.0'
    fill_method = symmetric_isotropic
  [../]
[]

[BCs]
  [./Periodic]
    [./cbc]
      auto_direction = 'x y'
      variable = c
    [../]
  [../]
  [./fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  nl_rel_tol = 1e-10
  nl_max_its = 5

  l_tol = 1e-4
  l_max_its = 20

  dt = 1
  num_steps = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/markers/two_circle_marker/two_circle_marker_gaussian_ic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./gaussian_ic]
    type = FunctionIC
    variable = u
    function = gaussian_2d
  [../]
[]

[Functions]
  [./gaussian_2d]
    type = ParsedFunction
    value = exp(-((x-x0)*(x-x0)+(y-y0)*(y-y0))/2.0/sigma/sigma)
    vars = 'sigma x0 y0'
    vals = '0.05 0.35 0.25'
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = u
    coef = 0.02
  [../]
  [./time]
    type = TimeDerivative
    variable = u
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = u
      auto_direction = 'x y'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 6
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Adaptivity]
  initial_steps = 1
  initial_marker = two_circle_marker
  cycles_per_step = 1
  marker = two_circle_marker
  max_h_level = 1
  [./Markers]
    [./two_circle_marker]
      type = TwoCircleMarker
      point1 = '0.5 0.5 0'
      radius1 = 0.3
      point2 = '0.35 0.25 0'
      radius2 = 0.3
      shut_off_time = 0.15
      inside = refine
      outside = coarsen
    [../]
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    print_mesh_changed_info = true
  [../]
[]

(modules/richards/test/tests/buckley_leverett/bl20_lumped_fu.i)

# two-phase version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 30
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '0.1 0.5 0.5 1 2  4'
    x = '0   0.1 1   5 40 42'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./w_aux_seff]
  [../]
[]



[Kernels]
  [./richardstwater]
    type = RichardsLumpedMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFullyUpwindFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsLumpedMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFullyUpwindFlux
    variable = pgas
  [../]
[]

[AuxKernels]
  [./w_aux_seff_auxk]
    type = RichardsSeffAux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
    variable = w_aux_seff
  [../]
[]


[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_water
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_gas
  [../]
[]

[BCs]
  [./left_w]
    type = DirichletBC
    variable = pwater
    boundary = left
    value = 1E6
  [../]
  [./left_g]
    type = DirichletBC
    variable = pgas
    boundary = left
    value = 1000
  [../]
  [./right_w]
    type = DirichletBC
    variable = pwater
    boundary = right
    value = -300000
  [../]
  [./right_g]
    type = DirichletBC
    variable = pgas
    boundary = right
    value = 0
  [../]
[]


[Functions]
  [./initial_water]
    type = ParsedFunction
    value = 1000000*(1-min(x/5,1))-if(x<5,0,300000)
  [../]
  [./initial_gas]
    type = ParsedFunction
    value = 1000
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    viscosity = '1E-3 1E-6'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'standard'

  [./bounded]
  # must use --use-petsc-dm command line argument
    type = SMP
    full = true
    petsc_options_iname = '-snes_type -pc_factor_shift_type'
    petsc_options_value = 'vinewtonssls nonzero'
  [../]

  [./standard]
    type = SMP
    full = true
    petsc_options_iname = '-pc_factor_shift_type'
    petsc_options_value = 'nonzero'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 50

  nl_rel_tol = 1.e-9
  nl_max_its = 10

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  file_base = bl20_lumped_fu
  execute_on = 'initial timestep_end final'
  interval = 100000
  exodus = true
  hide = pgas
  [./console_out]
    type = Console
    interval = 1
  [../]
[]

(modules/porous_flow/test/tests/hysteresis/hys_pc_03.i)

# Capillary-pressure calculation.  Primary drying curve with low_extension_type = exponential
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 100
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = ''
  []
[]

[Variables]
  [sat]
  []
[]

[ICs]
  [sat]
    type = FunctionIC
    variable = sat
    function = 'x'
  []
[]

[BCs]
  [sat]
    type = FunctionDirichletBC
    variable = sat
    function = 'x'
    boundary = 'left right'
  []
[]


[Kernels]
  [dummy]
    type = Diffusion
    variable = sat
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
  []
  [pc_calculator]
    type = PorousFlowHystereticInfo
    alpha_d = 10.0
    alpha_w = 10.0
    n_d = 1.5
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 12.0
    low_extension_type = exponential
    sat_var = sat
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [pc]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [pc]
    type = PorousFlowPropertyAux
    variable = pc
    property = hysteretic_info
  []
[]

[VectorPostprocessors]
  [pc]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 10
    sort_by = x
    variable = 'sat pc'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/relperm/vangenuchten1.i)

# Test van Genuchten relative permeability curve by varying saturation over the mesh
# van Genuchten exponent m = 0.5 for both phases
# No residual saturation in either phase

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityVG
    phase = 1
    m = 0.5
    wetting = false
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-7
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/phase_field/test/tests/free_energy_material/RegularSolutionFreeEnergy.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 1
  ymax = 500
  elem_type = QUAD4
[]

[Variables]
  [./c]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
  [./myT]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = y
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = c
  [../]
  [./diff2]
    type = Diffusion
    variable = myT
  [../]
[]

[BCs]
  [./left]
    type = FunctionDirichletBC
    variable = c
    boundary = left
    function = x
  [../]
  [./bottom]
    type = FunctionDirichletBC
    variable = myT
    boundary = bottom
    function = y
  [../]
  [./right]
    type = FunctionDirichletBC
    variable = c
    boundary = right
    function = x
  [../]
  [./top]
    type = FunctionDirichletBC
    variable = myT
    boundary = top
    function = y
  [../]
[]

[Materials]
  [./free_energy]
    type = RegularSolutionFreeEnergy
    f_name = F
    c = c
    T = myT
    outputs = out
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  l_max_its = 1
  nl_max_its = 1
  nl_abs_tol = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  [./out]
    type = Exodus
    execute_on = timestep_end
  [../]
[]

(test/tests/meshgenerators/mesh_side_set_generator/mesh_side_set_generator.i)

[Mesh]
  [./gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 4
    nz = 4
    elem_type = TET4
  []

  [./left_block]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    block_id = 1
    block_name = left_block
    bottom_left = '0 0 0'
    top_right = '0.5 1 1'
  []

  [./right_block]
    type = SubdomainBoundingBoxGenerator
    input = left_block
    block_id = 2
    block_name = right_block
    bottom_left = '0.5 0 0'
    top_right = '1 1 1'
  []

  [./center_side_set]
    type = SideSetsBetweenSubdomainsGenerator
    input = right_block
    primary_block = left_block
    paired_block = right_block
    new_boundary = center_side_set
  []

  [./center_mesh]
    type = MeshSideSetGenerator
    input = center_side_set
    boundaries = center_side_set
    block_id = 10
    block_name = center_mesh
  []
[]

[Variables]
  [./c_volume]
    [./InitialCondition]
      type = FunctionIC
      function = '1-(x-0.5)^2+(y-0.5)^2+(z-0.5)^2'
    [../]
  [../]
  [./c_plane]
    block = 'center_mesh'
  [../]
[]

[Kernels]
  [./volume_diff]
    type = Diffusion
    variable = c_volume
    block = 'left_block right_block'
  [../]
  [./volume_dt]
    type = TimeDerivative
    variable = c_volume
    block = 'left_block right_block'
  [../]

  # couple the lower dimensional variable to the volume variable
  [./plane_reaction]
    type = Reaction
    variable = c_plane
    block = 'center_mesh'
  [../]
  [./plane_coupled]
    type = CoupledForce
    variable = c_plane
    v = c_volume
    block = 'center_mesh'
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.01
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(test/tests/vectorpostprocessors/element_value_sampler/element_value_sampler.i)

# Tests the ElementValueSampler vector post-processor. In this test, 2 constant
# monomial variables are given distributions by a function and are output to a CSV file.

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Functions]
  [./u_fn]
    type = ParsedFunction
    value = '2 * x + 3 * y'
  [../]
  [./v_fn]
    type = ParsedFunction
    value = 'x + y'
  [../]
[]

[AuxVariables]
  [./u]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./v]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = u_fn
  [../]
  [./v_ic]
    type = FunctionIC
    variable = v
    function = v_fn
  [../]
[]

[VectorPostprocessors]
  [./element_value_sampler]
    type = ElementValueSampler
    variable = 'u v'
    sort_by = id
    execute_on = 'initial'
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  file_base = 'element_value_sampler'
  csv = true
  execute_on = 'initial'
[]

(modules/phase_field/test/tests/phase_field_kernels/AllenCahnVariableL.i)

#
# Test the parsed function free enery Allen-Cahn Bulk kernel
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 12
  ymax = 12
  elem_type = QUAD4
[]

[AuxVariables]
  [./chi]
    [./InitialCondition]
      type = FunctionIC
      function = 'x/24+0.5'
    [../]
  [../]
[]

[Variables]
  [./eta]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = 0.0
      y1 = 0.0
      radius = 6.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 3.0
    [../]
  [../]
[]

[Kernels]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]

  [./ACBulk]
    type = AllenCahn
    variable = eta
    f_name = F
  [../]

  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = 1
    variable_L = true
    args = chi
  [../]
[]

[Materials]
  [./L]
    type = DerivativeParsedMaterial
    f_name = L
    args = 'eta chi'
    function = '0.1 * eta^2 + chi^2'
    derivative_order = 2
  [../]

  [./free_energy]
    type = DerivativeParsedMaterial
    f_name = F
    args = 'eta'
    function = '2 * eta^2 * (1-eta)^2 - 0.2*eta'
    derivative_order = 2
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'
  solve_type = 'NEWTON'
  num_steps = 2
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/mass_conservation/mass01.i)

# checking that the mass postprocessor correctly calculates the mass
# 1phase, 1component, constant porosity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 3
  xmin = -1
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = x
    variable = pp
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [total_mass]
    type = PorousFlowFluidMass
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = mass01
  csv = true
[]

(test/tests/time_steppers/timesequence_stepper/timesequence.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  end_time = 4.0
  [./TimeStepper]
    type = TimeSequenceStepper
    time_sequence  = '0   0.85 1.3 2 4'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/fltvd_1D_adaptivity.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, with antidiffusion from superbee flux limiting
# 1D version with mesh adaptivity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[Adaptivity]
  initial_steps = 1
  initial_marker = tracer_marker
  marker = tracer_marker
  max_h_level = 1
  [Markers]
    [tracer_marker]
      type = ValueRangeMarker
      variable = tracer
      lower_bound = 0.02
      upper_bound = 0.98
    []
  []
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  nl_max_its = 500
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/porous_flow/test/tests/capillary_pressure/vangenuchten2.i)

# Test van Genuchten relative permeability curve by varying saturation over the mesh
# van Genuchten exponent m = 0.5 for both phases
# No residual saturation in either phase

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [p0]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 0
    variable = p0aux
  []
  [p1]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = p1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1e-5
    m = 0.5
    sat_lr = 0.1
    log_extension = true
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    variable = 's0aux s1aux p0aux p1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 500
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-6
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(test/tests/indicators/laplacian_jump_indicator/biharmonic_transient.i)

[GlobalParams]
  # Parameters used by Functions.
  vars   = 'c'
  vals   = '50'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -.5
  xmax = .5
  ymin = -.5
  ymax = .5
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Kernels]
  [./biharmonic]
    type = Biharmonic
    variable = u
  [../]
  [./body_force]
    type = BodyForce
    variable = u
    function = forcing_func
  [../]
[]

[BCs]
  [./all_value]
    type = FunctionPenaltyDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
  [./all_flux]
    type = FunctionPenaltyFluxBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
[]

[Adaptivity]
  [./Indicators]
    [./error]
      type = LaplacianJumpIndicator
      variable = u
      scale_by_flux_faces = true
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.1

  # Note: the unusually tight tolerances here are due to the penalty
  # BCs (currently the only way of accurately Dirichlet boundary
  # conditions on Hermite elements in MOOSE).
  nl_rel_tol = 1.e-15
  l_tol = 1.e-15

  # We have exact Jacobians
  solve_type = 'NEWTON'

  # Use 6x6 quadrature to ensure the forcing function is integrated
  # accurately.
  [./Quadrature]
    type = GAUSS
    order = ELEVENTH
  [../]
[]

[Functions]
  [./u_func]
    type   = ParsedGradFunction
    value  = 'exp(-c*(x^2+y^2))*exp(-t)'
    grad_x = '-2*c*exp(-c*(x^2+y^2))*x*exp(-t)'
    grad_y = '-2*c*exp(-c*(x^2+y^2))*y*exp(-t)'
  [../]
  [./forcing_func]
    type   = ParsedFunction
    value  = '16*c^2*(c^2*(x^2+y^2)^2 - 4*c*(x^2+y^2) + 2)*exp(-c*(x^2+y^2))*exp(-t)'
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    function = u_func
    variable = u
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = u_func
  [../]
  [./h1_error]
    type = ElementH1Error
    variable = u
    function = u_func
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/time_integrators/actually_explicit_euler_verification/ee-2d-linear.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = (x+y)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*(x+y)
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    preset = false
    boundary = '0 1 2 3'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  start_time = 0.0
  num_steps = 20
  dt = 0.00005
  l_tol = 1e-12

  [./TimeIntegrator]
    type = ActuallyExplicitEuler
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/cns/userobject/HLLC/hllc_uo_1D.i)

rho_left = 1.162633159
E_left = 2.1502913276e+05
u_left = 100

rho_right = 1.116127833
E_right = 1.7919094397e+05
u_right = 90

[Mesh]
  allow_renumbering = false
  [./cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 2
  [../]
[]

[Modules]
  [./FluidProperties]
    [./fp]
      type = IdealGasFluidProperties
      allow_imperfect_jacobians = true
    [../]
  [../]
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./rho]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./rho_u]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./rho_E]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./rho_ic]
    type = FunctionIC
    variable = rho
    function = 'if (x < 0.5, ${rho_left}, ${rho_right})'
  [../]

  [./rho_u_ic]
    type = FunctionIC
    variable = rho_u
    function = 'if (x < 0.5, ${fparse rho_left * u_left}, ${fparse rho_right * u_right})'
  [../]

  [./rho_E_ic]
    type = FunctionIC
    variable = rho_E
    function = 'if (x < 0.5, ${fparse E_left * rho_left}, ${fparse E_right * rho_right})'
  [../]
[]

[Materials]
  [./var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = rho_u
    rho_et = rho_E
    fp = fp
  [../]
[]

[UserObjects]
  [./hllc]
    type = HLLCUserObject
    fp = fp
  [../]
[]

[VectorPostprocessors]
  [./wave_speeds]
    type = WaveSpeedVPP
    hllc_uo = hllc
    elem_id = 0
    side_id = 1
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/capillary_pressure/brooks_corey1.i)

# Test Brooks-Corey capillary pressure curve by varying saturation over the mesh
# lambda = 2, sat_lr = 0.1, log_extension = false

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [p0]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 0
    variable = p0aux
  []
  [p1]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = p1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureBC
    lambda = 2
    log_extension = false
    pe = 1e5
    sat_lr = 0.1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    variable = 's0aux s1aux p0aux p1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 500
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-6
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/poroperm/linear_test_vals.i)

# Testing PorousFlowPorosityLinear produces correct values:
# porosity = porosity_ref + P_coeff * (P - P_ref) + T_coeff * (T - T_ref) + epv_coeff * (epv - epv_coeff)
#          = 0.5 + 2 * (1 - 0.5) + 0.5 * (2 - -3) + 4 * (3 - 2.5)
#          = 6
[GlobalParams]
  PorousFlowDictator = dictator
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = pp
  []
[]

[Variables]
  [pp]
    initial_condition = 1
  []
  [T]
    initial_condition = 2
  []
  [disp]
  []
[]

[ICs]
  [disp]
    type = FunctionIC
    variable = disp
    function = '3 * x'
  []
[]

[Kernels]
  [pp]
    type = TimeDerivative
    variable = pp
  []
  [T]
    type = TimeDerivative
    variable = T
  []
  [disp]
    type = TimeDerivative
    variable = disp
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [porosity]
    type = PorousFlowPropertyAux
    variable = porosity
    property = porosity
  []
[]

[Postprocessors]
  [porosity]
    type = PointValue
    point = '0 0 0'
    variable = porosity
  []
[]

[Materials]
  [ps]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [temperature]
    type = PorousFlowTemperature
    temperature = T
  []
  [pf]
    type = PorousFlowEffectiveFluidPressure
  []
  [total_strain]
    type = ComputeSmallStrain
    displacements = disp
  []
  [volstrain]
    type = PorousFlowVolumetricStrain
    displacements = disp
  []
  [porosity]
    type = PorousFlowPorosityLinear
    porosity_ref = 0.5
    P_ref = 0.5
    P_coeff = 2.0
    T_ref = -3.0
    T_coeff = 0.5
    epv_ref = 2.5
    epv_coeff = 4.0
  []
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 1
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/multiphase_mechanics/twophasestress.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  xmin = 0
  xmax = 2
  ymin = 0
  ymax = 2
  elem_type = QUAD4
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./eta]
    [./InitialCondition]
      type = FunctionIC
      function = 'x/2'
    [../]
  [../]
  [./e11_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_e11]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = e11_aux
  [../]
[]

[Kernels]
  [./TensorMechanics]
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ComputeElasticityTensor
    base_name = A
    fill_method = symmetric9
    C_ijkl = '1e6 1e5 1e5 1e6 0 1e6 .4e6 .2e6 .5e6'
  [../]
  [./strain_A]
    type = ComputeSmallStrain
    base_name = A
    eigenstrain_names = eigenstrain
  [../]
  [./stress_A]
    type = ComputeLinearElasticStress
    base_name = A
  [../]
  [./eigenstrain_A]
    type = ComputeEigenstrain
    base_name = A
    eigen_base = '0.1 0.05 0 0 0 0.01'
    prefactor = -1
    eigenstrain_name = eigenstrain
  [../]

  [./elasticity_tensor_B]
    type = ComputeElasticityTensor
    base_name = B
    fill_method = symmetric9
    C_ijkl = '1e6 0 0 1e6 0 1e6 .5e6 .5e6 .5e6'
  [../]
  [./strain_B]
    type = ComputeSmallStrain
    base_name = B
    eigenstrain_names = 'B_eigenstrain'
  [../]
  [./stress_B]
    type = ComputeLinearElasticStress
    base_name = B
  [../]
  [./eigenstrain_B]
    type = ComputeEigenstrain
    base_name = B
    eigen_base = '0.1 0.05 0 0 0 0.01'
    prefactor = -1
    eigenstrain_name = 'B_eigenstrain'
  [../]

  [./switching]
    type = SwitchingFunctionMaterial
    eta = eta
  [../]
  [./combined]
    type = TwoPhaseStressMaterial
    base_A = A
    base_B = B
  [../]
[]

[BCs]
  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0
  [../]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(modules/porous_flow/test/tests/sinks/s01.i)

# apply a sink flux and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = y+1
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-5 0 0 0 1E-5 0 0 0 1E-5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[AuxVariables]
  [flux_out]
  []
  [xval]
  []
  [yval]
  []
[]

[ICs]
  [xval]
    type = FunctionIC
    variable = xval
    function = x
  []
  [yval]
    type = FunctionIC
    variable = yval
    function = y
  []
[]

[Functions]
  [mass00]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)'
    vars = 'vol por dens0 pp bulk'
    vals = '0.25 0.1 1.1 p00 1.3'
  []
  [mass01]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)'
    vars = 'vol por dens0 pp bulk'
    vals = '0.25 0.1 1.1 p01 1.3'
  []
  [expected_mass_change00]
    type = ParsedFunction
    value = 'fcn*perm*dens0*exp(pp/bulk)/visc*area*dt'
    vars = 'fcn perm dens0 pp bulk visc area dt'
    vals = '6   1    1      0  1.3  1  0.5  1E-3'
  []
[]

[Postprocessors]
  [p00]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m00]
    type = FunctionValuePostprocessor
    function = mass00
    execute_on = 'initial timestep_end'
  []
  [del_m00]
    type = FunctionValuePostprocessor
    function = expected_mass_change00
    execute_on = 'timestep_end'
  []
  [p10]
    type = PointValue
    point = '1 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p01]
    type = PointValue
    point = '0 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m01]
    type = FunctionValuePostprocessor
    function = mass01
    execute_on = 'initial timestep_end'
  []
  [p11]
    type = PointValue
    point = '1 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [flux]
    type = PorousFlowSink
    boundary = 'left'
    variable = pp
    use_mobility = false
    use_relperm = true
    fluid_phase = 0
    flux_function = 6
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10000 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-3
  end_time = 1E-2
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s01
  [console]
    type = Console
    execute_on = 'nonlinear linear'
  []
  [csv]
    type = CSV
    execute_on = 'initial timestep_end'
  []
[]

(test/tests/misc/check_error/function_file_test3.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_mixed_lengths.csv #Will generate error because length of data doesn't match on all rows
    format = rows
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/fvkernels/vector-interpolation/test.i)

a=1.1

[Mesh]
  [gen_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0.1
    xmax = 1.1
    nx = 20
  []
[]

[GlobalParams]
  limiter = 'vanLeer'
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = exact
  []
  [v]
    type = FunctionIC
    variable = v
    function = exact
  []
  [w]
    type = FunctionIC
    variable = w
    function = exact
  []
[]

[Variables]
  [u]
    type = MooseVariableFVReal
  []
  [v]
    type = MooseVariableFVReal
  []
  [w]
    type = MooseVariableFVReal
  []
[]

[FVKernels]
  [advection_u]
    type = FVLimitedVectorAdvection
    variable = u
    velocity = '${a} 0 0'
    boundaries_to_force = 'right'
    x_functor = 'u'
    y_functor = 'v'
    z_functor = 'w'
    component = 0
  []
  [body_u]
    type = FVBodyForce
    variable = u
    function = 'forcing'
  []
  [advection_v]
    type = FVLimitedVectorAdvection
    variable = v
    velocity = '${a} 0 0'
    boundaries_to_force = 'right'
    x_functor = 'u'
    y_functor = 'v'
    z_functor = 'w'
    component = 1
  []
  [body_v]
    type = FVBodyForce
    variable = v
    function = 'forcing'
  []
  [advection_w]
    type = FVLimitedVectorAdvection
    variable = w
    velocity = '${a} 0 0'
    boundaries_to_force = 'right'
    x_functor = 'u'
    y_functor = 'v'
    z_functor = 'w'
    component = 2
  []
  [body_w]
    type = FVBodyForce
    variable = w
    function = 'forcing'
  []
[]

[FVBCs]
  [left_u]
    type = FVFunctionNeumannBC
    boundary = 'left'
    function = 'advection'
    variable = u
  []
  [left_v]
    type = FVFunctionNeumannBC
    boundary = 'left'
    function = 'advection'
    variable = v
  []
  [left_w]
    type = FVFunctionNeumannBC
    boundary = 'left'
    function = 'advection'
    variable = w
  []
[]

[Functions]
  [exact]
    type = ParsedFunction
    value = 'cos(x)'
  []
  [advection]
    type = ParsedFunction
    value = '${a} * cos(x)'
  []
  [forcing]
    type = ParsedFunction
    value = '-${a} * sin(x)'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/mass_conservation/mass06.i)

# Checking that the mass postprocessor correctly calculates the mass
# of each component in each phase, as well as the total mass of each
# component in all phases. Also tests that optional saturation threshold
# gives the correct mass
# 2phase, 2component, constant porosity
# saturation_threshold set to 0.6 for phase 1

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [sat]
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[ICs]
  [pinit]
    type = ConstantIC
    value = 1
    variable = pp
  []
  [satinit]
    type = FunctionIC
    function = 1-x
    variable = sat
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sat
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp sat'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 0.1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp
    phase1_saturation = sat
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [comp0_phase0_mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = 0
  []
  [comp0_phase1_mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = 1
  []
  [comp0_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 0
  []
  [comp1_phase0_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = 0
  []
  [comp1_phase1_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = 1
  []
  [comp1_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
  []
  [comp1_phase1_threshold_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = 1
    saturation_threshold = 0.6
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  nl_abs_tol = 1e-16
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = mass06
  csv = true
[]

(modules/combined/examples/periodic_strain/global_strain_pfm.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
  []
  [./cnode]
    input = gen
    type = ExtraNodesetGenerator
    coord = '0.0 0.0'
    new_boundary = 100
  [../]
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./global_strain]
    order = THIRD
    family = SCALAR
  [../]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'sin(2*x*pi)*sin(2*y*pi)*0.05+0.6'
    [../]
  [../]
  [./w]
  [../]
[]

[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./s00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./local_free_energy]
    type = TotalFreeEnergy
    execute_on = 'initial LINEAR'
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
  [../]
  [./s00]
    type = RankTwoAux
    variable = s00
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
  [./s10]
    type = RankTwoAux
    variable = s10
    rank_two_tensor = stress
    index_i = 1
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./e00]
    type = RankTwoAux
    variable = e00
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
  [../]
  [./e01]
    type = RankTwoAux
    variable = e01
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 1
  [../]
  [./e10]
    type = RankTwoAux
    variable = e10
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 0
  [../]
  [./e11]
    type = RankTwoAux
    variable = e11
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
  [../]
[]

[GlobalParams]
  derivative_order = 2
  enable_jit = true
  displacements = 'u_x u_y'
  block = 0
[]

[Kernels]
  [./TensorMechanics]
  [../]

  # Cahn-Hilliard kernels
  [./c_dot]
    type = CoupledTimeDerivative
    variable = w
    v = c
    block = 0
  [../]
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = kappa_c
    w = w
    block = 0
  [../]
  [./w_res]
    type = SplitCHWRes
    variable = w
    mob_name = M
    block = 0
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y'
      variable = 'c w u_x u_y'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M   kappa_c'
    prop_values = '0.2 0.01   '
  [../]

  [./shear1]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 0 0 0.5'
    tensor_name = shear1
  [../]
  [./shear2]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 0 0 -0.5'
    tensor_name = shear2
  [../]
  [./expand3]
    type = GenericConstantRankTwoTensor
    tensor_values = '1 1 0 0 0 0'
    tensor_name = expand3
  [../]

  [./weight1]
    type = DerivativeParsedMaterial
    function = '0.3*c^2'
    f_name = weight1
    args = c
  [../]
  [./weight2]
    type = DerivativeParsedMaterial
    function = '0.3*(1-c)^2'
    f_name = weight2
    args = c
  [../]
  [./weight3]
    type = DerivativeParsedMaterial
    function = '4*(0.5-c)^2'
    f_name = weight3
    args = c
  [../]

  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
    eigenstrain_names = eigenstrain
  [../]

  [./eigenstrain]
    type = CompositeEigenstrain
    tensors = 'shear1  shear2  expand3'
    weights = 'weight1 weight2 weight3'
    args = c
    eigenstrain_name = eigenstrain
  [../]

  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]

  [./stress]
    type = ComputeLinearElasticStress
  [../]

  # chemical free energies
  [./chemical_free_energy]
    type = DerivativeParsedMaterial
    f_name = Fc
    function = '4*c^2*(1-c)^2'
    args = 'c'
    outputs = exodus
    output_properties = Fc
  [../]

  # elastic free energies
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = Fe
    args = 'c'
    outputs = exodus
    output_properties = Fe
  [../]

  # free energy (chemical + elastic)
  [./free_energy]
    type = DerivativeSumMaterial
    block = 0
    f_name = F
    sum_materials = 'Fc Fe'
    args = 'c'
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = local_energy
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = c
  [../]
  [./min]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = min
    variable = c
  [../]
  [./max]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = max
    variable = c
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  end_time = 2.0

  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.01
    growth_factor = 1.5
    cutback_factor = 0.8
    optimal_iterations = 9
    iteration_window = 2
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  print_linear_residuals = false
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

(test/tests/dgkernels/dg_displacement/dg_displacement.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  displacements = 'disp_x disp_y'
[]

[Variables]
  [./u]
    order = FIRST
    family = MONOMIAL
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Functions]
  [./forcing_fn]
    type = ParsedFunction
    value = 2*pow(e,-x-(y*y))*(1-2*y*y)
  [../]
  [./exact_fn]
    type = ParsedGradFunction
    value = pow(e,-x-(y*y))
    grad_x = -pow(e,-x-(y*y))
    grad_y = -2*y*pow(e,-x-(y*y))
  [../]
  [./disp_func]
    type = ParsedFunction
    value = x
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./abs]
    type = Reaction
    variable = u
  [../]
  [./forcing]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[DGKernels]
  [./dg_diff]
    type = DGDiffusion
    variable = u
    epsilon = -1
    sigma = 6
    use_displaced_mesh = true
  [../]
[]

[BCs]
  [./all]
    type = DGFunctionDiffusionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
    epsilon = -1
    sigma = 6
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_rel_tol = 1e-10
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = out
  exodus = true
[]

[ICs]
  [./disp_x_ic]
    function = disp_func
    variable = disp_x
    type = FunctionIC
  [../]
[]

(modules/porous_flow/test/tests/chemistry/2species_equilibrium.i)

# PorousFlow analogy of chemical_reactions/test/tests/aqueous_equilibrium/2species.i
#
# Simple equilibrium reaction example to illustrate the use of PorousFlowMassFractionAqueousEquilibriumChemistry
#
# In this example, two primary species a and b are transported by diffusion and convection
# from the left of the porous medium, reacting to form two equilibrium species pa2 and pab
# according to the equilibrium reaction:
#
#      reactions = '2a = pa2     rate = 10^2
#                   a + b = pab  rate = 10^-2'
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
[]

[Variables]
  [a]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    []
  []
  [b]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    []
  []
[]

[AuxVariables]
  [eqm_k0]
    initial_condition = 1E2
  []
  [eqm_k1]
    initial_condition = 1E-2
  []
  [pressure]
  []
  [pa2]
    family = MONOMIAL
    order = CONSTANT
  []
  [pab]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [pa2]
    type = PorousFlowPropertyAux
    property = secondary_concentration
    secondary_species = 0
    variable = pa2
  []
  [pab]
    type = PorousFlowPropertyAux
    property = secondary_concentration
    secondary_species = 1
    variable = pab
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Kernels]
  [mass_a]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = a
  []
  [flux_a]
    type = PorousFlowFullySaturatedDarcyFlow
    variable = a
    fluid_component = 0
  []
  [diff_a]
    type = PorousFlowDispersiveFlux
    variable = a
    fluid_component = 0
    disp_trans = 0
    disp_long = 0
  []
  [mass_b]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = b
  []
  [flux_b]
    type = PorousFlowFullySaturatedDarcyFlow
    variable = b
    fluid_component = 1
  []
  [diff_b]
    type = PorousFlowDispersiveFlux
    variable = b
    fluid_component = 1
    disp_trans = 0
    disp_long = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'a b'
    number_fluid_phases = 1
    number_fluid_components = 3
    number_aqueous_equilibrium = 2
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9 # huge, so mimic chemical_reactions
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pressure
  []
  [massfrac]
    type = PorousFlowMassFractionAqueousEquilibriumChemistry
    mass_fraction_vars = 'a b'
    num_reactions = 2
    equilibrium_constants = 'eqm_k0 eqm_k1'
    primary_activity_coefficients = '1 1'
    secondary_activity_coefficients = '1 1'
    reactions = '2 0
                 1 1'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    # porous_flow permeability / porous_flow viscosity = chemical_reactions conductivity = 1E-4
    permeability = '1E-7 0 0 0 1E-7 0 0 0 1E-7'
  []
  [relp]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [diff]
    type = PorousFlowDiffusivityConst
    # porous_flow diffusion_coeff * tortuousity * porosity = chemical_reactions diffusivity = 1E-4
    diffusion_coeff = '5E-4 5E-4 5E-4'
    tortuosity = 1.0
  []
[]

[BCs]
  [a_left]
    type = DirichletBC
    variable = a
    boundary = left
    value = 1.0e-2
  []
  [b_left]
    type = DirichletBC
    variable = b
    boundary = left
    value = 1.0e-2
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 10
  end_time = 100
[]

[Outputs]
  print_linear_residuals = true
  exodus = true
  perf_graph = true
[]

(test/tests/functions/solution_function/solution_function_grad_p1.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  parallel_type = replicated
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./test_variable]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_cond_func
    [../]
  [../]
[]

[Functions]
  [./initial_cond_func]
    type = ParsedFunction
    value = 2*x+4*y
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-10
[]

[Outputs]
  file_base = solution_function_grad_p1
  exodus = true
[]

(modules/combined/examples/publications/rapid_dev/fig6.i)

#
# Fig. 6 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Three phase interface simulation demonstrating the interfacial stability
# w.r.t. formation of a tspurious third phase
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 120
  ny = 120
  nz = 0
  xmin = 0
  xmax = 40
  ymin = 0
  ymax = 40
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Variables]
  # concentration
  [./c]
  [../]

  # order parameter 1
  [./eta1]
  [../]

  # order parameter 2
  [./eta2]
  [../]

  # order parameter 3
  [./eta3]
  [../]

  # phase concentration 1
  [./c1]
    initial_condition = 0.4
  [../]

  # phase concentration 2
  [./c2]
    initial_condition = 0.5
  [../]

  # phase concentration 3
  [./c3]
    initial_condition = 0.8
  [../]

  # Lagrange multiplier
  [./lambda]
    initial_condition = 0.0
  [../]
[]

[AuxVariables]
  [./T]
    [./InitialCondition]
      type = FunctionIC
      function = 'x-10'
    [../]
  [../]
[]


[Functions]
  [./ic_func_eta1]
    type = ParsedFunction
    value = '0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0)))'
  [../]
  [./ic_func_eta2]
    type = ParsedFunction
    value = '0.5*(1.0-tanh((x-10)/sqrt(2.0)))'
  [../]
  [./ic_func_eta3]
    type = ParsedFunction
    value = '1 - 0.5*(1.0-tanh((x-10)/sqrt(2.0)))
              - 0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0)))'
  [../]
  [./ic_func_c]
    type = ParsedFunction
    value = '0.5 * 0.5*(1.0-tanh((x-10)/sqrt(2.0)))
              + 0.4 * 0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0)))
              + 0.8 * (1 - 0.5*(1.0-tanh((x-10)/sqrt(2.0)))
                        - 0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0))))'
  [../]
[]

[ICs]
  [./eta1]
    variable = eta1
    type = FunctionIC
    function = ic_func_eta1
  [../]
  [./eta2]
    variable = eta2
    type = FunctionIC
    function = ic_func_eta2
  [../]
  [./eta3]
    variable = eta3
    type = FunctionIC
    function = ic_func_eta3
  [../]
  [./c]
    variable = c
    type = FunctionIC
    function = ic_func_c
  [../]
[]

[Materials]
  # simple toy free energies
  [./f1]
    type = DerivativeParsedMaterial
    f_name = F1
    args = 'c1'
    function = '20*(c1-0.4)^2'
  [../]
  [./f2]
    type = DerivativeParsedMaterial
    f_name = F2
    args = 'c2 T'
    function = '20*(c2-0.5)^2 + 0.01*T'
  [../]
  [./f3]
    type = DerivativeParsedMaterial
    f_name = F3
    args = 'c3'
    function = '20*(c3-0.8)^2'
  [../]

  # Switching functions for each phase
  # h1(eta1, eta2, eta3)
  [./h1]
    type = SwitchingFunction3PhaseMaterial
    eta_i = eta1
    eta_j = eta2
    eta_k = eta3
    f_name = h1
  [../]
  # h2(eta1, eta2, eta3)
  [./h2]
    type = SwitchingFunction3PhaseMaterial
    eta_i = eta2
    eta_j = eta3
    eta_k = eta1
    f_name = h2
  [../]
  # h3(eta1, eta2, eta3)
  [./h3]
    type = SwitchingFunction3PhaseMaterial
    eta_i = eta3
    eta_j = eta1
    eta_k = eta2
    f_name = h3
  [../]

  # Coefficients for diffusion equation
  [./Dh1]
    type = DerivativeParsedMaterial
    material_property_names = 'D h1'
    function = D*h1
    f_name = Dh1
  [../]
  [./Dh2]
    type = DerivativeParsedMaterial
    material_property_names = 'D h2'
    function = D*h2
    f_name = Dh2
  [../]
  [./Dh3]
    type = DerivativeParsedMaterial
    material_property_names = 'D h3'
    function = D*h3
    f_name = Dh3
  [../]

  # Barrier functions for each phase
  [./g1]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta1
    function_name = g1
  [../]
  [./g2]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta2
    function_name = g2
  [../]
  [./g3]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta3
    function_name = g3
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'L   kappa  D'
    prop_values = '1.0 1.0    1'
  [../]
[]

[Kernels]
  #Kernels for diffusion equation
  [./diff_time]
    type = TimeDerivative
    variable = c
  [../]
  [./diff_c1]
    type = MatDiffusion
    variable = c
    diffusivity = Dh1
    v = c1
  [../]
  [./diff_c2]
    type = MatDiffusion
    variable = c
    diffusivity = Dh2
    v = c2
  [../]
  [./diff_c3]
    type = MatDiffusion
    variable = c
    diffusivity = Dh3
    v = c3
  [../]

  # Kernels for Allen-Cahn equation for eta1
  [./deta1dt]
    type = TimeDerivative
    variable = eta1
  [../]
  [./ACBulkF1]
    type = KKSMultiACBulkF
    variable  = eta1
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    gi_name   = g1
    eta_i     = eta1
    wi        = 1.0
    args      = 'c1 c2 c3 eta2 eta3'
  [../]
  [./ACBulkC1]
    type = KKSMultiACBulkC
    variable  = eta1
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    cj_names  = 'c1 c2 c3'
    eta_i     = eta1
    args      = 'eta2 eta3'
  [../]
  [./ACInterface1]
    type = ACInterface
    variable = eta1
    kappa_name = kappa
  [../]
  [./multipler1]
    type = MatReaction
    variable = eta1
    v = lambda
    mob_name = L
  [../]

  # Kernels for Allen-Cahn equation for eta2
  [./deta2dt]
    type = TimeDerivative
    variable = eta2
  [../]
  [./ACBulkF2]
    type = KKSMultiACBulkF
    variable  = eta2
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    gi_name   = g2
    eta_i     = eta2
    wi        = 1.0
    args      = 'c1 c2 c3 eta1 eta3'
  [../]
  [./ACBulkC2]
    type = KKSMultiACBulkC
    variable  = eta2
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    cj_names  = 'c1 c2 c3'
    eta_i     = eta2
    args      = 'eta1 eta3'
  [../]
  [./ACInterface2]
    type = ACInterface
    variable = eta2
    kappa_name = kappa
  [../]
  [./multipler2]
    type = MatReaction
    variable = eta2
    v = lambda
    mob_name = L
  [../]

  # Kernels for the Lagrange multiplier equation
  [./mult_lambda]
    type = MatReaction
    variable = lambda
    mob_name = 3
  [../]
  [./mult_ACBulkF_1]
    type = KKSMultiACBulkF
    variable  = lambda
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    gi_name   = g1
    eta_i     = eta1
    wi        = 1.0
    mob_name  = 1
    args      = 'c1 c2 c3 eta2 eta3'
  [../]
  [./mult_ACBulkC_1]
    type = KKSMultiACBulkC
    variable  = lambda
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    cj_names  = 'c1 c2 c3'
    eta_i     = eta1
    args      = 'eta2 eta3'
    mob_name  = 1
  [../]
  [./mult_CoupledACint_1]
    type = SimpleCoupledACInterface
    variable = lambda
    v = eta1
    kappa_name = kappa
    mob_name = 1
  [../]
  [./mult_ACBulkF_2]
    type = KKSMultiACBulkF
    variable  = lambda
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    gi_name   = g2
    eta_i     = eta2
    wi        = 1.0
    mob_name  = 1
    args      = 'c1 c2 c3 eta1 eta3'
  [../]
  [./mult_ACBulkC_2]
    type = KKSMultiACBulkC
    variable  = lambda
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    cj_names  = 'c1 c2 c3'
    eta_i     = eta2
    args      = 'eta1 eta3'
    mob_name  = 1
  [../]
  [./mult_CoupledACint_2]
    type = SimpleCoupledACInterface
    variable = lambda
    v = eta2
    kappa_name = kappa
    mob_name = 1
  [../]
  [./mult_ACBulkF_3]
    type = KKSMultiACBulkF
    variable  = lambda
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    gi_name   = g3
    eta_i     = eta3
    wi        = 1.0
    mob_name  = 1
    args      = 'c1 c2 c3 eta1 eta2'
  [../]
  [./mult_ACBulkC_3]
    type = KKSMultiACBulkC
    variable  = lambda
    Fj_names  = 'F1 F2 F3'
    hj_names  = 'h1 h2 h3'
    cj_names  = 'c1 c2 c3'
    eta_i     = eta3
    args      = 'eta1 eta2'
    mob_name  = 1
  [../]
  [./mult_CoupledACint_3]
    type = SimpleCoupledACInterface
    variable = lambda
    v = eta3
    kappa_name = kappa
    mob_name = 1
  [../]

  # Kernels for constraint equation eta1 + eta2 + eta3 = 1
  # eta3 is the nonlinear variable for the constraint equation
  [./eta3reaction]
    type = MatReaction
    variable = eta3
    mob_name = 1
  [../]
  [./eta1reaction]
    type = MatReaction
    variable = eta3
    v = eta1
    mob_name = 1
  [../]
  [./eta2reaction]
    type = MatReaction
    variable = eta3
    v = eta2
    mob_name = 1
  [../]
  [./one]
    type = BodyForce
    variable = eta3
    value = -1.0
  [../]

  # Phase concentration constraints
  [./chempot12]
    type = KKSPhaseChemicalPotential
    variable = c1
    cb       = c2
    fa_name  = F1
    fb_name  = F2
  [../]
  [./chempot23]
    type = KKSPhaseChemicalPotential
    variable = c2
    cb       = c3
    fa_name  = F2
    fb_name  = F3
  [../]
  [./phaseconcentration]
    type = KKSMultiPhaseConcentration
    variable = c3
    cj = 'c1 c2 c3'
    hj_names = 'h1 h2 h3'
    etas = 'eta1 eta2 eta3'
    c = c
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -sub_pc_type   -sub_pc_factor_shift_type'
  petsc_options_value = 'asm       ilu            nonzero'
  l_max_its = 30
  nl_max_its = 10
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-10
  nl_abs_tol = 1.0e-11

  num_steps = 1000
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.2
    optimal_iterations = 10
    iteration_window = 2
  [../]
[]

[Preconditioning]
  active = 'full'
  [./full]
    type = SMP
    full = true
  [../]
  [./mydebug]
    type = FDP
    full = true
  [../]
[]

[Outputs]
  exodus = true
  checkpoint = true
  print_linear_residuals = false
  [./csv]
    type = CSV
    execute_on = 'final'
  [../]
[]

#[VectorPostprocessors]
#  [./c]
#    type =  LineValueSampler
#    start_point = '-25 0 0'
#    end_point = '25 0 0'
#    variable = c
#    num_points = 151
#    sort_by =  id
#    execute_on = timestep_end
#  [../]
#  [./eta1]
#    type =  LineValueSampler
#    start_point = '-25 0 0'
#    end_point = '25 0 0'
#    variable = eta1
#    num_points = 151
#    sort_by =  id
#    execute_on = timestep_end
#  [../]
#  [./eta2]
#    type =  LineValueSampler
#    start_point = '-25 0 0'
#    end_point = '25 0 0'
#    variable = eta2
#    num_points = 151
#    sort_by =  id
#    execute_on = timestep_end
#  [../]
#  [./eta3]
#    type =  LineValueSampler
#    start_point = '-25 0 0'
#    end_point = '25 0 0'
#    variable = eta3
#    num_points = 151
#    sort_by =  id
#    execute_on = timestep_end
#  [../]
#[]

(modules/porous_flow/test/tests/flux_limited_TVD_pflow/pffltvd_2D_trimesh.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, mploying PorousFlow Kernels and UserObjects, with superbee flux-limiter
# 2D version
[Mesh]
  type = FileMesh
  file = trimesh.msh
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
  block = '50'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.305,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0.04 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/thermal_hydraulics/test/tests/userobjects/layered_flow_area_change/layered_flow_area_2D.i)

[Mesh]
  [generated]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1 1'
    dy = '4'
    ix = '1 1 1'
    iy = '40'
    subdomain_id = '1 2 1'
  []

  [interior_walls]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = interior
    input = generated
  []
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [disp_x]
  []

  [disp_y]
  []

  [channel_dA]
  []
[]

[ICs]
  [disp_x_ic]
    type = FunctionIC
    variable = disp_x
    function = 'if (x < 1.5, 0.5 * (y - 2) * 0.1, 0)'
  []
[]

[AuxKernels]
  [channel_dA_aux]
    type = SpatialUserObjectAux
    variable = channel_dA
    user_object = layered_area_change
  []
[]

[UserObjects]
  [layered_area_change]
    type = LayeredFlowAreaChange
    direction = y
    displacements = 'disp_x disp_y'
    boundary = interior
    num_layers = 40
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/tensor_mechanics/test/tests/elasticitytensor/composite.i)

# This input file is designed to test the RankTwoAux and RankFourAux
# auxkernels, which report values out of the Tensors used in materials
# properties.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmax = 1
[]

[AuxVariables]
  [./c]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]

  [./C1111_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./C1122_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./C1133_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./C3313_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]


  [./dC1111_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./dC1122_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./dC1133_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./dC3313_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]


  [./d2C1111_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./d2C1122_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./d2C1133_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./d2C3313_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

#[Kernels]
#  [./diff]
#    type = Diffusion
#    variable = diffused
#  [../]
#[]

[AuxKernels]
  [./matl_C1111]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux
    execute_on = initial
  [../]

   [./matl_C1122]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux
    execute_on = initial
  [../]

  [./matl_C1133]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux
    execute_on = initial
  [../]

  [./matl_C3313]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 2
    index_j = 2
    index_k = 0
    index_l = 2
    variable = C3313_aux
    execute_on = initial
  [../]


  [./matl_dC1111]
    type = RankFourAux
    rank_four_tensor = delasticity_tensor/dc
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = dC1111_aux
    execute_on = initial
  [../]

   [./matl_dC1122]
    type = RankFourAux
    rank_four_tensor = delasticity_tensor/dc
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = dC1122_aux
    execute_on = initial
  [../]

  [./matl_dC1133]
    type = RankFourAux
    rank_four_tensor = delasticity_tensor/dc
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = dC1133_aux
    execute_on = initial
  [../]

  [./matl_dC3313]
    type = RankFourAux
    rank_four_tensor = delasticity_tensor/dc
    index_i = 2
    index_j = 2
    index_k = 0
    index_l = 2
    variable = dC3313_aux
    execute_on = initial
  [../]


  [./matl_d2C1111]
    type = RankFourAux
    rank_four_tensor = d^2elasticity_tensor/dc^2
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = d2C1111_aux
    execute_on = initial
  [../]

   [./matl_d2C1122]
    type = RankFourAux
    rank_four_tensor = d^2elasticity_tensor/dc^2
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = d2C1122_aux
    execute_on = initial
  [../]

  [./matl_d2C1133]
    type = RankFourAux
    rank_four_tensor = d^2elasticity_tensor/dc^2
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = d2C1133_aux
    execute_on = initial
  [../]

  [./matl_d2C3313]
    type = RankFourAux
    rank_four_tensor = d^2elasticity_tensor/dc^2
    index_i = 2
    index_j = 2
    index_k = 0
    index_l = 2
    variable = d2C3313_aux
    execute_on = initial
  [../]
[]

[Materials]
  [./Ca]
    type = ComputeElasticityTensor
    base_name = Ca
    block = 0
    fill_method = symmetric21
    C_ijkl ='1111 .1122 1133 1123 1113 1112 2222 2233 2223 2213 2212 3333 3323 3313 3312 2323 2313 2312 1313 1312 1212'
  [../]
  [./Cb]
    type = ComputeElasticityTensor
    base_name = Cb
    block = 0
    fill_method = symmetric21
    C_ijkl ='.1111 1122 .1133 .1123 .1113 .1112 .2222 .2233 .2223 .2213 .2212 .3333 .3323 .3313 .3312 .2323 .2313 .2312 .1313 .1312 .1212'
  [../]
  [./Fa]
    type = DerivativeParsedMaterial
    block = 0
    f_name = Fa
    function = c^2
    args = c
  [../]
  [./Fb]
    type = DerivativeParsedMaterial
    block = 0
    f_name = Fb
    function = (1-c)^3
    args = c
  [../]
  [./C]
    type = CompositeElasticityTensor
    block = 0
    args = c
    tensors = 'Ca Cb'
    weights = 'Fa Fb'
  [../]
[]
[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/buckley_leverett/bl01.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2.0E6
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-4
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]


[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]

[AuxKernels]
  active = 'calculate_seff'
  [./calculate_seff]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffVG
    pressure_vars = pressure
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[BCs]
  active = 'left'
  [./left]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 980000
  [../]
[]

[Kernels]
  active = 'richardsf richardst'

  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]


[Functions]
 active = 'initial_pressure'
  [./initial_pressure]
    type = ParsedFunction
    value = max((1000000-x/5*1000000)-20000,-20000)
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'andy'

  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 20'
  [../]

[]

[Executioner]
  type = Transient
  end_time = 50
  dt = 2
  snesmf_reuse_base = false
[]

[Outputs]
  file_base = bl01
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
[]

(modules/porous_flow/test/tests/sinks/s05.i)

# apply a half-gaussian sink flux and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1.1
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = y+1.4
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-5 0 0 0 1E-5 0 0 0 1E-5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[AuxVariables]
  [flux_out]
  []
[]

[Functions]
  [mass10]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)*if(pp>=0,1,pow(1+pow(-al*pp,1.0/(1-m)),-m))'
    vars = 'vol por dens0 pp bulk al m'
    vals = '0.25 0.1 1.1 p10 1.3 1.1 0.5'
  []
  [rate10]
    type = ParsedFunction
    value = 'if(pp>center,fcn,fcn*exp(-0.5*(pp-center)*(pp-center)/sd/sd))'
    vars = 'fcn pp  center sd'
    vals = '6   p10 0.9    0.5'
  []
  [mass10_expect]
    type = ParsedFunction
    value = 'mass_prev-rate*area*dt'
    vars = 'mass_prev rate     area dt'
    vals = 'm10_prev  m10_rate 0.5 2E-3'
  []
  [mass11]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)*if(pp>=0,1,pow(1+pow(-al*pp,1.0/(1-m)),-m))'
    vars = 'vol por dens0 pp bulk al m'
    vals = '0.25 0.1 1.1 p11 1.3 1.1 0.5'
  []
  [rate11]
    type = ParsedFunction
    value = 'if(pp>center,fcn,fcn*exp(-0.5*(pp-center)*(pp-center)/sd/sd))'
    vars = 'fcn pp  center sd'
    vals = '6   p11 0.9    0.5'
  []
  [mass11_expect]
    type = ParsedFunction
    value = 'mass_prev-rate*area*dt'
    vars = 'mass_prev rate     area dt'
    vals = 'm11_prev  m11_rate 0.5 2E-3'
  []
[]

[Postprocessors]
  [flux10]
    type = PointValue
    variable = flux_out
    point = '1 0 0'
  []
  [p00]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p10]
    type = PointValue
    point = '1 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m10]
    type = FunctionValuePostprocessor
    function = mass10
    execute_on = 'initial timestep_end'
  []
  [m10_prev]
    type = FunctionValuePostprocessor
    function = mass10
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [m10_rate]
    type = FunctionValuePostprocessor
    function = rate10
    execute_on = 'timestep_end'
  []
  [m10_expect]
    type = FunctionValuePostprocessor
    function = mass10_expect
    execute_on = 'timestep_end'
  []
  [p01]
    type = PointValue
    point = '0 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p11]
    type = PointValue
    point = '1 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m11]
    type = FunctionValuePostprocessor
    function = mass11
    execute_on = 'initial timestep_end'
  []
  [m11_prev]
    type = FunctionValuePostprocessor
    function = mass11
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [m11_rate]
    type = FunctionValuePostprocessor
    function = rate11
    execute_on = 'timestep_end'
  []
  [m11_expect]
    type = FunctionValuePostprocessor
    function = mass11_expect
    execute_on = 'timestep_end'
  []
[]

[BCs]
  [flux]
    type = PorousFlowHalfGaussianSink
    boundary = 'right'
    max = 6
    sd = 0.5
    center = 0.9
    variable = pp
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 1
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10000 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2E-3
  end_time = 6E-2
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s05
  [console]
    type = Console
    execute_on = 'nonlinear linear'
    interval = 5
  []
  [csv]
    type = CSV
    execute_on = 'timestep_end'
    interval = 3
  []
[]

(test/tests/auxkernels/diffusion_flux/normal_diffusion_flux.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 1.0
  ymax = 1.0
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./T]
  [../]
  [./flux_n]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Functions]
  [./T]
    type = ParsedFunction
    value = 'x*x*y*y+1'
  [../]
[]

[ICs]
  [./T]
    type = FunctionIC
    variable = T
    function = T
  [../]
[]

[Kernels]
  [./dummy]
    type = Diffusion
    variable = dummy
  [../]
[]

[AuxKernels]
  [./flux_n]
    type = DiffusionFluxAux
    diffusivity = 'thermal_conductivity'
    variable = flux_n
    diffusion_variable = T
    component = normal
    boundary = 'left right'
    check_boundary_restricted = false
  [../]
[]

[Materials]
  [./k]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '10'
  [../]
[]

[Postprocessors]
  [flux_right]
    type = SideIntegralVariablePostprocessor
    variable = flux_n
    boundary = 'right'
  []
  [flux_right_exact]
    type = SideFluxIntegral
    variable = T
    diffusivity = 'thermal_conductivity'
    boundary = 'right'
  []
  [flux_left]
    type = SideIntegralVariablePostprocessor
    variable = flux_n
    boundary = 'left'
  []
  [flux_left_exact]
    type = SideFluxIntegral
    variable = T
    diffusivity = 'thermal_conductivity'
    boundary = 'left'
  []
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  hide = 'dummy'
[]

(test/tests/misc/check_error/function_file_test4.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = dummy #we don't get that far
    format = rowls
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/thermal_hydraulics/test/tests/utils/smooth_transition/smooth_transition.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -2
  xmax = 2
[]

[Variables]
  [u]
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    variable = u
    function = u_ic_fn
  []
[]

[Functions]
  [u_ic_fn]
    type = ParsedFunction
    value = 'x'
  []
[]

[Materials]
  [test_mat]
    type = SmoothTransitionTestMaterial
    transition_type = cubic
    var = u
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[VectorPostprocessors]
  [test_vpp]
    type = Sampler1DReal
    block = 0
    property = mymatprop
    sort_by = x
    execute_on = 'INITIAL'
  []
[]

[Outputs]
  csv = true
  file_base = 'cubic_nonad'
  execute_on = 'INITIAL'
[]

(modules/phase_field/test/tests/free_energy_material/IdealGasFreeEnergy.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  elem_type = QUAD4
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = x*0.4+0.001
    [../]
  [../]
  [./T]
    [./InitialCondition]
      type = FunctionIC
      function = y*1999+1
    [../]
  [../]
[]

[Materials]
  [./free_energy]
    type = IdealGasFreeEnergy
    f_name = Fgas
    m = 134 # Xenon
    omega = 41
    c = c
    T = T
    outputs = exodus
  [../]
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/fltvd_2D_angle.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, with antidiffusion from superbee flux limiting
# 2D version with velocity = (0.1, 0.2, 0)
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  xmin = 0
  xmax = 1
  ny = 10
  ymin = 0
  ymax = 1
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1 | x > 0.3 | y < 0.1 | y > 0.3, 0, 1)'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0.2 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 2
  dt = 0.1
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = Exodus
    execute_on = 'initial final'
  []
[]

(test/tests/time_integrators/multi_stage_time_integrator/unconverged_1st_stage.i)

# This test is designed to check that a time step solve should stop if *any*
# time integrator solve stage fails, not just the *last* stage. If a time
# integrator does not check convergence per stage, then a time step proceeds
# past intermediate stages without checking nonlinear convergence. This test
# is designed to check that the 2nd stage is never even entered by making it
# impossible for the first stage to converge.

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 5
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x
  [../]
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./body]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = ic
  [../]
[]

[BCs]
  [./bcs]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = LStableDirk2
  [../]
  num_steps = 1
  abort_on_solve_fail = true

  solve_type = NEWTON
  nl_max_its = 0
[]

(modules/porous_flow/test/tests/mass_conservation/mass09.i)

# Checking that the mass postprocessor throws the correct error when more than a single
# phase index is given when using the saturation_threshold parameter

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [sat]
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[ICs]
  [pinit]
    type = ConstantIC
    value = 1
    variable = pp
  []
  [satinit]
    type = FunctionIC
    function = 1-x
    variable = sat
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sat
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp sat'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 0.1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp
    phase1_saturation = sat
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [comp1_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    saturation_threshold = 0.5
    phase = '0 1'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

(test/tests/userobjects/postprocessor_spatial_user_object/master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 4
  ny = 4
[]

[Functions]
  [./ic_fn]
    type = ParsedFunction
    value = 'x * y'
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = FIRST
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = ic_fn
  [../]

  [./a_ic]
    type = ConstantIC
    variable = a
    value = 1
  [../]
[]

[AuxVariables]
  [./a]
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]
  [./rhs]
    type = BodyForce
    variable = u
    function = 1
  [../]
[]

[MultiApps]
  [./sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    input_files = 'sub.i'
    positions = '
      0.25 0.25 0
      0.75 0.75 0'
    execute_on = 'initial timestep_end'
  [../]
[]

[Transfers]
  [./master_to_sub]
    type = MultiAppNearestNodeTransfer
    to_multi_app = sub
    source_variable = u
    variable = a
  [../]

  [./sub_to_master]
    type = MultiAppUserObjectTransfer
    from_multi_app = sub
    user_object = fn_uo
    variable = a
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.1
  num_steps = 10
[]

[Outputs]
  exodus = true
[]

(test/tests/interfacekernels/ik_displaced/displaced.i)

[Mesh]
  displacements = 'disp_x disp_y'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    xmax = 2
    ny = 2
    ymax = 2
  []
  [./subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 1 0'
    block_id = 1
  [../]
  [./interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = subdomain1
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
  [../]
  [./break_boundary]
    input = interface
    type = BreakBoundaryOnSubdomainGenerator
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = 0
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
    block = 1
  [../]
[]

[Kernels]
  [./diff_u]
    type = CoeffParamDiffusion
    variable = u
    D = 4
    block = 0
  [../]
  [./diff_v]
    type = CoeffParamDiffusion
    variable = v
    D = 2
    block = 1
  [../]
  [./source_u]
    type = BodyForce
    variable = u
    value = 1
  [../]
[]

[InterfaceKernels]
  [./interface]
    type = InterfacialSource
    variable = u
    neighbor_var = v
    boundary = primary0_interface
    use_displaced_mesh = true
  [../]
[]

[BCs]
  [./u]
    type = VacuumBC
    variable = u
    boundary = 'left_to_0 bottom_to_0 right top'
  [../]
  [./v]
    type = VacuumBC
    variable = v
    boundary = 'left_to_1 bottom_to_1'
  [../]
[]

[Postprocessors]
  [./u_int]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = 0
  [../]
  [./v_int]
    type = ElementIntegralVariablePostprocessor
    variable = v
    block = 1
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  file_base = displaced
  exodus = true
[]

[Functions]
  [./disp_x_func]
    type = ParsedFunction
    value = x
  [../]
  [./disp_y_func]
    type = ParsedFunction
    value = y
  [../]
[]

[ICs]
  [./disp_x_ic]
    function = disp_x_func
    variable = disp_x
    type = FunctionIC
  [../]
  [./disp_y_ic]
    function = disp_y_func
    variable = disp_y
    type = FunctionIC
  [../]
[]

(test/tests/bcs/sin_bc/sin_neumann_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  nz = 0
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Functions]
  [./initial_value]
    type = ParsedFunction
    value = 'x'
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE

#    [./InitialCondition]
#      type = FunctionIC
 #     function = initial_value
#    [../]
  [../]
[]

[Kernels]
  active = 'diff ie'

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ie]
    type = TimeDerivative
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 1
  [../]

  [./right]
    type = SinNeumannBC
    variable = u
    boundary = 1
    initial = 1.0
    final = 2.0
    duration = 10.0
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  num_steps = 10
  dt = 1.0
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/numerical_diffusion/framework.i)

# Using framework objects: no mass lumping or upwinding
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = TimeDerivative
    variable = tracer
  []
  [flux]
    type = ConservativeAdvection
    velocity = '0.1 0 0'
    variable = tracer
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
    # Ideally, an OutflowBC would be used, but that does not exist in the framework
    # In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-1
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/porous_flow/test/tests/capillary_pressure/vangenuchten3.i)

# Test van Genuchten relative permeability curve by varying saturation over the mesh
# van Genuchten exponent m = 0.5 for both phases
# No residual saturation in either phase

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [p1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [p0]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 0
    variable = p0aux
  []
  [p1]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = p1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1e-5
    m = 0.5
    sat_lr = 0.1
    s_scale = 0.8
    log_extension = false
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    variable = 's0aux s1aux p0aux p1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 500
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-6
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-basic-kt-primitive.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_vel_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_vel_x]
    type = FunctionIC
    variable = sup_vel_x
    function = 'exact_sup_vel_x'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = sup_vel_x
    momentum_component = x
    eqn = "momentum"
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_vel_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_vel_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [pressure_right]
    type = FVFunctionDirichletBC
    variable = pressure
    function = exact_p
    boundary = 'right'
  []
  [sup_vel_x_left]
    type = FVFunctionDirichletBC
    variable = sup_vel_x
    function = exact_sup_vel_x
    boundary = 'left'
  []
  [T_fluid_left]
    type = FVFunctionDirichletBC
    variable = T_fluid
    function = exact_T
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    superficial_vel_x = sup_vel_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  value = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  value = '-3.83667087618017*sin(1.1*x)*cos(1.3*x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  value = '3.48788261470924*cos(1.1*x)*cos(1.3*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  value = '(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x))*cos(1.3*x) + 3.48788261470924*sin(x)*cos(1.1*x)^2*cos(1.3*x)/cos(x)^2 - 7.67334175236034*sin(1.1*x)*cos(1.1*x)*cos(1.3*x)/cos(x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)^2/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  value = '26.7439413073546*cos(1.5*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  value = '1.0*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(x)*cos(1.1*x)*cos(1.3*x)/cos(x)^2 - 1.1*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.1*x)*cos(1.3*x)/cos(x) - 1.3*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.3*x)*cos(1.1*x)/cos(x) + 1.0*(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x) - 40.1159119610319*sin(1.5*x))*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  value = '0.0106975765229418*cos(1.5*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)*cos(1.3*x)'
[]
[exact_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  value = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  value = 'cos(1.3*x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  value_x = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_vel_x]
    variable = sup_vel_x
    function = exact_sup_vel_x
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/porous_flow/test/tests/newton_cooling/nc02.i)

# Newton cooling from a bar.  1-phase steady
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1000
  ny = 1
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pressure'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.8
    alpha = 1e-5
  []
[]

[Variables]
  [pressure]
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = '(2-x/100)*1E6'
  []
[]

[Kernels]
  [flux]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    gravity = '0 0 0'
    variable = pressure
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1e6
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-15'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey # irrelevant in this fully-saturated situation
    n = 2
    phase = 0
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 2E6
  []
  [newton]
    type = PorousFlowPiecewiseLinearSink
    variable = pressure
    boundary = right
    pt_vals = '0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000 1100000 1200000 1300000 1400000 1500000 1600000 1700000 1800000 1900000 2000000'
    multipliers = '0. 5.6677197748570516e-6 0.000011931518841831313 0.00001885408740732065 0.000026504708864284114 0.000034959953203725676 0.000044304443352900224 0.00005463170211001232 0.00006604508815181467 0.00007865883048198513 0.00009259917167338928 0.00010800563134618119 0.00012503240252705603 0.00014384989486488752 0.00016464644014777016 0.00018763017719085535 0.0002130311349595711 0.00024110353477682344 0.00027212833465544285 0.00030641604122040985 0.00034430981736352295'
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 1
  []
[]

[VectorPostprocessors]
  [porepressure]
    type = LineValueSampler
    variable = pressure
    start_point = '0 0.5 0'
    end_point = '100 0.5 0'
    sort_by = x
    num_points = 20
    execute_on = timestep_end
  []
[]

[Preconditioning]
  active = 'andy'
  [andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol '
    petsc_options_value = 'gmres asm lu 100 NONZERO 2 1E-12 1E-15'
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  file_base = nc02
  execute_on = timestep_end
  exodus = false
  [along_line]
    type = CSV
    execute_vector_postprocessors_on = timestep_end
  []
[]

(modules/porous_flow/test/tests/jacobian/linear_por.i)

# Testing Jacobian resulting from PorousFlowPorosityLinear in a THM situation
[GlobalParams]
  PorousFlowDictator = dictator
  strain_at_nearest_qp = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]

[Variables]
  [pp]
    initial_condition = 1
  []
  [T]
    initial_condition = 2
  []
  [disp]
  []
[]

[ICs]
  [disp]
    type = FunctionIC
    variable = disp
    function = '3 * x'
  []
[]

[BCs]
  [disp]
    type = FunctionDirichletBC
    boundary = 'left right top bottom front back'
    variable = disp
    function = '3 * x'
  []
[]

[PorousFlowFullySaturated]
  coupling_type = ThermoHydroMechanical
  fp = simple_fluid
  porepressure = pp
  temperature = T
  displacements = 'disp disp disp'
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityLinear
    porosity_ref = 0.5
    P_ref = 0.5
    P_coeff = 1.0
    T_ref = -3.0
    T_coeff = 1.0
    epv_ref = 2.5
    epv_coeff = 1.0
  []
  [perm]
    type = PorousFlowPermeabilityConst
    permeability = '0 0 0  0 0 0  0 0 0'
  []
  [matrix_energy]
    type = PorousFlowMatrixInternalEnergy
    density = 0.0
    specific_heat_capacity = 0.0
  []
  [thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '0 0 0  0 0 0  0 0 0'
  []
  [density]
    type = GenericConstantMaterial
    prop_names = density
    prop_values = 0.0
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1E-99
    poissons_ratio = 0
  []
  [strain]
    type = ComputeSmallStrain
    displacements = 'disp disp disp'
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 1
#  petsc_options = '-snes_test_jacobian -snes_force_iteration'
#  petsc_options_iname = '-snes_type --ksp_type -pc_type -snes_convergence_test'
#  petsc_options_value = ' ksponly     preonly   none     skip'
[]

(test/tests/functions/image_function/threshold.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    threshold = 2.7e4
    upper_value = 1
    lower_value = -1
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/GrandPotentialPFM/SinteringDilute.i)

#input file to test the GrandPotentialSinteringMaterial using the dilute energy profile

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 17
  ny = 10
  xmin = 0
  xmax = 660
  ymin = 0
  ymax = 380
[]

[GlobalParams]
  op_num = 2
  var_name_base = gr
  int_width = 40
[]

[Variables]
  [./w]
    [./InitialCondition]
      type = FunctionIC
      variable = w
      function = f_w
    [../]
  [../]
  [./phi]
  [../]
  [./PolycrystalVariables]
  [../]
[]

[AuxVariables]
  [./T]
    order = CONSTANT
    family = MONOMIAL
    [./InitialCondition]
      type = FunctionIC
      variable = T
      function = f_T
    [../]
  [../]
[]

[ICs]
  [./phi_IC]
    type = SpecifiedSmoothCircleIC
    variable = phi
    x_positions = '190 470'
    y_positions = '190 190'
    z_positions = '  0   0'
    radii = '150 150'
    invalue = 0
    outvalue = 1
  [../]
  [./gr0_IC]
    type = SmoothCircleIC
    variable = gr0
    x1 = 190
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
  [./gr1_IC]
    type = SmoothCircleIC
    variable = gr1
    x1 = 470
    y1 = 190
    z1 = 0
    radius = 150
    invalue = 1
    outvalue = 0
  [../]
[]

[Functions]
  [./f_T]
    type = ConstantFunction
    value = 1600
  [../]
  [./f_w]
    type = ParsedFunction
    value = '1.515e-7 * x'
  [../]
[]

[Materials]
  # Free energy coefficients for parabolic curve
  [./kv]
    type = ParsedMaterial
    f_name = kv
    args = 'T'
    constant_names = 'a b'
    constant_expressions = '-0.025 1571.6'
    function = 'a*T + b'
  [../]
  # Diffusivity and mobilities
  [./chiD]
    type = GrandPotentialTensorMaterial
    f_name = chiD
    solid_mobility = L
    void_mobility = Lv
    chi = chi
    surface_energy = 19.7
    c = phi
    T = T
    D0 = 2.0e11
    GBmob0 = 1.4759e9
    Q = 2.77
    Em = 2.40
    bulkindex = 1
    gbindex = 20
    surfindex = 100
  [../]
  # Equilibrium vacancy concentration
  [./cs_eq]
    type = DerivativeParsedMaterial
    f_name = cs_eq
    args = 'gr0 gr1 T'
    constant_names = 'Ef Egb kB'
    constant_expressions = '2.69 2.1 8.617343e-5'
    function = 'bnds:=gr0^2 + gr1^2; cb:=exp(-Ef/kB/T); cgb:=exp(-(Ef-Egb)/kB/T);
                cb + 4.0*(cgb-cb)*(1.0 - bnds)^2'
  [../]
  # Everything else
  [./sintering]
    type = GrandPotentialSinteringMaterial
    chemical_potential = w
    void_op = phi
    Temperature = T
    surface_energy = 19.7
    grainboundary_energy = 9.86
    void_energy_coefficient = kv
    equilibrium_vacancy_concentration = cs_eq
    solid_energy_model = DILUTE
    outputs = exodus
  [../]

  # Concentration is only meant for output
  [./c]
    type = ParsedMaterial
    f_name = c
    material_property_names = 'hs rhos hv rhov'
    constant_names = 'Va'
    constant_expressions = '0.04092'
    function = 'Va*(hs*rhos + hv*rhov)'
    outputs = exodus
  [../]
[]

[Kernels]
  [./dt_gr0]
    type = TimeDerivative
    variable = gr0
  [../]
  [./dt_gr1]
    type = TimeDerivative
    variable = gr1
  [../]
  [./dt_phi]
    type = TimeDerivative
    variable = phi
  [../]
  [./dt_w]
    type = TimeDerivative
    variable = w
  [../]
[]

[AuxKernels]
  [./T_aux]
    type = FunctionAux
    variable = T
    function = f_T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = JFNK
  dt = 1
  num_steps = 2
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/missing_function_file_test.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = nonexistent_file #should generate error
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/porous-hllc.i)

eps=0.9

[GlobalParams]
  fp = fp
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = 1.1
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Variables]
  [rho]
    type = MooseVariableFVReal
  []
  [rho_ud]
    type = MooseVariableFVReal
  []
  [rho_et]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [rho]
    type = FunctionIC
    variable = rho
    function = 'exact_rho'
  []
  [rho_ud]
    type = FunctionIC
    variable = rho_ud
    function = 'exact_rho_ud'
  []
  [rho_et]
    type = FunctionIC
    variable = rho_et
    function = 'exact_rho_et'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVMassHLLC
    variable = rho
    fp = fp
  []
  [mass_fn]
    type = FVBodyForce
    variable = rho
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVMomentumHLLC
    variable = rho_ud
    momentum_component = x
    fp = fp
  []
  [momentum_fn]
    type = FVBodyForce
    variable = rho_ud
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVFluidEnergyHLLC
    variable = rho_et
    fp = fp
  []
  [energy_fn]
    type = FVBodyForce
    variable = rho_et
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_in]
    variable = rho
    type = PCNSFVHLLCSpecifiedMassFluxAndTemperatureMassBC
    boundary = left
    temperature = 'exact_T'
    superficial_rhou = 'exact_rho_ud'
  []
  [momentum_in]
    variable = rho_ud
    type = PCNSFVHLLCSpecifiedMassFluxAndTemperatureMomentumBC
    boundary = left
    temperature = 'exact_T'
    superficial_rhou = 'exact_rho_ud'
    momentum_component = 'x'
  []
  [energy_in]
    variable = rho_et
    type = PCNSFVHLLCSpecifiedMassFluxAndTemperatureFluidEnergyBC
    boundary = left
    temperature = 'exact_T'
    superficial_rhou = 'exact_rho_ud'
  []

  [mass_out]
    variable = rho
    type = PCNSFVHLLCSpecifiedPressureMassBC
    boundary = right
    pressure = 'exact_p'
  []
  [momentum_out]
    variable = rho_ud
    type = PCNSFVHLLCSpecifiedPressureMomentumBC
    boundary = right
    pressure = 'exact_p'
    momentum_component = 'x'
  []
  [energy_out]
    variable = rho_et
    type = PCNSFVHLLCSpecifiedPressureFluidEnergyBC
    boundary = right
    pressure = 'exact_p'
  []
[]

[Materials]
  [var_mat]
    type = PorousConservedVarMaterial
    rho = rho
    superficial_rhou = rho_ud
    rho_et = rho_et
    porosity = porosity
  []
  [porosity]
    type = GenericConstantMaterial
    prop_names = 'porosity'
    prop_values = '${eps}'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  value = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  value = '-3.83667087618017*eps*sin(1.1*x)'
  vars = 'eps'
  vals = '${eps}'
[]
[exact_rho_ud]
  type = ParsedFunction
  value = '3.48788261470924*eps*cos(1.1*x)'
  vars = 'eps'
  vals = '${eps}'
[]
[forcing_rho_ud]
  type = ParsedFunction
  value = 'eps*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x)) + 3.48788261470924*eps*sin(x)*cos(1.1*x)^2/cos(x)^2 - 7.67334175236034*eps*sin(1.1*x)*cos(1.1*x)/cos(x)'
  vars = 'eps'
  vals = '${eps}'
[]
[exact_rho_et]
  type = ParsedFunction
  value = '26.7439413073546*cos(1.2*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  value = '1.0*eps*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(x)*cos(1.1*x)/cos(x)^2 - 1.1*eps*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(1.1*x)/cos(x) + 1.0*eps*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) - 32.0927295688256*sin(1.2*x))*cos(1.1*x)/cos(x)'
  vars = 'eps'
  vals = '${eps}'
[]
[exact_T]
  type = ParsedFunction
  value = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
  vars = 'eps'
  vals = '${eps}'
[]
[exact_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
  vars = 'eps'
  vals = '${eps}'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = none
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho]
    type = ElementL2Error
    variable = rho
    function = exact_rho
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_ud]
    variable = rho_ud
    function = exact_rho_ud
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_et]
    variable = rho_et
    function = exact_rho_et
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/kernels/ad_mat_diffusion/1D_transient.i)

# This test solves a 1D transient heat equation
# The error is calculated by comparing to the analytical solution
# The problem setup and analytical solution are taken from "Advanced Engineering
# Mathematics, 10th edition" by Erwin Kreyszig.
# http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364
# It is Example 1 in section 12.6 on page 561

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 160
  xmax = 80
[]

[Variables]
  [./T]
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '100*sin(pi*x/80)'
  [../]
[]

[Kernels]
  [./diff]
    type = MatDiffusion
    variable = T
    diffusivity = 0.95
  [../]
  [./dt]
    type = CoefTimeDerivative
    variable = T
    Coefficient = 0.82064
  [../]
[]

[BCs]
  [./sides]
    type = DirichletBC
    variable = T
    boundary = 'left right'
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  dt = 1e-2
  end_time = 1
[]

[Postprocessors]
  [./error]
    type = NodalL2Error
    function = '100*sin(pi*x/80)*exp(-0.95/(0.092*8.92)*pi^2/80^2*t)'
    variable = T
    outputs = console
  [../]
[]

[Outputs]
  exodus = true
[]

(tutorials/tutorial03_verification/app/test/tests/step04_mms/2d_mms_temporal.i)

[ICs]
  active = 'mms'
  [mms]
    type = FunctionIC
    variable = T
    function = mms_exact
  []
[]

[BCs]
  active = 'mms'
  [mms]
    type = FunctionDirichletBC
    variable = T
    boundary = 'left right top bottom'
    function = mms_exact
  []
[]

[Kernels]
  [mms]
    type = HeatSource
    variable = T
    function = mms_force
  []
[]

[Functions]
  [mms_force]
    type = ParsedFunction
    value = '-3.08641975308642e-5*x*y*cp*rho*exp(-3.08641975308642e-5*t) - shortwave*exp(y*kappa)*sin((1/2)*x*pi)*sin((1/3600)*pi*t/hours)'
    vars = 'rho cp   k     kappa shortwave hours'
    vals = '150 2000 0.01  40    650       9'
  []
  [mms_exact]
    type = ParsedFunction
    value = 'x*y*exp(-3.08641975308642e-5*t)'
  []
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [error]
    type = ElementL2Error
    variable = T
    function = mms_exact
  []
  [delta_t]
    type = TimestepSize
  []
[]

(modules/ray_tracing/test/tests/outputs/ray_tracing_mesh_output/ray_mesh_output_data.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmax = 5
    ymax = 5
  []
[]

[Variables/u]
  [InitialCondition]
    type = FunctionIC
    variable = u
    function = '(x < 2) * (x + 2 * y) + (x >= 2) * (2 * x + 2 * y - 2)'
  []
[]

[UserObjects]
  [study]
    type = RepeatableRayStudy
    names = 'diag
             top_across
             bottom_across
             partial'
    start_points = '0 0 0
                    0 5 0
                    0 0 0
                    0.5 0.5 0'
    end_points = '5 5 0
                  5 5 0
                  5 0 0
                  4.5 0.5 0'
    always_cache_traces = true
    data_on_cache_traces = true
    aux_data_on_cache_traces = true
    ray_aux_data_names = 'test_aux'
    initial_ray_aux_data = '1; 2; 3; 4'
  []
[]

[RayKernels]
  [variable_integral]
    type = VariableIntegralRayKernel
    study = study
    variable = u
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  [rays]
    type = RayTracingExodus
    study = study
    output_data = true
    output_aux_data = true
    execute_on = final
  []
  [rays_nodal]
    type = RayTracingExodus
    study = study
    output_data_nodal = true
    execute_on = final
  []
[]

(test/tests/nodalkernels/constraint_enforcement/ad-upper-and-lower-bound.i)

l=10
nx=100
num_steps=10

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
  [lm_upper]
  []
  [lm_lower]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = ADTimeDerivative
    variable = u
  []
  [diff]
    type = ADDiffusion
    variable = u
  []
  [ffn]
    type = ADBodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[NodalKernels]
  [upper_bound]
    type = ADUpperBoundNodalKernel
    variable = lm_upper
    v = u
    exclude_boundaries = 'left right'
    upper_bound = 10
  []
  [forces_from_upper]
    type = ADCoupledForceNodalKernel
    variable = u
    v = lm_upper
    coef = -1
  []
  [lower_bound]
    type = ADLowerBoundNodalKernel
    variable = lm_lower
    v = u
    exclude_boundaries = 'left right'
    lower_bound = 0
  []
  [forces_from_lower]
    type = ADCoupledForceNodalKernel
    variable = u
    v = lm_lower
    coef = 1
  []
[]


[BCs]
  [left]
    type = ADDirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = ADDirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type'
  petsc_options_value = '0                           30          asm      16                    basic'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [active_upper_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm_upper
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
    comparator = 'greater'
  []
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [active_lower_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm_lower
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

(test/tests/kernels/material_coupled_force/material_coupled_force.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  nx = 10
  ymin = 0
  ymax = 2
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./v1]
    initial_condition = 3
  [../]

  [./v2]
  [../]
[]

[ICs]
  [./v2_ic]
    type = FunctionIC
    variable = v2
    function = v2_func
  [../]
[]

[Functions]
  [./v2_func]
    type = ParsedFunction
    value = 'x + 2 * y'
  [../]

  [./reference]
    type = ParsedFunction
    value = '3 * (-1) * 3.5 + (x + 2 * y) * 15 * 1.2'
  [../]
[]

[Materials]
  [./mat]
    type = GenericConstantMaterial
    prop_names = 'm1 m2'
    prop_values = '-1 15'
  [../]
[]

[Kernels]
  [./reaction]
    type = Reaction
    variable = u
  [../]

  [./coupled]
    type = MatCoupledForce
    variable = u
    v = 'v1 v2'
    coef = '3.5 1.2'
    material_properties = 'm1 m2'
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    function = reference
    variable = u
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/examples/multiapp_fracture_flow/diffusion_multiapp/single_var.i)

# No heat transfer between matrix and fracture, with the matrix and fracture being identical spatial domains
[Mesh]
  [generate]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 100
    xmin = 0
    xmax = 50.0
  []
[]

[Variables]
  [T]
  []
[]

[ICs]
  [T]
    type = FunctionIC
    variable = T
    function = 'if(x<0.5, 2, 0)'  # delta function
  []
[]

[Kernels]
  [dot]
    type = TimeDerivative
    variable = T
  []
  [fracture_diffusion]
    type = Diffusion
    variable = T
  []
[]

[Preconditioning]
  [entire_jacobian]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 100
  end_time = 100
[]

[VectorPostprocessors]
  [final_results]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '50 0 0'
    num_points = 11
    sort_by = x
    variable = T
    outputs = final_csv
  []
[]

[Outputs]
  print_linear_residuals = false
  [final_csv]
    type = CSV
    sync_times = 100
    sync_only = true
  []
[]

(modules/porous_flow/test/tests/dirackernels/pls03.i)

# Test that the upwinding works correctly.
#
# A poly-line sink sits at the centre of the element.
# It has length=4 and weight=0.5, and extracts fluid
# at a constant rate of
# (1 * relative_permeability) kg.m^-1.s^-1
# Since it sits at the centre of the element, it extracts
# equally from each node, so the rate of extraction from
# each node is
# (0.5 * relative_permeability) kg.s^-1
# including the length and weight effects.
#
# There is no fluid flow.
#
# The initial conditions are such that all nodes have
# relative_permeability=0, except for one which has
# relative_permeaility = 1.  Therefore, all nodes should
# remain at their initial porepressure, except the one.
#
# The porosity is 0.1, and the elemental volume is 2,
# so the fluid mass at the node in question = 0.2 * density / 4,
# where the 4 is the number of nodes in the element.
# In this simulation density = dens0 * exp(P / bulk), with
# dens0 = 100, and bulk = 20 MPa.
# The initial porepressure P0 = 10 MPa, so the final (after
# 1 second of simulation) is
# P(t=1) = 8.748592 MPa
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 2
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    #function = if((x<1)&(y<0.5),1E7,-1E7)
    function = if((x<1)&(y>0.5),1E7,-1E7)
    #function = if((x>1)&(y<0.5),1E7,-1E7)
    #function = if((x>1)&(y>0.5),1E7,-1E7)
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pls_total_outflow_mass]
    type = PorousFlowSumQuantity
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1e-7
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e7
      density0 = 100
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [relperm]
    type = PorousFlowRelativePermeabilityFLAC
    phase = 0
    m = 2
    s_res = 0.99
    sum_s_res = 0.99
  []
[]

[DiracKernels]
  [pls]
    type = PorousFlowPolyLineSink
    fluid_phase = 0
    point_file = pls03.bh
    use_relative_permeability = true
    line_length = 4
    SumQuantityUO = pls_total_outflow_mass
    variable = pp
    p_or_t_vals = '0 1E7'
    fluxes = '1 1'
  []
[]

[Postprocessors]
  [pls_report]
    type = PorousFlowPlotQuantity
    uo = pls_total_outflow_mass
  []

  [fluid_mass0]
    type = PorousFlowFluidMass
    execute_on = timestep_begin
  []

  [fluid_mass1]
    type = PorousFlowFluidMass
    execute_on = timestep_end
  []

  [zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  []

  [p00]
    type = PointValue
    variable = pp
    point = '0 0 0'
    execute_on = timestep_end
  []
  [p01]
    type = PointValue
    variable = pp
    point = '0 1 0'
    execute_on = timestep_end
  []
  [p20]
    type = PointValue
    variable = pp
    point = '2 0 0'
    execute_on = timestep_end
  []
  [p21]
    type = PointValue
    variable = pp
    point = '2 1 0'
    execute_on = timestep_end
  []
[]

[Functions]
  [mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 pls_report'
  []
[]

[Preconditioning]
  [usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  []
[]

[Executioner]
  type = Transient
  end_time = 1
  dt = 1
  solve_type = NEWTON
[]

[Outputs]
  file_base = pls03
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(test/tests/executioners/nullspace/singular_contaminated.i)

[Mesh]
 type = GeneratedMesh
 dim = 1
 xmin = 0
 xmax = 10
 nx = 8
[]

[Problem]
  null_space_dimension = 1
  transpose_null_space_dimension = 1
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./eig]
    type = MassEigenKernel
    variable = u
    eigen_postprocessor = 1.0002920196258376e+01
    eigen = false
  [../]

  [./force]
    type = CoupledForce
    variable = u
    v = aux_v
  [../]
[]

[AuxVariables]
  [./aux_v]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = eigen_mode
    [../]
  [../]
[]

[AuxKernels]
  [./set_source]
    type = FunctionAux
    variable = aux_v
    function = contaminated_second_harmonic
    execute_on = timestep_begin
  [../]
[]

[Functions]
  [./eigen_mode]
    type = ParsedFunction
    value = 'sqrt(2.0 / L) * sin(mode * pi  * x / L)'
    vars = 'L  mode'
    vals = '10 1'
  [../]

  [./contaminated_second_harmonic]
    type = ParsedFunction
    value = 'sqrt(2.0 / L) * sin(mode * pi  * x / L) + a * sqrt(2.0 / L) * sin(pi * x / L)'
    vars = 'L  mode a'
    vals = '10 2    1'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1'
    value = 0
  [../]
[]

[VectorPostprocessors]
  [./sample_solution]
    type = LineValueSampler
    variable = u
    start_point = '0 0 0'
    end_point = '10 0 0'
    sort_by = x
    num_points = 9
    execute_on = timestep_end
  [../]
[]

[Preconditioning]
  [./prec]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = SteadyWithNull
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_pc_side -snes_type -ksp_norm_type'
  petsc_options_value = 'hypre boomeramg  left ksponly preconditioned'
  nl_rel_tol = 1.0e-14
  nl_abs_tol = 1.0e-14
[]

[Outputs]
  execute_on = 'timestep_end'
  csv = true
[]

(modules/porous_flow/test/tests/heat_advection/heat_advection_1d_fully_saturated_action.i)

# 1phase, heat advecting with a moving fluid
# Using the PorousFlowFullySaturated Action with various stabilization options
# With stabilization=none, this should produce an identical result to heat_advection_1d_fully_saturated.i
# With stabilization=Full, this should produce an identical result to heat_advection_1d.i and heat_advection_1d_fullsat.i
# With stabilization=KT, this should produce an identical result to heat_advection_1D_KT.i
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 50
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [temp]
    initial_condition = 200
  []
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1-x'
  []
[]

[BCs]
  [pp0]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 1
  []
  [pp1]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 0
  []
  [spit_heat]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  []
  [suck_heat]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 200
  []
[]

[PorousFlowFullySaturated]
  porepressure = pp
  temperature = temp
  coupling_type = ThermoHydro
  fp = simple_fluid
  add_darcy_aux = false
  stabilization = none
  flux_limiter_type = superbee
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 100
      density0 = 1000
      viscosity = 4.4
      thermal_expansion = 0
      cv = 2
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [zero_thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '0 0 0  0 0 0  0 0 0'
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 1.0
    density = 125
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 2 0 0 0 3'
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.01
  end_time = 0.6
[]

[VectorPostprocessors]
  [T]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 51
    sort_by = x
    variable = temp
  []
[]

[Outputs]
  file_base = heat_advection_1d_fully_saturation_action
  [csv]
    type = CSV
    sync_times = '0.1 0.6'
    sync_only = true
  []
[]

(modules/porous_flow/test/tests/heat_advection/heat_advection_1d_fullsat.i)

# 1phase, heat advecting with a moving fluid
# Full upwinding is used, as implemented by the PorousFlowFullySaturatedUpwindHeatAdvection added
# In this case, the results should be identical to the case when the PorousFlowHeatAdvection Kernel is used.
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 50
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [temp]
    initial_condition = 200
  []
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1-x'
  []
[]

[BCs]
  [pp0]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 1
  []
  [pp1]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 0
  []
  [spit_heat]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  []
  [suck_heat]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 200
  []
[]

[Kernels]
  [mass_dot]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [advection]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
  []
  [energy_dot]
    type = PorousFlowEnergyTimeDerivative
    variable = temp
  []
  [heat_advection]
    type = PorousFlowFullySaturatedUpwindHeatAdvection
    variable = temp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.6
    alpha = 1.3
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 100
      density0 = 1000
      viscosity = 4.4
      thermal_expansion = 0
      cv = 2
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 1.0
    density = 125
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 2 0 0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [PS]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres bjacobi 1E-15 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.01
  end_time = 0.6
[]

[VectorPostprocessors]
  [T]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 51
    sort_by = x
    variable = temp
  []
[]

[Outputs]
  [csv]
    type = CSV
    sync_times = '0.1 0.6'
    sync_only = true
  []
[]

(test/tests/functions/image_function/component.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    component = 0
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/multiphase_mechanics/multiphasestress.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  xmin = 0
  xmax = 2
  ymin = 0
  ymax = 2
  elem_type = QUAD4
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./eta1]
    [./InitialCondition]
      type = FunctionIC
      function = 'x/2'
    [../]
  [../]
  [./eta2]
    [./InitialCondition]
      type = FunctionIC
      function = 'y/2'
    [../]
  [../]
  [./eta3]
    [./InitialCondition]
      type = FunctionIC
      function = '(2^0.5-(y-1)^2=(y-1)^2)/2'
    [../]
  [../]
  [./e11_aux]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_e11]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = e11_aux
  [../]
[]

[Kernels]
  [./TensorMechanics]
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ComputeElasticityTensor
    base_name = A
    fill_method = symmetric9
    C_ijkl = '1e6 1e5 1e5 1e6 0 1e6 .4e6 .2e6 .5e6'
  [../]
  [./strain_A]
    type = ComputeSmallStrain
    base_name = A
    eigenstrain_names = eigenstrain
  [../]
  [./stress_A]
    type = ComputeLinearElasticStress
    base_name = A
  [../]
  [./eigenstrain_A]
    type = ComputeEigenstrain
    base_name = A
    eigen_base = '0.1 0.05 0 0 0 0.01'
    prefactor = -1
    eigenstrain_name = eigenstrain
  [../]

  [./elasticity_tensor_B]
    type = ComputeElasticityTensor
    base_name = B
    fill_method = symmetric9
    C_ijkl = '1e6 0 0 1e6 0 1e6 .5e6 .5e6 .5e6'
  [../]
  [./strain_B]
    type = ComputeSmallStrain
    base_name = B
    eigenstrain_names = 'B_eigenstrain'
  [../]
  [./stress_B]
    type = ComputeLinearElasticStress
    base_name = B
  [../]
  [./eigenstrain_B]
    type = ComputeEigenstrain
    base_name = B
    eigen_base = '0.1 0.05 0 0 0 0.01'
    prefactor = -1
    eigenstrain_name = 'B_eigenstrain'
  [../]

  [./elasticity_tensor_C]
    type = ComputeElasticityTensor
    base_name = C
    fill_method = symmetric9
    C_ijkl = '1.1e6 1e5 0 1e6 0 1e6 .5e6 .2e6 .5e6'
  [../]
  [./strain_C]
    type = ComputeSmallStrain
    base_name = C
    eigenstrain_names = 'C_eigenstrain'
  [../]
  [./stress_C]
    type = ComputeLinearElasticStress
    base_name = C
  [../]
  [./eigenstrain_C]
    type = ComputeEigenstrain
    base_name = C
    eigen_base = '0.1 0.05 0 0 0 0.01'
    prefactor = -1
    eigenstrain_name = 'C_eigenstrain'
  [../]


  [./switching_A]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
  [../]
  [./switching_B]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
  [../]
  [./switching_C]
    type = SwitchingFunctionMaterial
    function_name = h3
    eta = eta3
  [../]

  [./combined]
    type = MultiPhaseStressMaterial
    phase_base = 'A  B  C'
    h          = 'h1 h2 h3'
  [../]
[]

[BCs]
  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0
  [../]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(modules/fsi/test/tests/fsi_acoustics/1D_fluid_only/1D_fluid_only.i)

# Test for `AcousticInertia` and `Diffusion` kernels with only the fluid domain. The
# domain is 1D with length 1m and is subjected to an initial condition composed of
# a combination of sine waves. Fluid pressure is recorded at the midpoint of the
# domain. The recorded fluid pressure should match with analytical results. Because
# this implementation is equivalent to solving a 1D wave equation, analytical results
# exist.
#
# Input parameters:
# Dimensions = 1
# Length = 1 meter
# Fluid speed of sound = 1 m/s
# Initial condition = sin(pi*x) + sin(3*pi*x) + sin(5*3.141*x) + sin(7*pi*x) + sin(9*pi*x)
# Fluid domain = true
# Fluid BCs = pressures are zero on both the boundaries
# Structural domain = false

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 500
    xmax = 1
  []
[]

[GlobalParams]
[]

[Variables]
  [./p]
  [../]
[]

[Kernels]
  [./diffusion]
    type = Diffusion
    variable = 'p'
  [../]
  [./inertia]
    type = AcousticInertia
    variable = p
  [../]
[]

[BCs]
  [./leftright_pressure]
    type = DirichletBC
    variable = p
    boundary = 'left right'
    value = 0
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = 'p'
    function = initial_cond
  [../]
[]

[Functions]
  [./initial_cond]
    type = ParsedFunction
    value = 'sin(pi*x) + sin(3*pi*x) + sin(5*3.141*x) + sin(7*pi*x) + sin(9*pi*x)'
  [../]
[]

[Materials]
  [./co_sq]
    type = GenericConstantMaterial
    prop_names = inv_co_sq
    prop_values = 1
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  start_time = 0.0
  end_time = 1.0
  dt = 0.005
  dtmin = 0.00001
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  l_max_its = 25
  timestep_tolerance = 1e-8
  automatic_scaling = true
  [TimeIntegrator]
    type = NewmarkBeta
  []
[]

[Postprocessors]
  [./p1]
    type = PointValue
    point = '0.5 0.0 0.0'
    variable = p
  [../]
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

(test/tests/ics/function_ic/spline_function.i)

#
# Test the gradient calculation in spline function and the gradient pass-through in FunctionIC
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 3
  ymin = 0
  ymax = 1
  nx = 10
  ny = 2
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Functions]
  [./spline_function]
    type = SplineFunction
    x = '0 1 2 3'
    y = '0 1 0 1'
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = 'u'
    function = spline_function
  [../]
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[]

[Outputs]
  file_base = spline
  [./OverSampling]
    type = Exodus
    refinements = 3
  [../]
[]

(test/tests/multiapps/grid-sequencing/vi-coarser.i)

l=10
nx=20
num_steps=2

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [bounds][]
[]

[Bounds]
  [./u_upper_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = upper
    bound_value = ${l}
  [../]
  [./u_lower_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = lower
    bound_value = 0
  [../]
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options = '-snes_vi_monitor'
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type -snes_type'
  petsc_options_value = '0                           30          asm      16                    basic                 vinewtonrsls'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  active = 'upper_violations lower_violations'
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

(test/tests/auxkernels/grad_component/grad_component_monomial.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 2
  nx = 20
  ny = 10
[]

[Variables]
  [./not_u]
  [../]
[]

[AuxVariables]
  [./u]
    family = MONOMIAL
    order = FIRST
  [../]
  [./grad_u_x]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./u]
    type = FunctionIC
    variable = u
    function = 'if(x>0.5,if(x<1.5,2*x,3),0)'
  [../]
[]

[AuxKernels]
  [./grad_u_x_aux]
    type = VariableGradientComponent
    variable = grad_u_x
    component = x
    gradient_variable = u
    execute_on = initial
  [../]
[]

[Problem]
  type = FEProblem
  solve = false
  kernel_coverage_check = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/theis/th01.i)

# fully-saturated
# production
[Mesh]
  type = FileMesh
  file = th01_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '0.5 1 2 10'
    x = '0 1 10 100'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]

  [./total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsPolyLineSink
    pressures = '-1E9 1E9'
    fluxes = '200 200'
    point_file = th01.points
    SumQuantityUO = total_outflow_mass
    variable = pressure
  [../]
[]


[Postprocessors]
  [./flow_report]
    type = RichardsPlotQuantity
    uo = total_outflow_mass
  [../]
  [./p50]
    type = PointValue
    variable = pressure
    point = '50 0 0'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E5
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-6 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 100
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = th01
  csv = true
[]

(modules/geochemistry/test/tests/nodal_void_volume/nodal_void_volume_adaptive.i)

# Computes nodal void volume, when using adaptivity, and compares with the Postprocessor hand-calculated values
[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1 2 2'
    dy = '1 4'
  []
[]

[Adaptivity]
  initial_marker = u_marker
  marker = u_marker
  max_h_level = 1
  [Markers]
    [u_marker]
      type = ValueRangeMarker
      variable = u
      invert = true
      lower_bound = 0.02
      upper_bound = 0.98
    []
  []
[]

[Variables]
  [u]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<2,0,1)'
  []
[]

[Kernels]
  [dot]
    type = TimeDerivative
    variable = u
  []
  [u]
    type = Diffusion
    variable = u
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 2
[]

[Outputs]
  csv = true
[]

[UserObjects]
  [nodal_void_volume]
    type = NodalVoidVolume
    porosity = porosity
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
  []
  [vol]
  []
[]

[AuxKernels]
  [porosity]
    type = FunctionAux
    variable = porosity
    function = 'if(x<4, 1, 2)'
  []
  [vol]
    type = NodalVoidVolumeAux
    variable = vol
    nodal_void_volume_uo = nodal_void_volume
  []
[]

[Postprocessors]
  [quarter]
    type = PointValue
    point = '0 0 0'
    variable = vol
  []
  [half]
    type = PointValue
    point = '1 0 0'
    variable = vol
  []
  [three_quarters]
    type = PointValue
    point = '2 0 0'
    variable = vol
  []
  [one_and_half_to_34s]
    type = PointValue
    point = '4 0 0'
    variable = vol
  []
  [one_to_14]
    type = PointValue
    point = '6 0 0'
    variable = vol
  []
  [one_and_quarter]
    type = PointValue
    point = '0 1 0'
    variable = vol
  []
  [two_and_half]
    type = PointValue
    point = '1 1 0'
    variable = vol
  []
  [three_and_three_quarters]
    type = PointValue
    point = '2 1 0'
    variable = vol
  []
  [seven_and_half_to_334]
    type = PointValue
    point = '4 1 0'
    variable = vol
  []
  [five_to_54]
    type = PointValue
    point = '6 1 0'
    variable = vol
  []
[]

(test/tests/controls/control_piecewise/controlled_piecewise.i)

[Mesh]
  [./generated]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 10
  [../]
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./u]
    initial_condition = 0.1
  [../]
[]

[AuxVariables]
  [./v]
  [../]
  [./x]
  [../]
[]

[ICs]
  [./x_ic]
    type = FunctionIC
    variable = x
    function = 'x'
  [../]
[]

[AuxKernels]
  [./v_aux]
    type = FunctionAux
    variable = v
    function = func
  [../]
[]

[Controls]
  [./func_control]
    type = RealFunctionControl
    parameter = '*/*/scale_factor'
    function = '2'
    execute_on = 'initial'
  [../]
[]

[Materials]
  [./mat]
    type = PiecewiseLinearInterpolationMaterial
    property = matprop
    variable = x
    x = '0 1'
    y = '0 10'
    outputs = all
  [../]
[]

[Functions]
  [./func]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 10'
    axis = x
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/image_function/image_2d.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/multiphase_mechanics/nonsplit_gradderiv_action.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 5
  xmax = 10
  ymax = 10
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
  displacement_gradients = 'gxx gxy gyx gyy'
[]

[Modules]
  [./PhaseField]
    [./DisplacementGradients]
    [../]
  [../]
[]

[AuxVariables]
  [./disp_x]
    [./InitialCondition]
      type = FunctionIC
      function = '0.1*sin(2*x/10*3.14159265359)'
    [../]
  [../]
  [./disp_y]
    [./InitialCondition]
      type = FunctionIC
      function = '0.1*sin(1*y/10*3.14159265359)'
    [../]
  [../]
[]

[Variables]
  [./c]
    order = THIRD
    family = HERMITE
    initial_condition = 0
  [../]
[]

[Kernels]
  [./dt]
    type = TimeDerivative
    variable = c
  [../]
  [./bulk]
    type = CahnHilliard
    variable = c
    mob_name = M
    f_name = F
  [../]
  [./int]
    type = CHInterface
    variable = c
    mob_name = M
    kappa_name = kappa_c
  [../]
[]

[BCs]
  [./Periodic]
    [./All]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M  kappa_c'
    prop_values = '1  0.1'
  [../]

  [./elasticity_tensor]
    type = ComputeConcentrationDependentElasticityTensor
    c = c
    C0_ijkl = '1.0 1.0'
    C1_ijkl = '3.0 3.0'
    fill_method0 = symmetric_isotropic
    fill_method1 = symmetric_isotropic
  [../]
  [./smallstrain]
    type = ComputeSmallStrain
  [../]
  [./linearelastic_a]
    type = ComputeLinearElasticStress
  [../]
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = F
    args = 'c'
    derivative_order = 3
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'

  solve_type = NEWTON

  l_max_its = 30
  l_tol = 1.0e-6

  nl_max_its = 15
  nl_rel_tol = 1.0e-7
  nl_abs_tol = 1.0e-10

  num_steps = 2
  dt = 1
[]

[Outputs]
  perf_graph = true
  file_base = nonsplit_gradderiv_out
  exodus = true
[]

(test/tests/meshgenerators/file_mesh_generator/2d_diffusion_iga.i)

[Mesh]
  [cyl2d_iga]
    type = FileMeshGenerator
    file = PressurizedCyl_Patch6_4Elem.e
  []
  allow_renumbering = false
  parallel_type = replicated
[]

[Variables]
  [u]
    order = SECOND  # Must match mesh order
    family = RATIONAL_BERNSTEIN
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
    block = 0  # Avoid direct calculations on spline nodes
  []
  [diff]
    type = Diffusion
    variable = u
    block = 0  # Avoid direct calculations on spline nodes
  []
  [null]
    type = NullKernel
    variable = u
    block = 1  # Keep kernel coverage check happy
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'sin(x)'
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
  solve_type = NEWTON
  dtmin = 1
[]

[Outputs]
  vtk = true
[]

(test/tests/kernels/conservative_advection/none_in_all_out.i)

# Using ConservativeAdvection with full upwinding
# This demonstrates BCs that introduce no mass into
# the domain but allow it to exit freely.
[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 10
  nx = 100
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u]
    type = FunctionIC
    variable = u
    function = 'if(x<5,x,10-x)'
  [../]
[]

[Kernels]
  [./dot]
    type = MassLumpedTimeDerivative
    variable = u
  [../]
  [./advection]
    type = ConservativeAdvection
    variable = u
    upwinding_type = full
    velocity = '1 0 0'
  [../]
[]

[BCs]
  [./allow_mass_out]
    type = OutflowBC
    boundary = right
    variable = u
    velocity = '1 0 0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 10
  l_tol = 1E-14
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/multiphase_mechanics/nonsplit_gradderiv.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 5
  xmax = 10
  ymax = 10
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
  displacement_gradients = 'gxx gxy gyx gyy'
[]

[AuxVariables]
  [./disp_x]
    [./InitialCondition]
      type = FunctionIC
      function = '0.1*sin(2*x/10*3.14159265359)'
    [../]
  [../]
  [./disp_y]
    [./InitialCondition]
      type = FunctionIC
      function = '0.1*sin(1*y/10*3.14159265359)'
    [../]
  [../]
[]

[Variables]
  [./c]
    order = THIRD
    family = HERMITE
    initial_condition = 0
  [../]

  [./gxx]
  [../]
  [./gxy]
  [../]
  [./gyx]
  [../]
  [./gyy]
  [../]
[]

[Kernels]
  [./dt]
    type = TimeDerivative
    variable = c
  [../]
  [./bulk]
    type = CahnHilliard
    variable = c
    mob_name = M
    f_name = F
  [../]
  [./int]
    type = CHInterface
    variable = c
    mob_name = M
    kappa_name = kappa_c
  [../]

  [./gxx]
    type = GradientComponent
    variable = gxx
    v = disp_x
    component = 0
  [../]
  [./gxy]
    type = GradientComponent
    variable = gxy
    v = disp_x
    component = 1
  [../]
  [./gyx]
    type = GradientComponent
    variable = gyx
    v = disp_y
    component = 0
  [../]
  [./gyy]
    type = GradientComponent
    variable = gyy
    v = disp_y
    component = 1
  [../]
[]

[BCs]
  [./Periodic]
    [./All]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M  kappa_c'
    prop_values = '1  0.1'
  [../]
  [./straingradderiv]
    type = StrainGradDispDerivatives
  [../]

  [./elasticity_tensor]
    type = ComputeConcentrationDependentElasticityTensor
    c = c
    C0_ijkl = '1.0 1.0'
    C1_ijkl = '3.0 3.0'
    fill_method0 = symmetric_isotropic
    fill_method1 = symmetric_isotropic
  [../]
  [./smallstrain]
    type = ComputeSmallStrain
  [../]
  [./linearelastic_a]
    type = ComputeLinearElasticStress
  [../]
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = F
    args = 'c'
    derivative_order = 3
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'

  solve_type = NEWTON

  l_max_its = 30
  l_tol = 1.0e-6

  nl_max_its = 15
  nl_rel_tol = 1.0e-7
  nl_abs_tol = 1.0e-10

  num_steps = 2
  dt = 1
[]

[Outputs]
  perf_graph = true
  exodus = true
[]

(modules/richards/test/tests/theis/th22.i)

# two-phase, fully-saturated
# production
[Mesh]
  type = FileMesh
  file = th02_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1 2 4 20'
    x = '0 1 10 100'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]

  [./total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]


[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_pressure
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsPolyLineSink
    pressures = '-1E9 1E9'
    fluxes = '200 200'
    point_file = th01.points
    SumQuantityUO = total_outflow_mass
    variable = pwater
  [../]
[]


[Postprocessors]
  [./flow_report]
    type = RichardsPlotQuantity
    uo = total_outflow_mass
  [../]
  [./p50]
    type = PointValue
    variable = pwater
    point = '50 0 0'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E5
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    mat_porosity = 0.1
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 1E-5'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]



[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt -snes_linesearch_monitor'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-7 1E-10 20 1E-10 1E-100'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 100
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = th22
  exodus = true
  csv = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/fltvd_2D_blocks.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek
# 2D version with blocks
# Top block: tracer is defined here, with velocity = (0.1, 0, 0)
# Central block: tracer is not defined here
# Bottom block: tracer is defined here, with velocity = (-0.1, 0, 0)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    xmin = 0
    xmax = 1
    ny = 5
    ymin = 0
    ymax = 1
  []
  [top]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0.6 0'
    top_right = '1 1 0'
    block_id = 1
  []
  [center]
    input = bottom
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0.4 0'
    top_right = '1 0.6 0'
    block_id = 2
  []
  [bottom]
    input = top
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 0.6 0'
    block_id = 3
  []
  [split_bdys]
    type = BreakBoundaryOnSubdomainGenerator
    input = center
    boundaries = 'left right'
  []
[]

[GlobalParams]
  block = '1 2 3'
[]

[Variables]
  [tracer]
    block = '1 3'
  []
  [dummy]
  []
[]

[ICs]
  [tracer_top]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1 | x>0.3, 0, 1)'
    block = '1'
  []
  [tracer_bot]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.7 | x > 0.9, 0, 1)'
    block = '3'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
    block = '1 3'
  []
  [flux_top]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo_top
    block = '1'
  []
  [flux_bot]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo_bot
    block = '3'
  []
  [.dummy]
    type = TimeDerivative
    variable = dummy
  []
[]

[UserObjects]
  [fluo_top]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0 0'
    block = '1'
  []
  [fluo_bot]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '-0.1 0 0'
    block = '3'
  []
[]

[BCs]
  [no_tracer_on_left_top]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = 'left_to_1'
  []
  [remove_tracer_top]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = 'right_to_1'
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
  [no_tracer_on_left_bot]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = 'left_to_3'
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
  [remove_tracer_bot]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = 'right_to_3'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer_bot]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
  [tracer_top]
    type = LineValueSampler
    start_point = '0 1 0'
    end_point = '1 1 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(test/tests/vectorpostprocessors/element_value_sampler/fv_element_value_sampler.i)

# Tests the ElementValueSampler vector post-processor. In this test, 2 FV
# variables are given distributions by a function and are output to a CSV file.

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Functions]
  [./u_fn]
    type = ParsedFunction
    value = '2 * x + 3 * y'
  [../]
  [./v_fn]
    type = ParsedFunction
    value = 'x + y'
  [../]
[]

[AuxVariables]
  [./u]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  [../]
  [./v]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = u_fn
  [../]
  [./v_ic]
    type = FunctionIC
    variable = v
    function = v_fn
  [../]
[]

[VectorPostprocessors]
  [./element_value_sampler]
    type = ElementValueSampler
    variable = 'u v'
    sort_by = id
    execute_on = 'initial'
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  file_base = 'element_value_sampler'
  csv = true
  execute_on = 'initial'
[]

(test/tests/materials/derivative_material_interface/parsed_material.i)

#
# Test the parsed function free enery Allen-Cahn Bulk kernel
#

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[AuxVariables]
  [./eta]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
[]

[Materials]
  [./consts]
    type = ParsedMaterial
    args  = 'eta'
    function ='(eta-0.5)^2'
    outputs = exodus
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(modules/phase_field/test/tests/free_energy_material/VanDerWaalsFreeEnergy.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  elem_type = QUAD4
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = x*0.4+0.001
    [../]
  [../]
  [./T]
    [./InitialCondition]
      type = FunctionIC
      function = y*1999+1
    [../]
  [../]
[]

[Materials]
  [./free_energy]
    type =  VanDerWaalsFreeEnergy
    f_name = Fgas
    m = 134 # Xenon
    a = 7.3138
    b = 84.77
    omega = 41
    c = c
    T = T
    outputs = exodus
  [../]
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/examples/multiapp_fracture_flow/diffusion_multiapp/fracture_app_heat.i)

# Heat energy from this fracture app is transferred to the matrix app
[Mesh]
  [generate]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 100
    xmin = 0
    xmax = 50.0
  []
[]

[Variables]
  [frac_T]
  []
[]

[ICs]
  [frac_T]
    type = FunctionIC
    variable = frac_T
    function = 'if(x<1E-6, 2, 0)'  # delta function
  []
[]

[AuxVariables]
  [transferred_matrix_T]
  []
  [heat_to_matrix]
  []
[]

[Kernels]
  [dot]
    type = TimeDerivative
    variable = frac_T
  []
  [fracture_diffusion]
    type = Diffusion
    variable = frac_T
  []
  [toMatrix]
    type = PorousFlowHeatMassTransfer
    variable = frac_T
    v = transferred_matrix_T
    transfer_coefficient = 0.004
  []
[]

[AuxKernels]
  [heat_to_matrix]
    type = ParsedAux
    variable = heat_to_matrix
    args = 'frac_T transferred_matrix_T'
    function = '0.004 * (frac_T - transferred_matrix_T)'
  []
[]

[Preconditioning]
  [entire_jacobian]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 100
  end_time = 100
[]

[VectorPostprocessors]
  [final_results]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '50 0 0'
    num_points = 11
    sort_by = x
    variable = frac_T
    outputs = final_csv
  []
[]

[Outputs]
  print_linear_residuals = false
  [final_csv]
    type = CSV
    sync_times = 100
    sync_only = true
  []
[]

[MultiApps]
  [matrix_app]
    type = TransientMultiApp
    input_files = matrix_app_heat.i
    execute_on = TIMESTEP_END
  []
[]

[Transfers]
  [heat_to_matrix]
    type = MultiAppCopyTransfer
    to_multi_app = matrix_app
    source_variable = heat_to_matrix
    variable = heat_from_frac
  []
  [T_from_matrix]
    type = MultiAppCopyTransfer
    from_multi_app = matrix_app
    source_variable = matrix_T
    variable = transferred_matrix_T
  []
[]

(test/tests/misc/check_error/function_file_test8.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    xy_data = '1 2 3'
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/xfem/test/tests/moving_interface/phase_transition_2d.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 11
    ny = 1
    xmin = 0.0
    xmax = 20.0
    ymin = 0.0
    ymax = 5.0
    elem_type = QUAD4
  []
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [velocity]
    type = XFEMPhaseTransitionMovingInterfaceVelocity
    diffusivity_at_positive_level_set = 5
    diffusivity_at_negative_level_set = 1
    equilibrium_concentration_jump = 1
    value_at_interface_uo = value_uo
  []
  [value_uo]
    type = NodeValueAtXFEMInterface
    variable = 'u'
    interface_mesh_cut_userobject = 'cut_mesh'
    execute_on = TIMESTEP_END
    level_set_var = ls
  []
  [cut_mesh]
    type = InterfaceMeshCut2DUserObject
    mesh_file = flat_interface_1d.e
    interface_velocity_uo = velocity
    heal_always = true
  []
[]

[Variables]
  [u]
  []
[]

[ICs]
  [ic_u]
    type = FunctionIC
    variable = u
    function = 'if(x<5.01, 2, 1)'
  []
[]

[AuxVariables]
  [ls]
    order = FIRST
    family = LAGRANGE
  []
[]

[Constraints]
  [u_constraint]
    type = XFEMEqualValueAtInterface
    geometric_cut_userobject = 'cut_mesh'
    use_displaced_mesh = false
    variable = u
    value = 2
    alpha = 1e6
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = diffusion_coefficient
  []
  [time]
    type = TimeDerivative
    variable = u
  []
[]

[AuxKernels]
  [ls]
    type = MeshCutLevelSetAux
    mesh_cut_user_object = cut_mesh
    variable = ls
    execute_on = 'TIMESTEP_BEGIN'
  []
[]

[Materials]
  [diffusivity_A]
    type = GenericConstantMaterial
    prop_names = A_diffusion_coefficient
    prop_values = 5
  []
  [diffusivity_B]
    type = GenericConstantMaterial
    prop_names = B_diffusion_coefficient
    prop_values = 1
  []
  [diff_combined]
    type = LevelSetBiMaterialReal
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = diffusion_coefficient
  []
[]

[BCs]
  # Define boundary conditions
  [left_u]
    type = DirichletBC
    variable = u
    value = 2
    boundary = left
  []

  [right_u]
    type = NeumannBC
    variable = u
    boundary = right
    value = 0
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = 'none'

  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-9
  nl_abs_tol = 1e-9

  start_time = 0.0
  dt = 1
  num_steps = 5
  max_xfem_update = 1
[]

[Outputs]
  execute_on = timestep_end
  exodus = true
  perf_graph = true
  csv = true
[]

(modules/porous_flow/examples/coal_mining/coarse_with_fluid.i)

# Strata deformation and fluid flow aaround a coal mine - 3D model
#
# A "half model" is used.  The mine is 400m deep and
# just the roof is studied (-400<=z<=0).  The mining panel
# sits between 0<=x<=150, and 0<=y<=1000, so this simulates
# a coal panel that is 300m wide and 1000m long.  The outer boundaries
# are 1km from the excavation boundaries.
#
# The excavation takes 0.5 years.
#
# The boundary conditions for this simulation are:
#  - disp_x = 0 at x=0 and x=1150
#  - disp_y = 0 at y=-1000 and y=1000
#  - disp_z = 0 at z=-400, but there is a time-dependent
#               Young modulus that simulates excavation
#  - wc_x = 0 at y=-1000 and y=1000
#  - wc_y = 0 at x=0 and x=1150
#  - no flow at x=0, z=-400 and z=0
#  - fixed porepressure at y=-1000, y=1000 and x=1150
# That is, rollers on the sides, free at top,
# and prescribed at bottom in the unexcavated portion.
#
# A single-phase unsaturated fluid is used.
#
# The small strain formulation is used.
#
# All stresses are measured in MPa, and time units are measured in years.
#
# The initial porepressure is hydrostatic with P=0 at z=0, so
# Porepressure ~ - 0.01*z MPa, where the fluid has density 1E3 kg/m^3 and
# gravity = = 10 m.s^-2 = 1E-5 MPa m^2/kg.
# To be more accurate, i use
# Porepressure = -bulk * log(1 + g*rho0*z/bulk)
# where bulk=2E3 MPa and rho0=1Ee kg/m^3.
# The initial stress is consistent with the weight force from undrained
# density 2500 kg/m^3, and fluid porepressure, and a Biot coefficient of 0.7, ie,
# stress_zz^effective = 0.025*z + 0.7 * initial_porepressure
# The maximum and minimum principal horizontal effective stresses are
# assumed to be equal to 0.8*stress_zz.
#
# Material properties:
# Young's modulus = 8 GPa
# Poisson's ratio = 0.25
# Cosserat layer thickness = 1 m
# Cosserat-joint normal stiffness = large
# Cosserat-joint shear stiffness = 1 GPa
# MC cohesion = 2 MPa
# MC friction angle = 35 deg
# MC dilation angle = 8 deg
# MC tensile strength = 1 MPa
# MC compressive strength = 100 MPa
# WeakPlane cohesion = 0.1 MPa
# WeakPlane friction angle = 30 deg
# WeakPlane dilation angle = 10 deg
# WeakPlane tensile strength = 0.1 MPa
# WeakPlane compressive strength = 100 MPa softening to 1 MPa at strain = 1
# Fluid density at zero porepressure = 1E3 kg/m^3
# Fluid bulk modulus = 2E3 MPa
# Fluid viscosity = 1.1E-3 Pa.s = 1.1E-9 MPa.s = 3.5E-17 MPa.year
#
[GlobalParams]
  perform_finite_strain_rotations = false
  displacements = 'disp_x disp_y disp_z'
  Cosserat_rotations = 'wc_x wc_y wc_z'
  PorousFlowDictator = dictator
  biot_coefficient = 0.7
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = mesh/coarse.e
  []
  [xmin]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    new_boundary = xmin
    normal = '-1 0 0'
    input = file
  []
  [xmax]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    new_boundary = xmax
    normal = '1 0 0'
    input = xmin
  []
  [ymin]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    new_boundary = ymin
    normal = '0 -1 0'
    input = xmax
  []
  [ymax]
    type = SideSetsAroundSubdomainGenerator
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    new_boundary = ymax
    normal = '0 1 0'
    input = ymin
  []
  [zmax]
    type = SideSetsAroundSubdomainGenerator
    block = 16
    new_boundary = zmax
    normal = '0 0 1'
    input = ymax
  []
  [zmin]
    type = SideSetsAroundSubdomainGenerator
    block = 2
    new_boundary = zmin
    normal = '0 0 -1'
    input = zmax
  []
  [excav]
    type = SubdomainBoundingBoxGenerator
    input = zmin
    block_id = 1
    bottom_left = '0 0 -400'
    top_right = '150 1000 -397'
  []
  [roof]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 3
    paired_block = 1
    input = excav
    new_boundary = roof
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [wc_x]
  []
  [wc_y]
  []
  [porepressure]
    scaling = 1E-5
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = ini_pp
  []
[]

[Kernels]
  [cx_elastic]
    type = CosseratStressDivergenceTensors
    use_displaced_mesh = false
    variable = disp_x
    component = 0
  []
  [cy_elastic]
    type = CosseratStressDivergenceTensors
    use_displaced_mesh = false
    variable = disp_y
    component = 1
  []
  [cz_elastic]
    type = CosseratStressDivergenceTensors
    use_displaced_mesh = false
    variable = disp_z
    component = 2
  []
  [x_couple]
    type = StressDivergenceTensors
    use_displaced_mesh = false
    variable = wc_x
    displacements = 'wc_x wc_y wc_z'
    component = 0
    base_name = couple
  []
  [y_couple]
    type = StressDivergenceTensors
    use_displaced_mesh = false
    variable = wc_y
    displacements = 'wc_x wc_y wc_z'
    component = 1
    base_name = couple
  []
  [x_moment]
    type = MomentBalancing
    use_displaced_mesh = false
    variable = wc_x
    component = 0
  []
  [y_moment]
    type = MomentBalancing
    use_displaced_mesh = false
    variable = wc_y
    component = 1
  []
  [gravity]
    type = Gravity
    use_displaced_mesh = false
    variable = disp_z
    value = -10E-6 # remember this is in MPa
  []
  [poro_x]
    type = PorousFlowEffectiveStressCoupling
    use_displaced_mesh = false
    variable = disp_x
    component = 0
  []
  [poro_y]
    type = PorousFlowEffectiveStressCoupling
    use_displaced_mesh = false
    variable = disp_y
    component = 1
  []
  [poro_z]
    type = PorousFlowEffectiveStressCoupling
    use_displaced_mesh = false
    component = 2
    variable = disp_z
  []
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = porepressure
  []
  [flux]
    type = PorousFlowAdvectiveFlux
    use_displaced_mesh = false
    variable = porepressure
    gravity = '0 0 -10E-6'
    fluid_component = 0
  []
  [poro_vol_exp]
    type = PorousFlowMassVolumetricExpansion
    block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    variable = porepressure
    fluid_component = 0
  []
[]


[AuxVariables]
  [saturation]
    order = CONSTANT
    family = MONOMIAL
  []
  [darcy_x]
    order = CONSTANT
    family = MONOMIAL
  []
  [darcy_y]
    order = CONSTANT
    family = MONOMIAL
  []
  [darcy_z]
    order = CONSTANT
    family = MONOMIAL
  []
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
  [wc_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [perm_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [perm_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [perm_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_shear]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_tensile]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_shear]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_tensile]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_shear_f]
    order = CONSTANT
    family = MONOMIAL
  []
  [wp_tensile_f]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_shear_f]
    order = CONSTANT
    family = MONOMIAL
  []
  [mc_tensile_f]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_water]
    type = PorousFlowPropertyAux
    variable = saturation
    property = saturation
    phase = 0
    execute_on = timestep_end
  []
  [darcy_x]
    type = PorousFlowDarcyVelocityComponent
    variable = darcy_x
    gravity = '0 0 -10E-6'
    component = x
  []
  [darcy_y]
    type = PorousFlowDarcyVelocityComponent
    variable = darcy_y
    gravity = '0 0 -10E-6'
    component = y
  []
  [darcy_z]
    type = PorousFlowDarcyVelocityComponent
    variable = darcy_z
    gravity = '0 0 -10E-6'
    component = z
  []
  [porosity]
    type = PorousFlowPropertyAux
    property = porosity
    variable = porosity
    execute_on = timestep_end
  []
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  []
  [stress_xz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xz
    index_i = 0
    index_j = 2
    execute_on = timestep_end
  []
  [stress_yx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yx
    index_i = 1
    index_j = 0
    execute_on = timestep_end
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yz
    index_i = 1
    index_j = 2
    execute_on = timestep_end
  []
  [stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
    execute_on = timestep_end
  []
  [stress_zy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zy
    index_i = 2
    index_j = 1
    execute_on = timestep_end
  []
  [stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_xz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xz
    index_i = 0
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_yx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yx
    index_i = 1
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_yz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yz
    index_i = 1
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_zx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zx
    index_i = 2
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_zy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zy
    index_i = 2
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [perm_xx]
    type = PorousFlowPropertyAux
    property = permeability
    variable = perm_xx
    row = 0
    column = 0
    execute_on = timestep_end
  []
  [perm_yy]
    type = PorousFlowPropertyAux
    property = permeability
    variable = perm_yy
    row = 1
    column = 1
    execute_on = timestep_end
  []
  [perm_zz]
    type = PorousFlowPropertyAux
    property = permeability
    variable = perm_zz
    row = 2
    column = 2
    execute_on = timestep_end
  []
  [mc_shear]
    type = MaterialStdVectorAux
    index = 0
    property = mc_plastic_internal_parameter
    variable = mc_shear
    execute_on = timestep_end
  []
  [mc_tensile]
    type = MaterialStdVectorAux
    index = 1
    property = mc_plastic_internal_parameter
    variable = mc_tensile
    execute_on = timestep_end
  []
  [wp_shear]
    type = MaterialStdVectorAux
    index = 0
    property = wp_plastic_internal_parameter
    variable = wp_shear
    execute_on = timestep_end
  []
  [wp_tensile]
    type = MaterialStdVectorAux
    index = 1
    property = wp_plastic_internal_parameter
    variable = wp_tensile
    execute_on = timestep_end
  []
  [mc_shear_f]
    type = MaterialStdVectorAux
    index = 6
    property = mc_plastic_yield_function
    variable = mc_shear_f
    execute_on = timestep_end
  []
  [mc_tensile_f]
    type = MaterialStdVectorAux
    index = 0
    property = mc_plastic_yield_function
    variable = mc_tensile_f
    execute_on = timestep_end
  []
  [wp_shear_f]
    type = MaterialStdVectorAux
    index = 0
    property = wp_plastic_yield_function
    variable = wp_shear_f
    execute_on = timestep_end
  []
  [wp_tensile_f]
    type = MaterialStdVectorAux
    index = 1
    property = wp_plastic_yield_function
    variable = wp_tensile_f
    execute_on = timestep_end
  []
[]



[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'xmin xmax'
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'ymin ymax'
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = zmin
    value = 0.0
  []
  [no_wc_x]
    type = DirichletBC
    variable = wc_x
    boundary = 'ymin ymax'
    value = 0.0
  []
  [no_wc_y]
    type = DirichletBC
    variable = wc_y
    boundary = 'xmin xmax'
    value = 0.0
  []
  [fix_porepressure]
    type = FunctionDirichletBC
    variable = porepressure
    boundary = 'ymin ymax xmax'
    function = ini_pp
  []
  [roof_porepressure]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    pt_vals = '-1E3 1E3'
    multipliers = '-1 1'
    fluid_phase = 0
    flux_function = roof_conductance
    boundary = roof
  []
  [roof_bcs]
    type = StickyBC
    variable = disp_z
    min_value = -3.0
    boundary = roof
  []
[]

[Functions]
  [ini_pp]
    type = ParsedFunction
    vars = 'bulk p0 g    rho0'
    vals = '2E3 0.0 1E-5 1E3'
    value = '-bulk*log(exp(-p0/bulk)+g*rho0*z/bulk)'
  []
  [ini_xx]
    type = ParsedFunction
    vars = 'bulk p0 g    rho0 biot'
    vals = '2E3 0.0 1E-5 1E3  0.7'
    value = '0.8*(2500*10E-6*z+biot*(-bulk*log(exp(-p0/bulk)+g*rho0*z/bulk)))'
  []
  [ini_zz]
    type = ParsedFunction
    vars = 'bulk p0 g    rho0 biot'
    vals = '2E3 0.0 1E-5 1E3  0.7'
    value = '2500*10E-6*z+biot*(-bulk*log(exp(-p0/bulk)+g*rho0*z/bulk))'
  []
  [excav_sideways]
    type = ParsedFunction
    vars = 'end_t ymin ymax  minval maxval slope'
    vals = '0.5   0    1000.0 1E-9 1 60'
    # excavation face at ymin+(ymax-ymin)*min(t/end_t,1)
    # slope is the distance over which the modulus reduces from maxval to minval
    value = 'if(y<ymin+(ymax-ymin)*min(t/end_t,1),minval,if(y<ymin+(ymax-ymin)*min(t/end_t,1)+slope,minval+(maxval-minval)*(y-(ymin+(ymax-ymin)*min(t/end_t,1)))/slope,maxval))'
  []
  [density_sideways]
    type = ParsedFunction
    vars = 'end_t ymin ymax  minval maxval'
    vals = '0.5   0    1000.0 0 2500'
    value = 'if(y<ymin+(ymax-ymin)*min(t/end_t,1),minval,maxval)'
  []
  [roof_conductance]
    type = ParsedFunction
    vars = 'end_t ymin ymax   maxval minval'
    vals = '0.5   0    1000.0 1E7      0'
    value = 'if(y<ymin+(ymax-ymin)*min(t/end_t,1),maxval,minval)'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure disp_x disp_y disp_z'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1 # MPa^-1
  []

  [mc_coh_strong_harden]
    type = TensorMechanicsHardeningExponential
    value_0 = 1.99 # MPa
    value_residual = 2.01 # MPa
    rate = 1.0
  []
  [mc_fric]
    type = TensorMechanicsHardeningConstant
    value = 0.61 # 35deg
  []
  [mc_dil]
    type = TensorMechanicsHardeningConstant
    value = 0.15 # 8deg
  []

  [mc_tensile_str_strong_harden]
    type = TensorMechanicsHardeningExponential
    value_0 = 1.0 # MPa
    value_residual = 1.0 # MPa
    rate = 1.0
  []
  [mc_compressive_str]
    type = TensorMechanicsHardeningCubic
    value_0 = 100 # Large!
    value_residual = 100
    internal_limit = 0.1
  []

  [wp_coh_harden]
    type = TensorMechanicsHardeningCubic
    value_0 = 0.05
    value_residual = 0.05
    internal_limit = 10
  []
  [wp_tan_fric]
    type = TensorMechanicsHardeningConstant
    value = 0.26 # 15deg
  []
  [wp_tan_dil]
    type = TensorMechanicsHardeningConstant
    value = 0.18 # 10deg
  []

  [wp_tensile_str_harden]
    type = TensorMechanicsHardeningCubic
    value_0 = 0.05
    value_residual = 0.05
    internal_limit = 10
  []
  [wp_compressive_str_soften]
    type = TensorMechanicsHardeningCubic
    value_0 = 100
    value_residual = 1
    internal_limit = 1.0
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E3
      density0 = 1000
      thermal_expansion = 0
      viscosity = 3.5E-17
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [eff_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [vol_strain]
    type = PorousFlowVolumetricStrain
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity_bulk]
    type = PorousFlowPorosity
    fluid = true
    mechanical = true
    block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    ensure_positive = true
    porosity_zero = 0.02
    solid_bulk = 5.3333E3
  []
  [porosity_excav]
    type = PorousFlowPorosityConst
    block = 1
    porosity = 1.0
  []
  [permeability_bulk]
    type = PorousFlowPermeabilityKozenyCarman
    block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    poroperm_function = kozeny_carman_phi0
    k0 = 1E-15
    phi0 = 0.02
    n = 2
    m = 2
  []
  [permeability_excav]
    type = PorousFlowPermeabilityConst
    block = 1
    permeability = '0 0 0   0 0 0   0 0 0'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 4
    s_res = 0.4
    sum_s_res = 0.4
    phase = 0
  []

  [elasticity_tensor_0]
    type = ComputeLayeredCosseratElasticityTensor
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    young = 8E3 # MPa
    poisson = 0.25
    layer_thickness = 1.0
    joint_normal_stiffness = 1E9 # huge
    joint_shear_stiffness = 1E3 # MPa
  []
  [elasticity_tensor_1]
    type = ComputeLayeredCosseratElasticityTensor
    block = 1
    young = 8E3 # MPa
    poisson = 0.25
    layer_thickness = 1.0
    joint_normal_stiffness = 1E9 # huge
    joint_shear_stiffness = 1E3 # MPa
    elasticity_tensor_prefactor = excav_sideways
  []
  [strain]
    type = ComputeCosseratIncrementalSmallStrain
    eigenstrain_names = ini_stress
  []
  [ini_stress]
    type = ComputeEigenstrainFromInitialStress
    eigenstrain_name = ini_stress
    initial_stress = 'ini_xx 0 0  0 ini_xx 0  0 0 ini_zz'
  []

  [stress_0]
    type = ComputeMultipleInelasticCosseratStress
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    inelastic_models = 'mc wp'
    cycle_models = true
    relative_tolerance = 2.0
    absolute_tolerance = 1E6
    max_iterations = 1
    tangent_operator = nonlinear
    perform_finite_strain_rotations = false
  []
  [stress_1]
    type = ComputeMultipleInelasticCosseratStress
    block = 1
    inelastic_models = ''
    relative_tolerance = 2.0
    absolute_tolerance = 1E6
    max_iterations = 1
    tangent_operator = nonlinear
    perform_finite_strain_rotations = false
  []
  [mc]
    type = CappedMohrCoulombCosseratStressUpdate
    warn_about_precision_loss = false
    host_youngs_modulus = 8E3
    host_poissons_ratio = 0.25
    base_name = mc
    tensile_strength = mc_tensile_str_strong_harden
    compressive_strength = mc_compressive_str
    cohesion = mc_coh_strong_harden
    friction_angle = mc_fric
    dilation_angle = mc_dil
    max_NR_iterations = 100000
    smoothing_tol = 0.1 # MPa  # Must be linked to cohesion
    yield_function_tol = 1E-9 # MPa.  this is essentially the lowest possible without lots of precision loss
    perfect_guess = true
    min_step_size = 1.0
  []
  [wp]
    type = CappedWeakPlaneCosseratStressUpdate
    warn_about_precision_loss = false
    base_name = wp
    cohesion = wp_coh_harden
    tan_friction_angle = wp_tan_fric
    tan_dilation_angle = wp_tan_dil
    tensile_strength = wp_tensile_str_harden
    compressive_strength = wp_compressive_str_soften
    max_NR_iterations = 10000
    tip_smoother = 0.05
    smoothing_tol = 0.05 # MPa  # Note, this must be tied to cohesion, otherwise get no possible return at cone apex
    yield_function_tol = 1E-11 # MPa.  this is essentially the lowest possible without lots of precision loss
    perfect_guess = true
    min_step_size = 1.0E-3
  []


  [undrained_density_0]
    type = GenericConstantMaterial
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    prop_names = density
    prop_values = 2500
  []
  [undrained_density_1]
    type = GenericFunctionMaterial
    block = 1
    prop_names = density
    prop_values = density_sideways
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[Postprocessors]
  [min_roof_disp]
    type = NodalExtremeValue
    boundary = roof
    value_type = min
    variable = disp_z
  []
  [min_roof_pp]
    type = NodalExtremeValue
    boundary = roof
    value_type = min
    variable = porepressure
  []
  [min_surface_disp]
    type = NodalExtremeValue
    boundary = zmax
    value_type = min
    variable = disp_z
  []
  [min_surface_pp]
    type = NodalExtremeValue
    boundary = zmax
    value_type = min
    variable = porepressure
  []
  [max_perm_zz]
    type = ElementExtremeValue
     block = '2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'
    variable = perm_zz
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  petsc_options = '-snes_converged_reason'

  # best overall
  # petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  # petsc_options_value = ' lu       mumps'

  # best if you do not have mumps:
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = ' lu       superlu_dist'

  # best if you do not have mumps or superlu_dist:
  #petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -ksp_type -ksp_gmres_restart'
  #petsc_options_value = ' asm      2              lu            gmres     200'

  # very basic:
  #petsc_options_iname = '-pc_type -ksp_type -ksp_gmres_restart'
  #petsc_options_value = ' bjacobi  gmres     200'

  line_search = bt

  nl_abs_tol = 1e-3
  nl_rel_tol = 1e-5

  l_max_its = 200
  nl_max_its = 30

  start_time = 0.0
  dt = 0.014706
  end_time = 0.014706 #0.5
[]

[Outputs]
  interval = 1
  print_linear_residuals = true
  exodus = true
  csv = true
  console = true
[]

(python/chigger/tests/input/block_vars.i)

[Mesh]
  [generator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    input = generator
    bottom_left = '0.5 0 0'
    top_right = '1 1 0'
    block_id = 1
  []
[]

[Variables]
  [right_elemental]
    block = 1
    family = MONOMIAL
    order = CONSTANT
  []
  [right_nodal]
    block = 1
  []
[]

[ICs]
  [right_elemental]
    type = FunctionIC
    variable = right_elemental
    function = 2*y
  []
  [right_nodal]
    type = FunctionIC
    variable = right_nodal
    function = 3*y
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(test/tests/materials/derivative_material_interface/ad_derivative_parsed_material.i)

#
# Test the AD version of derivative parsed material
#

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./eta]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = ADMatDiffusion
    variable = eta
    diffusivity = F
  []
  [./dt]
    type = TimeDerivative
    variable = eta
  []
[]

[Materials]
  [./Fbar]
    type = ADDerivativeParsedMaterial
    args  = 'eta'
    f_name = Fbar
    function ='1/3*(eta-0.5)^3'
  []
  [./F]
    type = ADParsedMaterial
    args  = 'eta'
    material_property_names = 'F:=D[Fbar,eta]'
    function ='F'
    outputs = exodus
  []
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(test/tests/multiapps/grid-sequencing/vi-coarse.i)

l=10
nx=40
num_steps=2

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [bounds][]
[]

[Bounds]
  [./u_upper_bound]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = upper
    bound_value = ${l}
  [../]
  [./u_lower_bound]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = lower
    bound_value = 0
  [../]
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options = '-snes_vi_monitor'
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type -snes_type'
  petsc_options_value = '0                           30          asm      16                    basic                 vinewtonrsls'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  active = 'upper_violations lower_violations'
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

[MultiApps]
  [./coarser]
    type = TransientMultiApp
    app_type = MooseTestApp
    execute_on = timestep_begin
    positions = '0 0 0'
    input_files = vi-coarser.i
  [../]
[]

[Transfers]
  [./mesh_function_begin]
    type = MultiAppMeshFunctionTransfer
    from_multi_app = coarser
    source_variable = u
    variable = u
    execute_on = timestep_begin
  [../]
[]

(modules/porous_flow/test/tests/heterogeneous_materials/constant_poroperm2.i)

# Assign porosity and permeability variables from constant AuxVariables to create
# a heterogeneous model

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 3
  ny = 3
  nz = 3
  xmin = 1
  xmax = 4
  ymin = 1
  ymax = 4
  zmin = 1
  zmax = 4
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 -10'
[]

[Variables]
  [ppwater]
    initial_condition = 1e6
  []
[]

[AuxVariables]
  [poro]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxx]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxy]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxz]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyx]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyy]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyz]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzx]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzy]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzz]
    family = MONOMIAL
    order = CONSTANT
  []
  [poromat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxxmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxymat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxzmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyxmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyymat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyzmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzxmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzymat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzzmat]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [poromat]
    type = PorousFlowPropertyAux
    property = porosity
    variable = poromat
  []
  [permxxmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permxxmat
    column = 0
    row = 0
  []
  [permxymat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permxymat
    column = 1
    row = 0
  []
  [permxzmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permxzmat
    column = 2
    row = 0
  []
  [permyxmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permyxmat
    column = 0
    row = 1
  []
  [permyymat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permyymat
    column = 1
    row = 1
  []
  [permyzmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permyzmat
    column = 2
    row = 1
  []
  [permzxmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permzxmat
    column = 0
    row = 2
  []
  [permzymat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permzymat
    column = 1
    row = 2
  []
  [permzzmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permzzmat
    column = 2
    row = 2
  []
[]

[ICs]
  [poro]
    type = RandomIC
    seed = 0
    variable = poro
    max = 0.5
    min = 0.1
  []
  [permxx]
    type = FunctionIC
    function = permxx
    variable = permxx
  []
  [permxy]
    type = FunctionIC
    function = permxy
    variable = permxy
  []
  [permxz]
    type = FunctionIC
    function = permxz
    variable = permxz
  []
  [permyx]
    type = FunctionIC
    function = permyx
    variable = permyx
  []
  [permyy]
    type = FunctionIC
    function = permyy
    variable = permyy
  []
  [permyz]
    type = FunctionIC
    function = permyz
    variable = permyz
  []
  [permzx]
    type = FunctionIC
    function = permzx
    variable = permzx
  []
  [permzy]
    type = FunctionIC
    function = permzy
    variable = permzy
  []
  [permzz]
    type = FunctionIC
    function = permzz
    variable = permzz
  []
[]

[Functions]
  [permxx]
    type = ParsedFunction
    value = '(x*x)*1e-11'
  []
  [permxy]
    type = ParsedFunction
    value = '(x*y)*1e-11'
  []
  [permxz]
    type = ParsedFunction
    value = '(x*z)*1e-11'
  []
  [permyx]
    type = ParsedFunction
    value = '(y*x)*1e-11'
  []
  [permyy]
    type = ParsedFunction
    value = '(y*y)*1e-11'
  []
  [permyz]
    type = ParsedFunction
    value = '(y*z)*1e-11'
  []
  [permzx]
    type = ParsedFunction
    value = '(z*x)*1e-11'
  []
  [permzy]
    type = ParsedFunction
    value = '(z*y)*1e-11'
  []
  [permzz]
    type = ParsedFunction
    value = '(z*z)*1e-11'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    variable = ppwater
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      viscosity = 1e-3
      thermal_expansion = 0
      cv = 2
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = ppwater
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = poro
  []
  [permeability]
    type = PorousFlowPermeabilityConstFromVar
    perm_xx = permxx
    perm_xy = permxy
    perm_xz = permxz
    perm_yx = permyx
    perm_yy = permyy
    perm_yz = permyz
    perm_zx = permzx
    perm_zy = permzy
    perm_zz = permzz
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 100
  dt = 100
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  perf_graph = true
[]

(test/tests/userobjects/shape_element_user_object/simple_shape_element_uo_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 2
  ny = 2
  nz = 2
  parallel_type = replicated
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = (x-0.5)^2
    [../]
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./time_u]
    type = TimeDerivative
    variable = u
  [../]
  [./shape_u]
    type = SimpleTestShapeElementKernel
    user_object = example_uo
    variable = u
  [../]
[]

[UserObjects]
  [./example_uo]
    type = SimpleTestShapeElementUserObject
    u = u
    # as this userobject computes quantities for both the residual AND the jacobian
    # it needs to have these execute_on flags set.
    execute_on = 'linear nonlinear'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options = '-snes_test_display'
  petsc_options_iname = '-snes_type'
  petsc_options_value = 'test'
  dt = 0.1
  num_steps = 2
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_pflow/pffltvd_1D_adaptivity.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, mploying PorousFlow Kernels and UserObjects, with superbee flux-limiter
# 1D version with adaptivity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[Adaptivity]
  initial_steps = 1
  initial_marker = tracer_marker
  marker = tracer_marker
  max_h_level = 1
  [Markers]
    [tracer_marker]
      type = ValueRangeMarker
      variable = tracer
      lower_bound = 0.02
      upper_bound = 0.98
    []
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/phase_field/test/tests/grain_boundary_area/diagonal.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 100
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  op_num = 2
  var_name_base = gr
[]

[Variables]
  [./gr0]
    [./InitialCondition]
      type = FunctionIC
      function = 'd:=(x-y)*80;if(d<pi&d>-pi,sin(d/2)/2+0.5,if(d<0,0,1))'
    [../]
  [../]
  [./gr1]
    [./InitialCondition]
      type = FunctionIC
      function = 'd:=(x-y)*80;1-if(d<pi&d>-pi,sin(d/2)/2+0.5,if(d<0,0,1))'
    [../]
  [../]
[]

[Postprocessors]
  [./area]
    type = GrainBoundaryArea
    grains_per_side = 2
  [../]
[]

[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/newton_cooling/nc04.i)

# Newton cooling from a bar.  Heat conduction
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 1
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp'
    number_fluid_phases = 0
    number_fluid_components = 0
  []
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [temp]
    type = FunctionIC
    variable = temp
    function = '2-x/100'
  []
[]

[Kernels]
  [conduction]
    type = PorousFlowHeatConduction
    variable = temp
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [thermal_conductivity_irrelevant]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '1E2 0 0 0 1E2 0 0 0 1E2'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 2
  []
  [newton]
    type = PorousFlowPiecewiseLinearSink
    variable = temp
    boundary = right
    pt_vals = '0 1 2'
    multipliers = '-1 0 1'
    flux_function = 1
  []
[]

[VectorPostprocessors]
  [temp]
    type = LineValueSampler
    variable = temp
    start_point = '0 0.5 0'
    end_point = '100 0.5 0'
    sort_by = x
    num_points = 11
    execute_on = timestep_end
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol '
    petsc_options_value = 'gmres asm lu 100 NONZERO 2 1E-14 1E-12'
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  file_base = nc04
  execute_on = timestep_end
  exodus = false
  [along_line]
    type = CSV
    execute_vector_postprocessors_on = timestep_end
  []
[]

(test/tests/userobjects/toggle_mesh_adaptivity/toggle_mesh_adaptivity_gaussian_ic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./gaussian_ic]
    type = FunctionIC
    variable = u
    function = gaussian_2d
  [../]
[]

[Functions]
  [./gaussian_2d]
    type = ParsedFunction
    value = exp(-((x-x0)*(x-x0)+(y-y0)*(y-y0))/2.0/sigma/sigma)
    vars = 'sigma x0 y0'
    vals = '0.05 0.35 0.25'
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = u
    coef = 0.02
  [../]
  [./time]
    type = TimeDerivative
    variable = u
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = u
      auto_direction = 'x y'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Adaptivity]
  initial_steps = 1
  initial_marker = marker
  cycles_per_step = 1
  marker = marker
  max_h_level = 2
  [./Markers]
    [./marker]
      type = CircleMarker
      point = '0.35 0.25 0'
      radius = 0.2
      inside = refine
      outside = coarsen
    [../]
  [../]
[]

[UserObjects]
  [./mesh_adaptivity_off]
    type = ToggleMeshAdaptivity
    mesh_adaptivity = 'off'
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    print_mesh_changed_info = true
  [../]
[]

(test/tests/functions/image_function/shift_and_scale.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    shift = -62735.0
    scale = 0.0001
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/function_file_test14.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_rows_more_data.csv # will generate an error because of more data lines than 2
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/time_steppers/postprocessor_dt/postprocessor_dt.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = exact_fn
    execute_on = 'initial timestep_end'
  [../]

  # Just use some postprocessor that gives values good enough for time stepping ;-)
  [./dt]
    type = ElementAverageValue
    variable = u
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'crank-nicolson'

  start_time = 1.0
  num_steps = 2
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = dt
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/sinks/s02.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1 # same deal with PETSc constant state
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 2
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-lfout-rfout-mf)/2/(mi+mf))
    vars = 'mi mf lfout rfout'
    vals = 'mass_init mass_fin left_flux_out right_flux_out'
  [../]
[]

[Postprocessors]
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]
  [./mass_fin]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]
  [./left_flux_out]
    type = RichardsHalfGaussianSinkFlux
    boundary = left
    variable = pressure
    centre = 1
    max = 2
    sd = 1
  [../]
  [./right_flux_out]
    type = RichardsHalfGaussianSinkFlux
    boundary = right
    variable = pressure
    centre = 1
    max = 2
    sd = 1
  [../]
  [./p0]
    type = PointValue
    point = '0 0 0'
    variable = pressure
  [../]
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]

[BCs]
  [./left_flux]
    type = RichardsHalfGaussianSink
    boundary = left
    variable = pressure
    centre = 1
    max = 2
    sd = 1
  [../]
  [./right_flux]
    type = RichardsHalfGaussianSink
    boundary = right
    variable = pressure
    centre = 1
    max = 2
    sd = 1
  [../]
[]

[Kernels]
  active = 'richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 4E-3
  end_time = 0.4
[]

[Outputs]
  file_base = s02
  csv = true
  execute_on = timestep_end
[]

(modules/richards/test/tests/buckley_leverett/bl01_lumped_fu.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  SUPG_UO = SUPGstandard
  sat_UO = Saturation
  seff_UO = SeffVG
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2.0E6
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-4
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]


[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]

[AuxKernels]
  active = 'calculate_seff'
  [./calculate_seff]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffVG
    pressure_vars = pressure
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[BCs]
  active = 'left'
  [./left]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 980000
  [../]
[]

[Kernels]
  active = 'richardsf richardst'

  [./richardst]
    type = RichardsLumpedMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFullyUpwindFlux
    variable = pressure
  [../]
[]


[Functions]
 active = 'initial_pressure'
  [./initial_pressure]
    type = ParsedFunction
    value = max((1000000-x/5*1000000)-20000,-20000)
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'andy'

  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 20'
  [../]

[]

[Executioner]
  type = Transient
  end_time = 50
  dt = 2
  snesmf_reuse_base = false
[]

[Outputs]
  file_base = bl01_lumped_fu
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
[]

(modules/porous_flow/test/tests/sinks/s03.i)

# apply a sink flux with use_relperm=true and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1.1
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = -y
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '0.2 0 0 0 0.1 0 0 0 0.1'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[AuxVariables]
  [flux_out]
  []
  [xval]
  []
  [yval]
  []
[]

[ICs]
  [xval]
    type = FunctionIC
    variable = xval
    function = x
  []
  [yval]
    type = FunctionIC
    variable = yval
    function = y
  []
[]

[Functions]
  [mass00]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)*pow(1+pow(-al*pp,1.0/(1-m)),-m)'
    vars = 'vol por dens0 pp bulk al m'
    vals = '0.25 0.1 1.1 p00 1.3 1.1 0.5'
  []
  [sat00]
    type = ParsedFunction
    value = 'pow(1+pow(-al*pp,1.0/(1-m)),-m)'
    vars = 'pp al m'
    vals = 'p00 1.1 0.5'
  []
  [mass01]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)*pow(1+pow(-al*pp,1.0/(1-m)),-m)'
    vars = 'vol por dens0 pp bulk al m'
    vals = '0.25 0.1 1.1 p01 1.3 1.1 0.5'
  []
  [expected_mass_change00]
    type = ParsedFunction
    value = 'fcn*pow(pow(1+pow(-al*pp,1.0/(1-m)),-m),2)*area*dt'
    vars = 'fcn perm dens0 pp bulk visc area dt   al  m'
    vals = '6   0.2  1.1  p00 1.3  1.1  0.5  1E-3 1.1 0.5'
  []
  [expected_mass_change01]
    type = ParsedFunction
    value = 'fcn*pow(pow(1+pow(-al*pp,1.0/(1-m)),-m),2)*area*dt'
    vars = 'fcn perm dens0 pp bulk visc area dt   al  m'
    vals = '6   0.2  1.1  p01 1.3  1.1  0.5  1E-3 1.1 0.5'
  []
  [mass00_expect]
    type = ParsedFunction
    value = 'mass_prev-mass_change'
    vars = 'mass_prev mass_change'
    vals = 'm00_prev  del_m00'
  []
  [mass01_expect]
    type = ParsedFunction
    value = 'mass_prev-mass_change'
    vars = 'mass_prev mass_change'
    vals = 'm01_prev  del_m01'
  []
  [sat01]
    type = ParsedFunction
    value = 'pow(1+pow(-al*pp,1.0/(1-m)),-m)'
    vars = 'pp al m'
    vals = 'p01 1.1 0.5'
  []
  [expected_mass_change_rate]
    type = ParsedFunction
    value = 'fcn*pow(pow(1+pow(-al*pp,1.0/(1-m)),-m),2)*area'
    vars = 'fcn perm dens0 pp bulk visc area dt   al  m'
    vals = '6   0.2  1.1  p00 1.3  1.1  0.5  1E-3 1.1 0.5'
  []
[]

[Postprocessors]
  [p00]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m00]
    type = FunctionValuePostprocessor
    function = mass00
    execute_on = 'initial timestep_end'
  []
  [m00_prev]
    type = FunctionValuePostprocessor
    function = mass00
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [del_m00]
    type = FunctionValuePostprocessor
    function = expected_mass_change00
    execute_on = 'timestep_end'
    outputs = 'console'
  []
  [m00_expect]
    type = FunctionValuePostprocessor
    function = mass00_expect
    execute_on = 'timestep_end'
  []
  [p10]
    type = PointValue
    point = '1 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p01]
    type = PointValue
    point = '0 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m01]
    type = FunctionValuePostprocessor
    function = mass01
    execute_on = 'initial timestep_end'
  []
  [m01_prev]
    type = FunctionValuePostprocessor
    function = mass01
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [del_m01]
    type = FunctionValuePostprocessor
    function = expected_mass_change01
    execute_on = 'timestep_end'
    outputs = 'console'
  []
  [m01_expect]
    type = FunctionValuePostprocessor
    function = mass01_expect
    execute_on = 'timestep_end'
  []
  [p11]
    type = PointValue
    point = '1 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [s00]
    type = FunctionValuePostprocessor
    function = sat00
    execute_on = 'initial timestep_end'
  []
  [mass00_rate]
    type = FunctionValuePostprocessor
    function = expected_mass_change_rate
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [flux]
    type = PorousFlowSink
    boundary = 'left'
    variable = pp
    use_mobility = false
    use_relperm = true
    fluid_phase = 0
    flux_function = 6
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-3
  end_time = 0.018
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s03
  [console]
    type = Console
    execute_on = 'nonlinear linear'
    interval = 5
  []
  [csv]
    type = CSV
    execute_on = 'timestep_end'
    interval = 2
  []
[]

(modules/porous_flow/test/tests/hysteresis/hys_pc_01.i)

# Capillary-pressure calculation.  Primary drying curve with low_extension_type = none
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 100
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = ''
  []
[]

[Variables]
  [sat]
  []
[]

[ICs]
  [sat]
    type = FunctionIC
    variable = sat
    function = 'x'
  []
[]

[BCs]
  [sat]
    type = FunctionDirichletBC
    variable = sat
    function = 'x'
    boundary = 'left right'
  []
[]


[Kernels]
  [dummy]
    type = Diffusion
    variable = sat
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
  []
  [pc_calculator]
    type = PorousFlowHystereticInfo
    alpha_d = 10.0
    alpha_w = 10.0
    n_d = 1.5
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 12.0
    low_extension_type = none
    sat_var = sat
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [pc]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [pc]
    type = PorousFlowPropertyAux
    variable = pc
    property = hysteretic_info
  []
[]

[VectorPostprocessors]
  [pc]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 10
    sort_by = x
    variable = 'sat pc'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(test/tests/misc/check_error/function_file_test7.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    x = '1'
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/userobjects/shape_element_user_object/jacobian.i)

[GlobalParams]
  use_displaced_mesh = true
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  parallel_type = replicated
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = (x-0.5)^2
    [../]
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = (x-0.5)^2
    [../]
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./shape_w]
    type = ExampleShapeElementKernel
    user_object = example_uo
    v = v
    variable = u
  [../]
  [./time_u]
    type = TimeDerivative
    variable = u
  [../]
  [./time_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[UserObjects]
  [./example_uo]
    type = ExampleShapeElementUserObject
    u = u
    v = v
    # as this userobject computes quantities for both the residual AND the jacobian
    # it needs to have these execute_on flags set.
    execute_on = 'linear nonlinear'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    #full = true
    off_diag_row =    'u'
    off_diag_column = 'v'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.1
  num_steps = 2
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/tensor_mechanics/test/tests/CylindricalRankTwoAux/test.i)

[Mesh]
  [file_mesh]
    type = FileMeshGenerator
    file = circle.e
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '1000.0 0.0'
    new_boundary = 10
    input = file_mesh
  []
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./T]
  [../]
  [./stress_rr]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_tt]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '1000-0.7*sqrt(x^2+y^2)'
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./stress_rr]
    type = CylindricalRankTwoAux
    variable = stress_rr
    rank_two_tensor = stress
    index_j = 0
    index_i = 0
    center_point = '0 0 0'
  [../]
  [./stress_tt]
    type = CylindricalRankTwoAux
    variable = stress_tt
    rank_two_tensor = stress
    index_j = 1
    index_i = 1
    center_point = '0 0 0'
  [../]
[]

[BCs]
  [./outer_x]
    type = DirichletBC
    variable = disp_x
    boundary = 2
    value = 0
  [../]
  [./outer_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2 10'
    value = 0
  [../]
[]

[Materials]
  [./iso_C]
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '2.15e5 0.74e5'
    block = 1
  [../]
  [./strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
    block = 1
    eigenstrain_names = eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
    block = 1
  [../]
  [./thermal_strain]
    type= ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    temperature = T
    stress_free_temperature = 273
    block = 1
    eigenstrain_name = eigenstrain
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 101'
  l_max_its = 30
  nl_max_its = 10
  nl_abs_tol = 1e-9
  nl_rel_tol = 1e-14
  l_tol = 1e-4
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(test/tests/misc/check_error/function_file_test13.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_columns_more_data.csv
    format = columns
    xy_in_file_only = false
    x_index_in_file = 3 #Will generate error because data does not contain 4 columns
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/porous_flow/examples/multiapp_fracture_flow/diffusion_multiapp/fracture_app.i)

# Temperature is transferred between the fracture and matrix apps
[Mesh]
  [generate]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 100
    xmin = 0
    xmax = 50.0
  []
[]

[Variables]
  [frac_T]
  []
[]

[ICs]
  [frac_T]
    type = FunctionIC
    variable = frac_T
    function = 'if(x<1E-6, 2, 0)'  # delta function
  []
[]

[AuxVariables]
  [transferred_matrix_T]
  []
[]

[Kernels]
  [dot]
    type = TimeDerivative
    variable = frac_T
  []
  [fracture_diffusion]
    type = Diffusion
    variable = frac_T
  []
  [toMatrix]
    type = PorousFlowHeatMassTransfer
    variable = frac_T
    v = transferred_matrix_T
    transfer_coefficient = 0.004
  []
[]

[Preconditioning]
  [entire_jacobian]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 100
  end_time = 100
[]

[VectorPostprocessors]
  [final_results]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '50 0 0'
    num_points = 11
    sort_by = x
    variable = frac_T
    outputs = final_csv
  []
[]

[Outputs]
  print_linear_residuals = false
  [final_csv]
    type = CSV
    sync_times = 100
    sync_only = true
  []
[]

[MultiApps]
  [matrix_app]
    type = TransientMultiApp
    input_files = matrix_app.i
    execute_on = TIMESTEP_END
  []
[]

[Transfers]
  [T_to_matrix]
    type = MultiAppCopyTransfer
    to_multi_app = matrix_app
    source_variable = frac_T
    variable = transferred_frac_T
  []
  [T_from_matrix]
    type = MultiAppCopyTransfer
    from_multi_app = matrix_app
    source_variable = matrix_T
    variable = transferred_matrix_T
  []
[]

(test/tests/transfers/multiapp_conservative_transfer/primary_negative_adjuster.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
[]

[Variables]
  [u]
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[AuxVariables]
  [var]
    family = MONOMIAL
    order = THIRD
  []
[]

[ICs]
  [var_ic]
    type = FunctionIC
    variable = var
    function = '-exp(x * y)'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    input_files = secondary_negative_adjuster.i
    execute_on = timestep_end
  []
[]

[Postprocessors]
  [from_postprocessor]
    type = ElementIntegralVariablePostprocessor
    variable = var
  []
[]

[Transfers]
  [to_sub]
    type = MultiAppMeshFunctionTransfer
    source_variable = var
    variable = var
    to_multi_app = sub
    from_postprocessors_to_be_preserved  = 'from_postprocessor'
    to_postprocessors_to_be_preserved  = 'to_postprocessor'
  []
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/shock_tube_2D_cavity/hllc_sod_shocktube_2D.i)

rho_left = 1
E_left = 2.501505578
u_left = 1e-15

rho_right = 0.125
E_right = 1.999770935
u_right = 1e-15

x_sep = 35

[GlobalParams]
  fp = fp
[]

[Mesh]
  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '40 20'
    ix = '200 100'
    dy = '1 20  2  20 1'
    iy = '4 100 10 100 4'
    subdomain_id = '0 0
                    0 1
                    1 1
                    0 1
                    0 0'
  [../]

  [./wall]
    type = SideSetsBetweenSubdomainsGenerator
    input = cartesian
    primary_block = 1
    paired_block = 0
    new_boundary = 'wall'
  [../]

  [./delete]
    type = BlockDeletionGenerator
    input = wall
    block = 0
  [../]
[]

[Modules]
  [./FluidProperties]
    [./fp]
      type = IdealGasFluidProperties
      allow_imperfect_jacobians = true
    [../]
  [../]
[]

[Variables]
  [./rho]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  [../]
  [./rho_u]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  [../]
  [./rho_v]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  [../]
  [./rho_E]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  [../]
[]

[AuxVariables]
  [./Ma]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./p]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./v_norm]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./temperature]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./Ma_aux]
    type = NSMachAux
    variable = Ma
    fluid_properties = fp
    use_material_properties = true
  [../]

  [./p_aux]
    type = ADMaterialRealAux
    variable = p
    property = pressure
  [../]

  [./v_norm_aux]
    type = ADMaterialRealAux
    variable = v_norm
    property = speed
  [../]

  [./temperature_aux]
    type = ADMaterialRealAux
    variable = temperature
    property = T_fluid
  [../]
[]

[FVKernels]
  [./mass_time]
    type = FVTimeKernel
    variable = rho
  [../]

  [./mass_advection]
    type = CNSFVMassHLLC
    variable = rho
  [../]

  [./momentum_x_time]
    type = FVTimeKernel
    variable = rho_u
  [../]

  [./momentum_x_advection]
    type = CNSFVMomentumHLLC
    variable = rho_u
    momentum_component = x
  [../]

  [./momentum_y_time]
    type = FVTimeKernel
    variable = rho_v
  [../]

  [./momentum_y_advection]
    type = CNSFVMomentumHLLC
    variable = rho_v
    momentum_component = y
  [../]

  [./fluid_energy_time]
    type = FVTimeKernel
    variable = rho_E
  [../]

  [./fluid_energy_advection]
    type = CNSFVFluidEnergyHLLC
    variable = rho_E
  [../]
[]

[FVBCs]
  [./mom_x_pressure]
    type = CNSFVMomImplicitPressureBC
    variable = rho_u
    momentum_component = x
    boundary = 'left right wall'
  [../]

  [./mom_y_pressure]
    type = CNSFVMomImplicitPressureBC
    variable = rho_v
    momentum_component = y
    boundary = 'wall'
  [../]
[]

[ICs]
  [./rho_ic]
    type = FunctionIC
    variable = rho
    function = 'if (x < ${x_sep}, ${rho_left}, ${rho_right})'
  [../]

  [./rho_u_ic]
    type = FunctionIC
    variable = rho_u
    function = 'if (x < ${x_sep}, ${fparse rho_left * u_left}, ${fparse rho_right * u_right})'
  [../]

  [./rho_E_ic]
    type = FunctionIC
    variable = rho_E
    function = 'if (x < ${x_sep}, ${fparse E_left * rho_left}, ${fparse E_right * rho_right})'
  [../]
[]

[Materials]
  [./var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = rho_u
    rhov = rho_v
    rho_et = rho_E
    fp = fp
  [../]
  [./sound_speed]
    type = SoundspeedMat
    fp = fp
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  [../]
[]

[Postprocessors]
  [./cfl_dt]
    type = ADCFLTimeStepSize
    c_names = 'sound_speed'
    vel_names = 'speed'
  [../]
[]

[Executioner]
  type = Transient
  end_time = 100
  [TimeIntegrator]
    type = ExplicitSSPRungeKutta
    order = 2
  []
  l_tol = 1e-8

  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl_dt
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/theis/th_lumped_01.i)

# fully-saturated
# production
# lumped
[Mesh]
  type = FileMesh
  file = th01_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '0.5 1 2 10'
    x = '0 1 10 100'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]

  [./total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsLumpedMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsPolyLineSink
    pressures = '-1E9 1E9'
    fluxes = '200 200'
    point_file = th01.points
    SumQuantityUO = total_outflow_mass
    variable = pressure
  [../]
[]


[Postprocessors]
  [./flow_report]
    type = RichardsPlotQuantity
    uo = total_outflow_mass
  [../]
  [./p50]
    type = PointValue
    variable = pressure
    point = '50 0 0'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E5
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-6 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 100
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = th_lumped_01
  csv = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_pflow/jacobian_05.i)

# Checking the Jacobian of Flux-Limited TVD Advection, 2 phases, 2 components, using flux_limiter_type != None
#
# Here we use snes_check_jacobian instead of snes_type=test.  The former just checks the Jacobian for the
# random initial conditions, while the latter checks for u=1 and u=-1
#
# The Jacobian is correct for u=1 and u=-1, but the finite-difference scheme used by snes_type=test gives the
# wrong answer.
# For u=constant, the Kuzmin-Turek scheme adds as much antidiffusion as possible, resulting in a central-difference
# version of advection (flux_limiter = 1).  This is correct, and the Jacobian is calculated correctly.
# However, when computing the Jacobian using finite differences, u is increased or decreased at a node.
# This results in that node being at a maximum or minimum, which means no antidiffusion should be added
# (flux_limiter = 0).  This corresponds to a full-upwind scheme.  So the finite-difference computes the
# Jacobian in the full-upwind scenario, which is incorrect (the original residual = 0, after finite-differencing
# the residual comes from the full-upwind scenario).
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 5
[]

[GlobalParams]
  gravity = '1.1 2 -0.5'
  PorousFlowDictator = dictator
[]

[Variables]
  [ppwater]
  []
  [ppgas]
  []
  [massfrac_ph0_sp0]
  []
  [massfrac_ph1_sp0]
  []
[]


[ICs]
  [ppwater]
    type = FunctionIC
    variable = ppwater
    function = 'if(x<1,0,if(x<4,sin(x-1),1))'
  []
  [ppgas]
    type = FunctionIC
    variable = ppgas
    function = 'x*(6-x)/6'
  []
  [massfrac_ph0_sp0]
    type = FunctionIC
    variable = massfrac_ph0_sp0
    function = 'x/6'
  []
  [massfrac_ph1_sp0]
    type = FunctionIC
    variable = massfrac_ph1_sp0
    function = '1-x/7'
  []
[]

[Kernels]
  [flux_ph0_sp0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = ppwater
    advective_flux_calculator = advective_flux_calculator_ph0_sp0
  []
  [flux_ph0_sp1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = ppgas
    advective_flux_calculator = advective_flux_calculator_ph0_sp1
  []
  [flux_ph1_sp0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = massfrac_ph0_sp0
    advective_flux_calculator = advective_flux_calculator_ph1_sp0
  []
  [flux_ph1_sp1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = massfrac_ph1_sp0
    advective_flux_calculator = advective_flux_calculator_ph1_sp1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      density0 = 1
      thermal_expansion = 0
      viscosity = 1
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 0.5
      density0 = 0.5
      thermal_expansion = 0
      viscosity = 1.4
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater ppgas massfrac_ph0_sp0 massfrac_ph1_sp0'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1
    m = 0.5
  []
  [advective_flux_calculator_ph0_sp0]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = minmod
    phase = 0
    fluid_component = 0
  []
  [advective_flux_calculator_ph0_sp1]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = vanleer
    phase = 0
    fluid_component = 1
  []
  [advective_flux_calculator_ph1_sp0]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = mc
    phase = 1
    fluid_component = 0
  []
  [advective_flux_calculator_ph1_sp1]
    type = PorousFlowAdvectiveFluxCalculatorUnsaturatedMultiComponent
    flux_limiter_type = superbee
    phase = 1
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = ppwater
    phase1_porepressure = ppgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.21 0 0  0 1.5 0  0 0 0.8'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options = '-snes_check_jacobian'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear # this is to force convergence even though the nonlinear residual is high: we just care about the Jacobian in this test
  end_time = 1
  num_steps = 1
  dt = 1
[]

(modules/porous_flow/test/tests/newton_cooling/nc08.i)

# Newton cooling from a bar.  1-phase ideal fluid and heat, steady
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 1
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pressure temp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.8
    alpha = 1e-5
  []
[]

[Variables]
  [pressure]
  []
  [temp]
  []
[]

[ICs]
  # have to start these reasonably close to their steady-state values
  [pressure]
    type = FunctionIC
    variable = pressure
    function = '200-0.5*x'
  []
  [temperature]
    type = FunctionIC
    variable = temp
    function = 180+0.1*x
  []
[]

[Kernels]
  [flux]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    gravity = '0 0 0'
    variable = pressure
  []
  [heat_advection]
    type = PorousFlowHeatAdvection
    gravity = '0 0 0'
    variable = temp
  []
[]

[Modules]
  [FluidProperties]
    [idealgas]
      type = IdealGasFluidProperties
      molar_mass = 1.4
      gamma = 1.2
      mu = 1.2
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [dens0]
    type = PorousFlowSingleComponentFluid
    fp = idealgas
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 1.1 0 0 0 1.1'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey # irrelevant in this fully-saturated situation
    n = 2
    phase = 0
  []
[]

[BCs]
  [leftp]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 200
  []
  [leftt]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 180
  []
  [newtonp]
    type = PorousFlowPiecewiseLinearSink
    variable = pressure
    boundary = right
    pt_vals = '-200 0 200'
    multipliers = '-200 0 200'
    use_mobility = true
    use_relperm = true
    fluid_phase = 0
    flux_function = 0.005 # 1/2/L
  []
  [newtont]
    type = PorousFlowPiecewiseLinearSink
    variable = temp
    boundary = right
    pt_vals = '-200 0 200'
    multipliers = '-200 0 200'
    use_mobility = true
    use_relperm = true
    use_enthalpy = true
    fluid_phase = 0
    flux_function = 0.005 # 1/2/L
  []
[]

[VectorPostprocessors]
  [porepressure]
    type = LineValueSampler
    variable = pressure
    start_point = '0 0.5 0'
    end_point = '100 0.5 0'
    sort_by = x
    num_points = 11
    execute_on = timestep_end
  []
  [temperature]
    type = LineValueSampler
    variable = temp
    start_point = '0 0.5 0'
    end_point = '100 0.5 0'
    sort_by = x
    num_points = 11
    execute_on = timestep_end
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Steady
  solve_type = Newton
  nl_rel_tol = 1E-10
  nl_abs_tol = 1E-15
[]

[Outputs]
  file_base = nc08
  execute_on = timestep_end
  exodus = true
  [along_line]
    type = CSV
    execute_vector_postprocessors_on = timestep_end
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-hllc.i)

[GlobalParams]
  fp = fp
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_mom_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_mom_x]
    type = FunctionIC
    variable = sup_mom_x
    function = 'exact_rho_ud'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVMassHLLC
    variable = pressure
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVMomentumHLLC
    variable = sup_mom_x
    momentum_component = x
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_mom_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_mom_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVFluidEnergyHLLC
    variable = T_fluid
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []
[]

[Materials]
  [var_mat]
    type = PorousMixedVarMaterial
    pressure = pressure
    superficial_rhou = sup_mom_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  value = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  value = '-3.83667087618017*sin(1.1*x)*cos(1.3*x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  value = '3.48788261470924*cos(1.1*x)*cos(1.3*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  value = '(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x))*cos(1.3*x) + 3.48788261470924*sin(x)*cos(1.1*x)^2*cos(1.3*x)/cos(x)^2 - 7.67334175236034*sin(1.1*x)*cos(1.1*x)*cos(1.3*x)/cos(x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)^2/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  value = '26.7439413073546*cos(1.5*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  value = '1.0*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(x)*cos(1.1*x)*cos(1.3*x)/cos(x)^2 - 1.1*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.1*x)*cos(1.3*x)/cos(x) - 1.3*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.3*x)*cos(1.1*x)/cos(x) + 1.0*(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x) - 40.1159119610319*sin(1.5*x))*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  value = '0.0106975765229418*cos(1.5*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)*cos(1.3*x)'
[]
[exact_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  value = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  value = 'cos(1.3*x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  value_x = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_mom_x]
    variable = sup_mom_x
    function = exact_rho_ud
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/time_integrators/actually_explicit_euler_verification/ee-2d-linear-adapt.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = (x+y)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*(x+y)
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    preset = false
    boundary = '0 1 2 3'
    function = exact_fn
  [../]
[]

[Adaptivity]
  steps = 1
  marker = box
  max_h_level = 2
  [./Markers]
    [./box]
      bottom_left = '-0.4 -0.4 0'
      inside = refine
      top_right = '0.4 0.4 0'
      outside = do_nothing
      type = BoxMarker
    [../]
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  start_time = 0.0
  num_steps = 4
  dt = 0.005
  l_tol = 1e-12

  [./TimeIntegrator]
    type = ActuallyExplicitEuler
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/combined/examples/periodic_strain/global_strain_pfm_3D.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 20
    ny = 20
    nz = 20
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
  []
  [./cnode]
    input = gen
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 100
  [../]
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'sin(2*x*pi)*sin(2*y*pi)*sin(2*z*pi)*0.05+0.6'
    [../]
  [../]
  [./w]
  [../]
[]

[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./s00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
  [./local_free_energy]
    type = TotalFreeEnergy
    execute_on = 'initial LINEAR'
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
  [../]
  [./s00]
    type = RankTwoAux
    variable = s00
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
  [./s10]
    type = RankTwoAux
    variable = s10
    rank_two_tensor = stress
    index_i = 1
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./e00]
    type = RankTwoAux
    variable = e00
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
  [../]
  [./e01]
    type = RankTwoAux
    variable = e01
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 1
  [../]
  [./e10]
    type = RankTwoAux
    variable = e10
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 0
  [../]
  [./e11]
    type = RankTwoAux
    variable = e11
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
  [../]
[]

[GlobalParams]
  derivative_order = 2
  enable_jit = true
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [./TensorMechanics]
  [../]

  # Cahn-Hilliard kernels
  [./c_dot]
    type = CoupledTimeDerivative
    variable = w
    v = c
    block = 0
  [../]
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = kappa_c
    w = w
    block = 0
  [../]
  [./w_res]
    type = SplitCHWRes
    variable = w
    mob_name = M
    block = 0
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y z'
      variable = 'c w u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M   kappa_c'
    prop_values = '0.2 0.01   '
  [../]

  [./shear1]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 0.5 0.5 0.5'
    tensor_name = shear1
  [../]
  [./shear2]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 -0.5 -0.5 -0.5'
    tensor_name = shear2
  [../]
  [./expand3]
    type = GenericConstantRankTwoTensor
    tensor_values = '1 1 1 0 0 0'
    tensor_name = expand3
  [../]

  [./weight1]
    type = DerivativeParsedMaterial
    function = '0.3*c^2'
    f_name = weight1
    args = c
  [../]
  [./weight2]
    type = DerivativeParsedMaterial
    function = '0.3*(1-c)^2'
    f_name = weight2
    args = c
  [../]
  [./weight3]
    type = DerivativeParsedMaterial
    function = '4*(0.5-c)^2'
    f_name = weight3
    args = c
  [../]

  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
    eigenstrain_names = eigenstrain
  [../]

  [./eigenstrain]
    type = CompositeEigenstrain
    tensors = 'shear1  shear2  expand3'
    weights = 'weight1 weight2 weight3'
    args = c
    eigenstrain_name = eigenstrain
  [../]

  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]

  [./stress]
    type = ComputeLinearElasticStress
  [../]

  # chemical free energies
  [./chemical_free_energy]
    type = DerivativeParsedMaterial
    f_name = Fc
    function = '4*c^2*(1-c)^2'
    args = 'c'
    outputs = exodus
    output_properties = Fc
  [../]

  # elastic free energies
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = Fe
    args = 'c'
    outputs = exodus
    output_properties = Fe
  [../]

  # free energy (chemical + elastic)
  [./free_energy]
    type = DerivativeSumMaterial
    block = 0
    f_name = F
    sum_materials = 'Fc Fe'
    args = 'c'
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = local_energy
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = c
  [../]
  [./min]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = min
    variable = c
  [../]
  [./max]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = max
    variable = c
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  end_time = 2.0

  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.01
    growth_factor = 1.5
    cutback_factor = 0.8
    optimal_iterations = 9
    iteration_window = 2
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  print_linear_residuals = false
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

(modules/ray_tracing/test/tests/raykernels/variable_integral_ray_kernel/variable_integral_ray_kernel.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmax = 5
    ymax = 5
  []
[]

[Variables/u]
  [InitialCondition]
    type = FunctionIC
    variable = u
    function = '(x < 2) * (x + 2 * y) + (x >= 2) * (2 * x + 2 * y - 2)'
  []
[]

[AuxVariables/aux]
  order = CONSTANT
  family = MONOMIAL
  [InitialCondition]
    type = FunctionIC
    variable = u_ag
    function = 'x + y + cos(x)'
  []
[]


[UserObjects]
  [study]
    type = RepeatableRayStudy
    names = 'diag
             top_across
             bottom_across
             partial'
    start_points = '0 0 0
                    0 5 0
                    0 0 0
                    0.5 0.5 0'
    end_points = '5 5 0
                  5 5 0
                  5 0 0
                  4.5 0.5 0'
  []
[]

[RayKernels]
  [variable_integral]
    type = VariableIntegralRayKernel
    study = study
    variable = u
  []
  [aux_variable_integral]
    type = VariableIntegralRayKernel
    study = study
    variable = aux
  []
[]

[Postprocessors]
  [diag_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = diag
  []
  [top_across_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = top_across
  []
  [bottom_across_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = bottom_across
  []
  [partial_value]
    type = RayIntegralValue
    ray_kernel = variable_integral
    ray = partial
  []

  [aux_diag_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = diag
  []
  [aux_top_across_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = top_across
  []
  [aux_bottom_across_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = bottom_across
  []
  [aux_partial_value]
    type = RayIntegralValue
    ray_kernel = aux_variable_integral
    ray = partial
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/richards/test/tests/mass/m_fu_01.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  xmin = -1
  xmax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  SUPG_UO = SUPGstandard
  sat_UO = Saturation
  seff_UO = SeffVG
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1 # same deal with PETScs constant state
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = x
  [../]
[]

[Postprocessors]
  [./total_mass]
    type = RichardsMass
    variable = pressure
  [../]
[]

[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFullyUpwindFlux
    variable = pressure
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-10
  end_time = 1E-10
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = m_fu_01
  csv = true
[]

(modules/chemical_reactions/test/tests/aqueous_equilibrium/1species.i)

# Simple equilibrium reaction example to illustrate the use of the AqueousEquilibriumReactions
# action.
# In this example, a single primary species a is transported by diffusion and convection
# from the left of the porous medium, reacting to form an equilibrium species pa2 according to
# the equilibrium reaction specified in the AqueousEquilibriumReactions block as:
#
#  reactions = '2a = pa2 1'
#
# where the 2 is the weight of the equilibrium species, and the 1 refers to the equilibrium
# constant (log10(Keq) = 1).
#
# The AqueousEquilibriumReactions action creates all the required kernels and auxkernels
# to compute the reaction given by the above equilibrium reaction equation.
#
# Specifically, it adds to following:
# * An AuxVariable named 'pa2' (given in the reactions equations)
# * A AqueousEquilibriumRxnAux AuxKernel for this AuxVariable with all parameters
# * A CoupledBEEquilibriumSub Kernel for each primary species with all parameters
# * A CoupledDiffusionReactionSub Kernel for each primary species with all parameters
# * A CoupledConvectionReactionSub Kernel for each primary species with all parameters if
# pressure is a coupled variable

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
[]

[Variables]
  [./a]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1e-2
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
      variable = a
    [../]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  [../]
[]

[ReactionNetwork]
  [./AqueousEquilibriumReactions]
    primary_species = a
    reactions = '2a = pa2 1'
    secondary_species = pa2
    pressure = pressure
  [../]
[]

[Kernels]
  [./a_ie]
    type = PrimaryTimeDerivative
    variable = a
  [../]
  [./a_diff]
    type = PrimaryDiffusion
    variable = a
  [../]
  [./a_conv]
    type = PrimaryConvection
    variable = a
    p = pressure
  [../]
[]

[BCs]
  [./a_right]
    type = ChemicalOutFlowBC
    variable = a
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-4 1e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-12
  start_time = 0.0
  end_time = 100
  dt = 10.0
[]

[Outputs]
  file_base = 1species_out
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

(modules/porous_flow/test/tests/numerical_diffusion/fltvd_none.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek
# No antidiffusion, so this is identical to full-upwinding
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculator
    flux_limiter_type = none
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-1
  nl_abs_tol = 1E-8
  nl_max_its = 500
  timestep_tolerance = 1E-3
[]

[Outputs]
  csv = true
  execute_on = final
[]

(modules/porous_flow/test/tests/sinks/s09.i)

# Apply a piecewise-linear sink flux to the right-hand side and watch fluid flow to it
#
# This test has a single phase with two components.  The test initialises with
# the porous material fully filled with component=1.  The left-hand side is fixed
# at porepressure=1 and mass-fraction of the zeroth component being unity.
# The right-hand side has a very strong piecewise-linear flux that keeps the
# porepressure~0 at that side.  Fluid mass is extracted by this flux in proportion
# to the fluid component mass fraction.
#
# Therefore, the zeroth fluid component will flow from left to right (down the
# pressure gradient).
#
# The important DE is
# porosity * dc/dt = (perm / visc) * grad(P) * grad(c)
# which is true for c = mass-fraction, and very large bulk modulus of the fluid.
# For grad(P) constant in time and space (as in this example) this is just the
# advection equation for c, with velocity = perm / visc / porosity.  The parameters
# are chosen to velocity = 1 m/s.
# In the numerical world, and especially with full upwinding, the advection equation
# suffers from diffusion.  In this example, the diffusion is obvious when plotting
# the mass-fraction along the line, but the average velocity of the front is still
# correct at 1 m/s.
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp frac'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Variables]
  [pp]
  []
  [frac]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = 1-x
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = frac
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = pp
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    gravity = '0 0 0'
    variable = frac
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    gravity = '0 0 0'
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1e10 # need large in order for constant-velocity advection
      density0 = 1 # almost irrelevant, except that the ability of the right BC to keep P fixed at zero is related to density_P0
      thermal_expansion = 0
      viscosity = 11
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = frac
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 1.1 0 0 0 1.1'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2 # irrelevant in this fully-saturated situation
    phase = 0
  []
[]


[BCs]
  [lhs_fixed_a]
    type = DirichletBC
    boundary = 'left'
    variable = frac
    value = 1
  []
  [lhs_fixed_b]
    type = DirichletBC
    boundary = 'left'
    variable = pp
    value = 1
  []
  [flux0]
    type = PorousFlowPiecewiseLinearSink
    boundary = 'right'
    pt_vals = '-100 100'
    multipliers = '-1 1'
    variable = frac # the zeroth comonent
    mass_fraction_component = 0
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 1E4
  []
  [flux1]
    type = PorousFlowPiecewiseLinearSink
    boundary = 'right'
    pt_vals = '-100 100'
    multipliers = '-1 1'
    variable = pp # comonent 1
    mass_fraction_component = 1
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 1E4
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10000 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-2
  end_time = 1
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[VectorPostprocessors]
  [mf]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 100
    sort_by = x
    variable = frac
  []
[]

[Outputs]
  file_base = s09
  [console]
    type = Console
    execute_on = 'nonlinear linear'
  []
  [csv]
    type = CSV
    sync_times = '0.1 0.5 1'
    sync_only = true
  []
  interval = 10
[]

(modules/combined/test/tests/DiffuseCreep/stress_based_chem_pot.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.1*v'
    [../]
  [../]
  [./mu]
  [../]
  [./jx]
  [../]
  [./jy]
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./creep_strain_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_xy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./mu_prop]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./mech_prop]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./total_potential]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = total_potential
    c = c
  [../]
  [./flux_x]
    type = CHSplitFlux
    variable = jx
    component = 0
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./flux_y]
    type = CHSplitFlux
    variable = jy
    component = 1
    mobility_name = mobility_prop
    mu = mu
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./creep_strain_xx]
    type = RankTwoAux
    variable = creep_strain_xx
    rank_two_tensor = creep_strain
    index_i = 0
    index_j = 0
  [../]
  [./stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    variable = stress_yy
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./stress_xy]
    type = RankTwoAux
    variable = stress_xy
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
  [./mu_prop]
    type = MaterialRealAux
    property = mu_prop
    variable = mu_prop
  [../]
  [./mech_prop]
    type = MaterialRealAux
    property = mech_prop
    variable = mech_prop
  [../]
  [./total_potential]
    type = MaterialRealAux
    property = total_potential
    variable = total_potential
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./mechanical_potential]
    type = StressBasedChemicalPotential
    property_name = mech_prop
    stress_name = stress
    direction_tensor_name = aniso_tensor
    prefactor_name = 1.0
  [../]
  [./total_potential]
    type = DerivativeSumMaterial
    block = 0
    f_name = total_potential
    sum_materials = 'mu_prop mech_prop'
    args = 'c'
    derivative_order = 2
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
  [./diffuse_strain_increment]
    type = FluxBasedStrainIncrement
    xflux = jx
    yflux = jy
    gb = gb
    property_name = diffuse
  [../]
  [./diffuse_creep_strain]
    type = SumTensorIncrements
    tensor_name = creep_strain
    coupled_tensor_increment_names = diffuse
  [../]
  [./strain]
   type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y'
  [../]
  [./stress]
    type = ComputeStrainIncrementBasedStress
    inelastic_strain_names = creep_strain
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '120.0 80.0'
    fill_method = symmetric_isotropic
  [../]
[]

[BCs]
  [./Periodic]
    [./cbc]
      auto_direction = 'x y'
      variable = c
    [../]
  [../]
  [./fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  nl_rel_tol = 1e-10
  nl_max_its = 5

  l_tol = 1e-4
  l_max_its = 20

  dt = 1
  num_steps = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/multiapps/grid-sequencing/vi-fine.i)

l=10
nx=80
num_steps=2

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [bounds][]
[]

[Bounds]
  [./u_upper_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = upper
    bound_value = ${l}
  [../]
  [./u_lower_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = lower
    bound_value = 0
  [../]
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options = '-snes_vi_monitor'
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type -snes_type'
  petsc_options_value = '0                           30          asm      16                    basic                 vinewtonrsls'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  active = 'upper_violations lower_violations'
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

[MultiApps]
  [./coarse]
    type = TransientMultiApp
    app_type = MooseTestApp
    execute_on = timestep_begin
    positions = '0 0 0'
    input_files = vi-coarse.i
  [../]
[]

[Transfers]
  [./mesh_function_begin]
    type = MultiAppMeshFunctionTransfer
    from_multi_app = coarse
    source_variable = u
    variable = u
    execute_on = timestep_begin
  [../]
[]

(modules/porous_flow/examples/multiapp_fracture_flow/3dFracture/fracture_only_aperture_changing.i)

# Cold water injection into one side of the fracture network, and production from the other side
injection_rate = 10 # kg/s

[Mesh]
  uniform_refine = 0
  [cluster34]
    type = FileMeshGenerator
    file = 'Cluster_34.exo'
  []
  [injection_node]
    type = BoundingBoxNodeSetGenerator
    input = cluster34
    bottom_left = '-1000 0 -1000'
    top_right = '1000 0.504 1000'
    new_boundary = injection_node
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 -9.81E-6' # Note the value, because of pressure_unit
[]

[Variables]
  [frac_P]
    scaling = 1E6
  []
  [frac_T]
    initial_condition = 473
  []
[]

[ICs]
  [frac_P]
    type = FunctionIC
    variable = frac_P
    function = insitu_pp
  []
[]

[PorousFlowFullySaturated]
  coupling_type = ThermoHydro
  porepressure = frac_P
  temperature = frac_T
  fp = water
  pressure_unit = MPa
[]

[Kernels]
  [toMatrix]
    type = PorousFlowHeatMassTransfer
    variable = frac_T
    v = transferred_matrix_T
    transfer_coefficient = heat_transfer_coefficient
    save_in = joules_per_s
  []
[]

[AuxVariables]
  [heat_transfer_coefficient]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0.0
  []
  [transferred_matrix_T]
    initial_condition = 473
  []
  [joules_per_s]
  []
  [normal_dirn_x]
    family = MONOMIAL
    order = CONSTANT
  []
  [normal_dirn_y]
    family = MONOMIAL
    order = CONSTANT
  []
  [normal_dirn_z]
    family = MONOMIAL
    order = CONSTANT
  []
  [enclosing_element_normal_length]
    family = MONOMIAL
    order = CONSTANT
  []
  [enclosing_element_normal_thermal_cond]
    family = MONOMIAL
    order = CONSTANT
  []
  [aperture]
    family = MONOMIAL
    order = CONSTANT
  []
  [perm_times_app]
    family = MONOMIAL
    order = CONSTANT
  []
  [density]
    family = MONOMIAL
    order = CONSTANT
  []
  [viscosity]
    family = MONOMIAL
    order = CONSTANT
  []
  [insitu_pp]
  []
[]

[AuxKernels]
  [normal_dirn_x_auxk]
    type = PorousFlowElementNormal
    variable = normal_dirn_x
    component = x
  []
  [normal_dirn_y]
    type = PorousFlowElementNormal
    variable = normal_dirn_y
    component = y
  []
  [normal_dirn_z]
    type = PorousFlowElementNormal
    variable = normal_dirn_z
    component = z
  []
  [heat_transfer_coefficient_auxk]
    type = ParsedAux
    variable = heat_transfer_coefficient
    args = 'enclosing_element_normal_length enclosing_element_normal_thermal_cond'
    constant_names = h_s
    constant_expressions = 1E3 # should be much bigger than thermal_conductivity / L ~ 1
    function = 'if(enclosing_element_normal_length = 0, 0, h_s * enclosing_element_normal_thermal_cond * 2 * enclosing_element_normal_length / (h_s * enclosing_element_normal_length * enclosing_element_normal_length + enclosing_element_normal_thermal_cond * 2 * enclosing_element_normal_length))'
  []
  [aperture]
    type = PorousFlowPropertyAux
    variable = aperture
    property = porosity
  []
  [perm_times_app]
    type = PorousFlowPropertyAux
    variable = perm_times_app
    property = permeability
    row = 0
    column = 0
  []
  [density]
    type = PorousFlowPropertyAux
    variable = density
    property = density
    phase = 0
  []
  [viscosity]
    type = PorousFlowPropertyAux
    variable = viscosity
    property = viscosity
    phase = 0
  []
  [insitu_pp]
    type = FunctionAux
    execute_on = initial
    variable = insitu_pp
    function = insitu_pp
  []
[]

[BCs]
  [inject_heat]
    type = DirichletBC
    boundary = injection_node
    variable = frac_T
    value = 373
  []
[]

[DiracKernels]
  [inject_fluid]
    type = PorousFlowPointSourceFromPostprocessor
    mass_flux = ${injection_rate}
    point = '58.8124 0.50384 74.7838'
    variable = frac_P
  []
  [withdraw_fluid]
    type = PorousFlowPeacemanBorehole
    SumQuantityUO = kg_out_uo
    bottom_p_or_t = 10.6 # 1MPa + approx insitu at production point, to prevent aperture closing due to low porepressures
    character = 1
    line_length = 1
    point_file = production.xyz
    unit_weight = '0 0 0'
    fluid_phase = 0
    use_mobility = true
    variable = frac_P
  []
  [withdraw_heat]
    type = PorousFlowPeacemanBorehole
    SumQuantityUO = J_out_uo
    bottom_p_or_t = 10.6 # 1MPa + approx insitu at production point, to prevent aperture closing due to low porepressures
    character = 1
    line_length = 1
    point_file = production.xyz
    unit_weight = '0 0 0'
    fluid_phase = 0
    use_mobility = true
    use_enthalpy = true
    variable = frac_T
  []
[]

[UserObjects]
  [kg_out_uo]
    type = PorousFlowSumQuantity
  []
  [J_out_uo]
    type = PorousFlowSumQuantity
  []
[]

[Modules]
  [FluidProperties]
    [true_water]
      type = Water97FluidProperties
    []
    [water]
      type = TabulatedFluidProperties
      fp = true_water
      temperature_min = 275 # K
      temperature_max = 600
      interpolated_properties = 'density viscosity enthalpy internal_energy'
      fluid_property_file = water97_tabulated.csv
    []
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityLinear
    porosity_ref = 1E-4 # fracture porosity = 1.0, but must include fracture aperture of 1E-4 at P = insitu_pp
    P_ref = insitu_pp
    P_coeff = 1E-3 # this is in metres/MPa, ie for P_ref = 1/P_coeff, the aperture becomes 1 metre
    porosity_min = 1E-5
  []
  [permeability]
    type = PorousFlowPermeabilityKozenyCarman
    k0 = 1E-15  # fracture perm = 1E-11 m^2, but must include fracture aperture of 1E-4
    poroperm_function = kozeny_carman_phi0
    m = 0
    n = 3
    phi0 = 1E-4
  []
  [internal_energy]
    type = PorousFlowMatrixInternalEnergy
    density = 2700 # kg/m^3
    specific_heat_capacity = 0 # basically no rock inside the fracture
  []
  [aq_thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '0.6E-4 0 0  0 0.6E-4 0  0 0 0.6E-4' # thermal conductivity of water times fracture aperture.  This should increase linearly with aperture, but is set constant in this model
  []
[]

[Functions]
  [kg_rate]
    type = ParsedFunction
    vals = 'dt kg_out'
    vars = 'dt kg_out'
    value = 'kg_out/dt'
  []
  [insitu_pp]
    type = ParsedFunction
    value = '10 - 0.847E-2 * z' # Approximate hydrostatic in MPa
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
    outputs = 'none'
  []
  [kg_out]
    type = PorousFlowPlotQuantity
    uo = kg_out_uo
  []
  [kg_per_s]
    type = FunctionValuePostprocessor
    function = kg_rate
  []
  [J_out]
    type = PorousFlowPlotQuantity
    uo = J_out_uo
  []
  [TK_out]
    type = PointValue
    variable = frac_T
    point = '101.705 160.459 39.5722'
  []
  [P_out]
    type = PointValue
    variable = frac_P
    point = '101.705 160.459 39.5722'
  []
  [P_in]
    type = PointValue
    variable = frac_P
    point = '58.8124 0.50384 74.7838'
  []
[]

[VectorPostprocessors]
  [heat_transfer_rate]
    type = NodalValueSampler
    outputs = none
    sort_by = id
    variable = joules_per_s
  []
[]

[Preconditioning]
  [entire_jacobian]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    optimal_iterations = 10
    growth_factor = 1.5
    timestep_limiting_postprocessor = 1E8
  []
  end_time = 1E8
  nl_abs_tol = 1E-3
  nl_max_its = 20
[]

[Outputs]
  print_linear_residuals = false
  csv = true
  [ex]
    type = Exodus
    sync_times = '1 10 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500 5600 5700 5800 5900 6000 6100 6200 6300 6400 6500 6600 6700 6800 6900 7000 7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 8100 8200 8300 8400 8500 8600 8700 8800 8900 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 30000 50000 70000 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000 1100000 1200000 1300000 1400000 1500000 1600000 1700000 1800000 1900000 2000000 2100000 2200000 2300000 2400000 2500000 2600000 2700000 2800000 2900000'
    sync_only = true
  []
[]

(modules/porous_flow/test/tests/sinks/s08.i)

# apply a sink flux on just one component of a 3-component, 2-phase system and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pwater frac_ph0_c0 pgas'
    number_fluid_phases = 2
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1.1
  []
[]

[Variables]
  [pwater]
  []
  [frac_ph0_c0]
    initial_condition = 0.3
  []
  [pgas]
  []
[]

[ICs]
  [pwater]
    type = FunctionIC
    variable = pwater
    function = y
  []
  [pgas]
    type = FunctionIC
    variable = pgas
    function = y+3
  []
[]

[Kernels]
  [mass_c0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = frac_ph0_c0
  []
  [mass_c1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = pwater
  []
  [mass_c2]
    type = PorousFlowMassTimeDerivative
    fluid_component = 2
    variable = pgas
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 2.3
      density0 = 1.5
      thermal_expansion = 0
      viscosity = 2.1
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = pwater
    phase1_porepressure = pgas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'frac_ph0_c0 frac_ph0_c1 frac_ph1_c0 frac_ph1_c1'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '0.2 0 0 0 0.1 0 0 0 0.1'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
  []
[]

[AuxVariables]
  [flux_out]
  []
  [frac_ph0_c1]
    initial_condition = 0.35
  []
  [frac_ph1_c0]
    initial_condition = 0.1
  []
  [frac_ph1_c1]
    initial_condition = 0.8
  []
[]

[Functions]
  [mass1_00]
    type = ParsedFunction
    value = 'fgas*vol*por*dens0gas*exp(pgas/bulkgas)*(1-pow(1+pow(al*(pgas-pwater),1.0/(1-m)),-m))+fwater*vol*por*dens0water*exp(pwater/bulkwater)*(pow(1+pow(al*(pgas-pwater),1.0/(1-m)),-m))'
    vars = 'vol  por dens0gas pgas    pwater    bulkgas al  m   dens0water bulkwater fgas           fwater'
    vals = '0.25 0.1 1.1      pgas_00 pwater_00 1.3     1.1 0.5 1.5        2.3       frac_ph1_c1_00 frac_ph0_c1_00'
  []
  [expected_mass_change1_00]
    type = ParsedFunction
    value = 'frac*fcn*area*dt*pow(1-pow(1+pow(al*(pgas-pwater),1.0/(1-m)),-m), 2)'
    vars = 'frac           fcn area dt  pgas    pwater    al m'
    vals = 'frac_ph1_c1_00 100 0.5 1E-3 pgas_00 pwater_00 1.1 0.5'
  []
  [mass1_00_expect]
    type = ParsedFunction
    value = 'mass_prev-mass_change'
    vars = 'mass_prev mass_change'
    vals = 'm1_00_prev  del_m1_00'
  []
[]

[Postprocessors]
  [total_mass_comp0]
    type = PorousFlowFluidMass
    fluid_component = 0
  []
  [total_mass_comp1]
    type = PorousFlowFluidMass
    fluid_component = 1
  []
  [total_mass_comp2]
    type = PorousFlowFluidMass
    fluid_component = 2
  []
  [frac_ph1_c1_00]
    type = PointValue
    point = '0 0 0'
    variable = frac_ph1_c1
    execute_on = 'initial timestep_end'
  []
  [frac_ph0_c1_00]
    type = PointValue
    point = '0 0 0'
    variable = frac_ph0_c1
    execute_on = 'initial timestep_end'
  []
  [flux_00]
    type = PointValue
    point = '0 0 0'
    variable = flux_out
    execute_on = 'initial timestep_end'
  []
  [pgas_00]
    type = PointValue
    point = '0 0 0'
    variable = pgas
    execute_on = 'initial timestep_end'
  []
  [pwater_00]
    type = PointValue
    point = '0 0 0'
    variable = pwater
    execute_on = 'initial timestep_end'
  []
  [m1_00]
    type = FunctionValuePostprocessor
    function = mass1_00
    execute_on = 'initial timestep_end'
  []
  [m1_00_prev]
    type = FunctionValuePostprocessor
    function = mass1_00
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [del_m1_00]
    type = FunctionValuePostprocessor
    function = expected_mass_change1_00
    execute_on = 'timestep_end'
    outputs = 'console'
  []
  [m1_00_expect]
    type = FunctionValuePostprocessor
    function = mass1_00_expect
    execute_on = 'timestep_end'
  []
[]

[BCs]
  [flux_ph1_c1]
    type = PorousFlowSink
    boundary = 'left'
    variable = pwater # sink applied to the mass_c1 Kernel
    use_mobility = false
    use_relperm = true
    mass_fraction_component = 1
    fluid_phase = 1
    flux_function = 100
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 100 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-3
  end_time = 0.01
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s08
  exodus = true
  [console]
    type = Console
    execute_on = 'nonlinear linear'
  []
  [csv]
    type = CSV
    execute_on = 'timestep_end'
  []
[]

(modules/richards/test/tests/user_objects/uo3.i)

# Seff User objects give the correct value
# Sat User objects give the correct value
#
# If you want to add another test for another UserObject
# then add the UserObject, add a Function defining the expected result,
# add an AuxVariable and AuxKernel that will record the UserObjects value
# and finally add a NodalL2Error that compares this with the Function
#
# Here pressure is x where x runs between -5E6 and 5E6

[UserObjects]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-6
  [../]
  [./Seff1BWsmall]
    type = RichardsSeff1BWsmall
    Sn = 0.0
    Ss = 1.0
    C = 1.01
    las = 1E5
  [../]
  [./Seff1RSC]
    type = RichardsSeff1RSC
    oil_viscosity = 4.0
    scale_ratio = 1E6
    shift = -2E6
  [../]
  [./Seff1VGcut]
    type = RichardsSeff1VGcut
    m = 0.8
    al = 1E-6
    p_cut = -1E6
  [../]

  # following are unimportant in this test
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.10101
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.054321
    sum_s_res = 0.054321
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E5
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = x
  [../]

  [./answer_Seff1VG]
    type = ParsedFunction
    value = (1+max((-x)*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '1E-6 0.8'
  [../]
  [./answer_dSeff1VG]
    type = GradParsedFunction
    direction = '1 0 0'
    value = (1+max((-x)*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '1E-6 0.8'
  [../]
  [./answer_d2Seff1VG]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = (1+max((-x)*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '1E-6 0.8'
  [../]

  [./answer_Seff1BW]
    type = PiecewiseLinear
    format = columns
    data_file = satBW.csv
    axis = x
  [../]
  [./answer_Seff1BWprime]
    type = PiecewiseLinear
    format = columns
    data_file = satBWprime.csv
    axis = x
  [../]
  [./answer_Seff1BW2prime]
    type = PiecewiseLinear
    format = columns
    data_file = satBW2prime.csv
    axis = x
  [../]

  [./answer_Seff1RSC]
    type = ParsedFunction
    value = (1+exp((-x-shift)/scale))^(-0.5)
    vars = 'shift scale'
    vals = '-2E6 1E6'
  [../]
  [./answer_dSeff1RSC]
    type = GradParsedFunction
    direction = '1 0 0'
    value = (1+exp((-x-shift)/scale))^(-0.5)
    vars = 'shift scale'
    vals = '-2E6 1E6'
  [../]
  [./answer_d2Seff1RSC]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = (1+exp((-x-shift)/scale))^(-0.5)
    vars = 'shift scale'
    vals = '-2E6 1E6'
  [../]

  [./answer_Seff1VGcut]
    type = ParsedFunction
    value = if(x<pcut,scut+dscut*(x-pcut),(1+max((-x)*al,0)^(1/(1-m)))^(-m))
    vars = 'al m pcut scut dscut'
    vals = '1E-6 0.8 -1E6 0.574349177498517 1.14869835499703e-06'
  [../]
  [./answer_dSeff1VGcut]
    type = GradParsedFunction
    direction = '1 0 0'
    value = if(x<pcut,scut+dscut*(x-pcut),(1+max((-x)*al,0)^(1/(1-m)))^(-m))
    vars = 'al m pcut scut dscut'
    vals = '1E-6 0.8 -1E6 0.574349177498517 1.14869835499703e-06'
  [../]
  [./answer_d2Seff1VGcut]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = if(x<pcut,scut+dscut*(x-pcut),(1+max((-x)*al,0)^(1/(1-m)))^(-m))
    vars = 'al m pcut scut dscut'
    vals = '1E-6 0.8 -1E6 0.574349177498517 1.14869835499703e-06'
  [../]

  [./answer_Sat]
    type = ParsedFunction
    value = sres+((1-sumsres)*((1+max((-x)*al,0)^(1/(1-m)))^(-m)))
    vars = 'al m sres sumsres'
    vals = '1E-6 0.8 0.054321 0.054321'
  [../]
  [./answer_dSat]
    type = ParsedFunction
    value = 1-sumsres
    vars = 'sumsres'
    vals = '0.054321'
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
  [./dSeff1VG_Aux]
  [../]
  [./d2Seff1VG_Aux]
  [../]

  [./Seff1BWsmall_Aux]
  [../]
  [./dSeff1BWsmall_Aux]
  [../]
  [./d2Seff1BWsmall_Aux]
  [../]

  [./Seff1RSC_Aux]
  [../]
  [./dSeff1RSC_Aux]
  [../]
  [./d2Seff1RSC_Aux]
  [../]

  [./Seff1VGcut_Aux]
  [../]
  [./dSeff1VGcut_Aux]
  [../]
  [./d2Seff1VGcut_Aux]
  [../]

  [./Sat_Aux]
  [../]
  [./dSat_Aux]
  [../]

  [./check_Aux]
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
  [./dSeff1VG_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
    wrtnum = 0
  [../]
  [./d2Seff1VG_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
    wrtnum1 = 0
    wrtnum2 = 0
  [../]

  [./Seff1BWsmall_AuxK]
    type = RichardsSeffAux
    variable = Seff1BWsmall_Aux
    seff_UO = Seff1BWsmall
    pressure_vars = pressure
  [../]
  [./dSeff1BWsmall_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff1BWsmall_Aux
    seff_UO = Seff1BWsmall
    pressure_vars = pressure
    wrtnum = 0
  [../]
  [./d2Seff1BWsmall_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff1BWsmall_Aux
    seff_UO = Seff1BWsmall
    pressure_vars = pressure
    wrtnum1 = 0
    wrtnum2 = 0
  [../]

  [./Seff1RSC_AuxK]
    type = RichardsSeffAux
    variable = Seff1RSC_Aux
    seff_UO = Seff1RSC
    pressure_vars = pressure
  [../]
  [./dSeff1RSC_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff1RSC_Aux
    seff_UO = Seff1RSC
    pressure_vars = pressure
    wrtnum = 0
  [../]
  [./d2Seff1RSC_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff1RSC_Aux
    seff_UO = Seff1RSC
    pressure_vars = pressure
    wrtnum1 = 0
    wrtnum2 = 0
  [../]

  [./Seff1VGcut_AuxK]
    type = RichardsSeffAux
    variable = Seff1VGcut_Aux
    seff_UO = Seff1VGcut
    pressure_vars = pressure
  [../]
  [./dSeff1VGcut_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff1VGcut_Aux
    seff_UO = Seff1VGcut
    pressure_vars = pressure
    wrtnum = 0
  [../]
  [./d2Seff1VGcut_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff1VGcut_Aux
    seff_UO = Seff1VGcut
    pressure_vars = pressure
    wrtnum1 = 0
    wrtnum2 = 0
  [../]

  [./Sat_AuxK]
    type = RichardsSatAux
    sat_UO = Saturation
    seff_var = Seff1VG_Aux
    variable = Sat_Aux
  [../]
  [./dSat_AuxK]
    type = RichardsSatPrimeAux
    sat_UO = Saturation
    seff_var = Seff1VG_Aux
    variable = dSat_Aux
  [../]

  [./check_AuxK]
    type = FunctionAux
    variable = check_Aux
    function = answer_Seff1VGcut
  [../]
[]

[Postprocessors]
  [./cf_Seff1VG]
    type = NodalL2Error
    function = answer_Seff1VG
    variable = Seff1VG_Aux
  [../]
  [./cf_dSeff1VG]
    type = NodalL2Error
    function = answer_dSeff1VG
    variable = dSeff1VG_Aux
  [../]
  [./cf_d2Seff1VG]
    type = NodalL2Error
    function = answer_d2Seff1VG
    variable = d2Seff1VG_Aux
  [../]

  [./cf_Seff1BW]
    type = NodalL2Error
    function = answer_Seff1BW
    variable = Seff1BWsmall_Aux
  [../]
  [./cf_Seff1BWprime]
    type = NodalL2Error
    function = answer_Seff1BWprime
    variable = dSeff1BWsmall_Aux
  [../]
  [./cf_Seff1BW2prime]
    type = NodalL2Error
    function = answer_Seff1BW2prime
    variable = d2Seff1BWsmall_Aux
  [../]

  [./cf_Seff1RSC]
    type = NodalL2Error
    function = answer_Seff1RSC
    variable = Seff1RSC_Aux
  [../]
  [./cf_dSeff1RSC]
    type = NodalL2Error
    function = answer_dSeff1RSC
    variable = dSeff1RSC_Aux
  [../]
  [./cf_d2Seff1RSC]
    type = NodalL2Error
    function = answer_d2Seff1RSC
    variable = d2Seff1RSC_Aux
  [../]

  [./cf_Seff1VGcut]
    type = NodalL2Error
    function = answer_Seff1VGcut
    variable = Seff1VGcut_Aux
  [../]
  [./cf_dSeff1VGcut]
    type = NodalL2Error
    function = answer_dSeff1VGcut
    variable = dSeff1VGcut_Aux
  [../]
  [./cf_d2Seff1VGcut]
    type = NodalL2Error
    function = answer_d2Seff1VGcut
    variable = d2Seff1VGcut_Aux
  [../]

  [./cf_Sat]
    type = NodalL2Error
    function = answer_Sat
    variable = Sat_Aux
  [../]
  [./cf_dSat]
    type = NodalL2Error
    function = answer_dSat
    variable = dSat_Aux
  [../]
[]



#############################################################################
#
# Following is largely unimportant as we are not running an actual similation
#
#############################################################################
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -5E6
  xmax = 5E6
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    richardsVarNames_UO = PPNames
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    richardsVarNames_UO = PPNames
    variable = pressure
  [../]
[]

[Materials]
  [./unimportant_material]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-20 0 0  0 1E-20 0  0 0 1E-20'
    richardsVarNames_UO = PPNames
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    viscosity = 1E-3
    gravity = '0 0 -10'
    linear_shape_fcns = true
  [../]
[]

[Preconditioning]
  [./does_nothing]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E50 1E50 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
  dt = 1E-100
[]

[Outputs]
  execute_on = 'timestep_end'
  active = 'csv'
  file_base = uo3
  [./csv]
    type = CSV
  [../]
  [./exodus]
    type = Exodus
    hide = pressure
  [../]
[]

(modules/porous_flow/test/tests/aux_kernels/darcy_velocity.i)

# checking that the PorousFlowDarcyVelocityComponent AuxKernel works as expected
# for the fully-saturated case (relative-permeability = 1)
# There is one element, of unit size.  The pressures and fluid densities at the qps are:
# (x,y,z)=( 0.211325 , 0.211325 , 0.211325 ).  p = 1.479   rho = 3.217
# (x,y,z)=( 0.788675 , 0.211325 , 0.211325 ).  p = 2.057   rho = 4.728
# (x,y,z)=( 0.211325 , 0.788675 , 0.211325 ).  p = 2.634   rho = 6.947
# (x,y,z)=( 0.788675 , 0.788675 , 0.211325 ).  p = 3.211   rho = 10.208
# (x,y,z)=( 0.211325 , 0.211325 , 0.788675 ).  p = 3.789   rho = 15.001
# (x,y,z)=( 0.788675 , 0.211325 , 0.788675 ).  p = 4.367   rho = 22.043
# (x,y,z)=( 0.211325 , 0.788675 , 0.788675 ).  p = 4.943   rho = 32.392
# (x,y,z)=( 0.788675 , 0.788675 , 0.788675 ).  p = 5.521   rho = 47.599
# Average density = 17.7668
# grad(P) = (1, 2, 4)
# with permeability = diag(1, 2, 3) and gravity = (1, -2, 3) and viscosity = 3.2
# So Darcy velocity = (5.23963, -23.4585, 46.2192)

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '1 -2 3'
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = x+2*y+4*z
    variable = pp
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[AuxVariables]
  [vel_x]
    order = CONSTANT
    family = MONOMIAL
  []
  [vel_y]
    order = CONSTANT
    family = MONOMIAL
  []
  [vel_z]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [vel_x]
    type = PorousFlowDarcyVelocityComponent
    variable = vel_x
    component = x
    fluid_phase = 0
  []
  [vel_y]
    type = PorousFlowDarcyVelocityComponent
    variable = vel_y
    component = y
    fluid_phase = 0
  []
  [vel_z]
    type = PorousFlowDarcyVelocityComponent
    variable = vel_z
    component = z
    fluid_phase = 0
 []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      viscosity = 3.2
      density0 = 1.2
      thermal_expansion = 0
    []
  []
[]

[Postprocessors]
  [vel_x]
    type = PointValue
    variable = vel_x
    point = '0.5 0.5 0.5'
  []
  [vel_y]
    type = PointValue
    variable = vel_y
    point = '0.5 0.5 0.5'
  []
  [vel_z]
    type = PointValue
    variable = vel_z
    point = '0.5 0.5 0.5'
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0 0 2 0 0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  nl_abs_tol = 1e-16
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = darcy_velocity
  csv = true
[]

(test/tests/mesh_modifiers/mesh_side_set/test.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 4
    nz = 4
    elem_type = TET4
  []

  [left_block]
    type = SubdomainBoundingBoxGenerator
    input = gen
    block_id = 1
    block_name = left_block
    bottom_left = '0 0 0'
    top_right = '0.5 1 1'
  []
  [right_block]
    type = SubdomainBoundingBoxGenerator
    input = left_block
    block_id = 2
    block_name = right_block
    bottom_left = '0.5 0 0'
    top_right = '1 1 1'
  []
  [center_side_set]
    type = SideSetsBetweenSubdomainsGenerator
    input = right_block
    primary_block = left_block
    paired_block = right_block
    new_boundary = center_side_set
  []
  [center_mesh]
    type = MeshSideSetGenerator
    input = center_side_set
    boundaries = center_side_set
    block_id = 10
    block_name = center_mesh
  []
[]

[Variables]
  [c_volume]
    [InitialCondition]
      type = FunctionIC
      function = '1-(x-0.5)^2+(y-0.5)^2+(z-0.5)^2'
    []
  []
  [c_plane]
    block = 'center_mesh'
  []
[]

[Kernels]
  [volume_diff]
    type = Diffusion
    variable = c_volume
    block = 'left_block right_block'
  []
  [volume_dt]
    type = TimeDerivative
    variable = c_volume
    block = 'left_block right_block'
  []

  # couple the lower dimensional variable to the volume variable
  [plane_reaction]
    type = Reaction
    variable = c_plane
    block = 'center_mesh'
  []
  [plane_coupled]
    type = CoupledForce
    variable = c_plane
    v = c_volume
    block = 'center_mesh'
  []
[]

[Executioner]
  type = Transient
  dt = 0.01
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/electrochem_sintering/ElectrochemicalSintering_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 800
  xmin = 0
  xmax = 80
[]

[GlobalParams]
  op_num = 2
  var_name_base = gr
  int_width = 4
[]

[Variables]
  [wvy]
  []
  [wvo]
  []
  [phi]
  []
  [PolycrystalVariables]
  []
  [V]
  []
[]

[AuxVariables]
  [bnds]
  []
  [negative_V]
  []
  [E_x]
    order = CONSTANT
    family = MONOMIAL
  []
  [E_y]
    order = CONSTANT
    family = MONOMIAL
  []
  [ns_cat_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [ns_an_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [T]
  []
[]

[Functions]
  [ic_func_gr0]
    type = ParsedFunction
    value = '0.5*(1.0-tanh((x)/sqrt(2.0*2.0)))'
  []
  [ic_func_gr1]
    type = ParsedFunction
    value = '0.5*(1.0+tanh((x)/sqrt(2.0*2.0)))'
  []
[]

[ICs]
  [gr0_IC]
    type = FunctionIC
    variable = gr0
    function = ic_func_gr0
  []
  [gr1_IC]
    type = FunctionIC
    variable = gr1
    function = ic_func_gr1
  []
  [wvy_IC]
    type = ConstantIC
    variable = wvy
    value = 2.7827
  []
  [wvo_IC]
    type = ConstantIC
    variable = wvo
    value = 2.7827
  []
  [T_IC]
    type = ConstantIC
    variable = T
    value = 1600
  []
[]

[BCs]
  [v_left]
    type = DirichletBC
    preset = true
    variable = V
    boundary = left
    value = 1e-2
  []
  [v_right]
    type = DirichletBC
    preset = true
    variable = V
    boundary = right
    value = 0
  []
  [gr0_left]
    type = DirichletBC
    preset = true
    variable = gr0
    boundary = left
    value = 0.5 #Grain boundary at left hand side of domain
  []
  [gr1_left]
    type = DirichletBC
    preset = true
    variable = gr1
    boundary = left
    value = 0.5 #Grain boundary at left hand side of domain
  []
  [wvo_right]
    type = DirichletBC
    preset = true
    variable = wvo
    boundary = right
    value = 2.7827
  []
  [wvy_right]
    type = DirichletBC
    preset = true
    variable = wvy
    boundary = right
    value = 2.7827
  []
[]

[Materials]
  # Free energy coefficients for parabolic curves
  [ks_cat]
    type = ParsedMaterial
    f_name = ks_cat
    args = 'T'
    constant_names = 'a b Va'
    constant_expressions = '-0.0017 140.44 0.03726'
    function = '(a*T + b) * Va^2'
  []
  [ks_an]
    type = ParsedMaterial
    f_name = ks_an
    args = 'T'
    constant_names = 'a b Va'
    constant_expressions = '-0.0017 140.44 0.03726'
    function = '(a*T + b) * Va^2'
  []
  [kv_cat]
    type = ParsedMaterial
    f_name = kv_cat
    material_property_names = 'ks_cat'
    function = '10*ks_cat'
  []
  [kv_an]
    type = ParsedMaterial
    f_name = kv_an
    material_property_names = 'ks_cat'
    function = '10*ks_cat'
  []
  # Diffusivity and mobilities
  [chiDy]
    type = GrandPotentialTensorMaterial
    f_name = chiDy
    diffusivity_name = Dvy
    solid_mobility = L
    void_mobility = Lv
    chi = chi_cat
    surface_energy = 6.24
    c = phi
    T = T
    D0 = 5.9e11
    GBmob0 = 1.60e12
    Q = 4.14
    Em = 4.25
    bulkindex = 1
    gbindex = 1
    surfindex = 1
  []
  [chiDo]
    type = GrandPotentialTensorMaterial
    f_name = chiDo
    diffusivity_name = Dvo
    solid_mobility = Lo
    void_mobility = Lvo
    chi = chi_an
    surface_energy = 6.24
    c = phi
    T = T
    D0 = 5.9e11
    GBmob0 = 1.60e12
    Q = 4.14
    Em = 4.25
    bulkindex = 1
    gbindex = 1
    surfindex = 1
  []
  # Everything else
  [ns_y_min]
    type = DerivativeParsedMaterial
    f_name = ns_y_min
    args = 'gr0 gr1 T'
    constant_names = 'Ef_B Ef_GB   kB          Va_Y'
    constant_expressions = '4.37 4.37    8.617343e-5 0.03726'
    derivative_order = 2
    function = 'bnds:=gr0^2 + gr1^2; Ef:=Ef_B + 4.0 * (Ef_GB - Ef_B) * (1.0 - bnds)^2;
              '
               '  exp(-Ef/kB/T) / Va_Y'
  []
  [ns_o_min]
    type = DerivativeParsedMaterial
    f_name = ns_o_min
    args = 'gr0 gr1 T'
    constant_names = 'Ef_B Ef_GB  kB          Va_O'
    constant_expressions = '4.37 4.37   8.617343e-5 0.02484'
    derivative_order = 2
    function = 'bnds:=gr0^2 + gr1^2; Ef:=Ef_B + 4.0 * (Ef_GB - Ef_B) * (1.0 - bnds)^2;
              '
               '  exp(-Ef/kB/T) / Va_O'
  []
  [sintering]
    type = ElectrochemicalSinteringMaterial
    chemical_potentials = 'wvy wvo'
    electric_potential = V
    void_op = phi
    Temperature = T
    surface_energy = 6.24
    grainboundary_energy = 5.18
    solid_energy_coefficients = 'kv_cat kv_cat'
    void_energy_coefficients = 'kv_cat kv_an'
    min_vacancy_concentrations_solid = 'ns_y_min ns_o_min'
    min_vacancy_concentrations_void = '26.837 40.256'
    defect_charges = '-3 2'
    solid_relative_permittivity = 30
    solid_energy_model = DILUTE
  []
  [density_chi_y]
    type = ElectrochemicalDefectMaterial
    chemical_potential = wvy
    void_op = phi
    Temperature = T
    electric_potential = V
    void_density_name = nv_cat
    solid_density_name = ns_cat
    chi_name = chi_cat
    void_energy_coefficient = kv_cat
    min_vacancy_concentration_solid = ns_y_min
    min_vacancy_concentration_void = 26.837
    solid_energy_model = DILUTE
    defect_charge = -3
    solid_relative_permittivity = 30
  []
  [density_chi_o]
    type = ElectrochemicalDefectMaterial
    chemical_potential = wvo
    void_op = phi
    Temperature = T
    electric_potential = V
    void_density_name = nv_an
    solid_density_name = ns_an
    chi_name = chi_an
    void_energy_coefficient = kv_an
    min_vacancy_concentration_solid = ns_o_min
    min_vacancy_concentration_void = 40.256
    solid_energy_model = DILUTE
    defect_charge = 2
    solid_relative_permittivity = 30
  []
  [permittivity]
    type = DerivativeParsedMaterial
    f_name = permittivity
    args = 'phi'
    material_property_names = 'hs hv'
    constant_names = 'eps_rel_solid   eps_void_over_e'
    constant_expressions = '30              5.52e-2' #eps_void_over_e in 1/V/nm
    derivative_order = 2
    function = '-hs * eps_rel_solid * eps_void_over_e - hv * eps_void_over_e'
  []
  [void_pre]
    type = DerivativeParsedMaterial
    f_name = void_pre
    material_property_names = 'hv'
    constant_names = 'Z_cat   Z_an nv_y_min nv_o_min'
    constant_expressions = '-3      2    26.837   40.256'
    derivative_order = 2
    function = '-hv * (Z_cat * nv_y_min + Z_an * nv_o_min)'
  []
  [cat_mu_pre]
    type = DerivativeParsedMaterial
    f_name = cat_mu_pre
    material_property_names = 'hv kv_cat'
    constant_names = 'Z_cat'
    constant_expressions = '-3'
    derivative_order = 2
    function = '-hv * Z_cat / kv_cat'
  []
  [an_mu_pre]
    type = DerivativeParsedMaterial
    f_name = an_mu_pre
    material_property_names = 'hv kv_an'
    constant_names = 'Z_an'
    constant_expressions = '2'
    derivative_order = 2
    function = '-hv * Z_an / kv_an'
  []
  [cat_V_pre]
    type = DerivativeParsedMaterial
    f_name = cat_V_pre
    material_property_names = 'hv kv_cat'
    constant_names = 'Z_cat   v_scale e '
    constant_expressions = '-3      1       1'
    derivative_order = 2
    function = 'hv * Z_cat^2 * e * v_scale / kv_cat'
  []
  [an_V_pre]
    type = DerivativeParsedMaterial
    f_name = an_V_pre
    material_property_names = 'hv kv_an'
    constant_names = 'Z_an    v_scale e '
    constant_expressions = '2       1       1'
    derivative_order = 2
    function = 'hv * Z_an^2 * e * v_scale / kv_an'
  []
[]

#This action adds most kernels needed for grand potential model
[Modules]
  [PhaseField]
    [GrandPotential]
      switching_function_names = 'hv hs'
      anisotropic = 'true true'

      chemical_potentials = 'wvy wvo'
      mobilities = 'chiDy chiDo'
      susceptibilities = 'chi_cat chi_an'
      free_energies_w = 'nv_cat ns_cat nv_an ns_an'

      gamma_gr = gamma
      mobility_name_gr = L
      kappa_gr = kappa
      free_energies_gr = 'omegav omegas'

      additional_ops = 'phi'
      gamma_grxop = gamma
      mobility_name_op = Lv
      kappa_op = kappa
      free_energies_op = 'omegav omegas'
    []
  []
[]

[Kernels]
  [barrier_phi]
    type = ACBarrierFunction
    variable = phi
    v = 'gr0 gr1'
    gamma = gamma
    mob_name = Lv
  []
  [kappa_phi]
    type = ACKappaFunction
    variable = phi
    mob_name = Lv
    kappa_name = kappa
  []
  [Laplace]
    type = MatDiffusion
    variable = V
    diffusivity = permittivity
    args = 'phi'
  []
  [potential_void_constants]
    type = MaskedBodyForce
    variable = V
    args = 'phi'
    mask = void_pre
  []
  [potential_cat_mu]
    type = MatReaction
    variable = V
    v = wvy
    mob_name = cat_mu_pre
  []
  [potential_an_mu]
    type = MatReaction
    variable = V
    v = wvo
    mob_name = an_mu_pre
  []
  [potential_cat_V]
    type = MatReaction
    variable = V
    mob_name = cat_V_pre
  []
  [potential_an_V]
    type = MatReaction
    variable = V
    mob_name = an_V_pre
  []
  [potential_solid_cat]
    type = MaskedExponential
    variable = V
    w = wvy
    T = T
    args = 'phi gr0 gr1'
    mask = hs
    species_charge = -3
    n_eq = ns_y_min
  []
  [potential_solid_an]
    type = MaskedExponential
    variable = V
    w = wvo
    T = T
    args = 'phi gr0 gr1'
    mask = hs
    species_charge = 2
    n_eq = ns_o_min
  []
[]

[AuxKernels]
  [bnds_aux]
    type = BndsCalcAux
    variable = bnds
    execute_on = 'initial timestep_end'
  []
  [negative_V]
    type = ParsedAux
    variable = negative_V
    args = V
    function = '-V'
  []
  [E_x]
    type = VariableGradientComponent
    variable = E_x
    gradient_variable = negative_V
    component = x
  []
  [E_y]
    type = VariableGradientComponent
    variable = E_y
    gradient_variable = negative_V
    component = y
  []
  [ns_cat_aux]
    type = MaterialRealAux
    variable = ns_cat_aux
    property = ns_cat
  []
  [ns_an_aux]
    type = MaterialRealAux
    variable = ns_an_aux
    property = ns_an
  []
[]

[Postprocessors]
  [ns_cat_total]
    type = ElementIntegralMaterialProperty
    mat_prop = ns_cat
  []
  [ns_an_total]
    type = ElementIntegralMaterialProperty
    mat_prop = ns_an
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -sub_pc_type -pc_asm_overlap -ksp_gmres_restart -sub_ksp_type'
  petsc_options_value = ' asm      lu           1               31                 preonly'
  nl_max_its = 40
  l_max_its = 30
  l_tol = 1e-4
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-13
  start_time = 0
  num_steps = 2
  automatic_scaling = true
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    optimal_iterations = 8
    iteration_window = 2
  []
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/energy_conservation/heat02.i)

# checking that the heat-energy postprocessor correctly calculates the energy
# 1phase, constant porosity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 3
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [temp]
  []
  [pp]
  []
[]

[ICs]
  [tinit]
    type = FunctionIC
    function = '100*x'
    variable = temp
  []
  [pinit]
    type = FunctionIC
    function = 'x'
    variable = pp
  []
[]

[Kernels]
  [dummyt]
    type = TimeDerivative
    variable = temp
  []
  [dummyp]
    type = TimeDerivative
    variable = pp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      viscosity = 0.001
      thermal_expansion = 0
      cv = 1.3
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 2.2
    density = 0.5
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
[]

[Postprocessors]
  [total_heat]
    type = PorousFlowHeatEnergy
    phase = 0
  []
  [rock_heat]
    type = PorousFlowHeatEnergy
  []
  [fluid_heat]
    type = PorousFlowHeatEnergy
    include_porous_skeleton = false
    phase = 0
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = heat02
  csv = true
[]

(modules/richards/test/tests/uo_egs/density.i)

# Outputs a density relationship into an exodus file
# and into a CSV file.
# In the exodus file, the density will be a function of "x", and
# this "x" is actually porepressure
# In the CSV file you will find the density at the "x" point
# specified by you below.
#
# You may specify:
#  - the "type" of density in the UserObjects block
#  - the parameters of this density function in the UserObjects block
#  - the "x" point (which is porepressure) that you want to extract
#       the density at, if you want a value at a particular point
#  - the range of "x" values (which is porepressure values) may be
#       changed in the Mesh block, below


[UserObjects]
  [./density]
    type = RichardsDensityVDW
    a = 0.2303
    b = 4.31E-5
    molar_mass = 16.04246E-3
    temperature = 293
  [../]
[]

[Postprocessors]
  [./point_val]
    type = PointValue
    execute_on = timestep_begin
    # note this point must lie inside the mesh below
    point = '1 0 0'
    variable = density
  [../]
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  # the following specify the range of porepressure
  xmin = -1E6
  xmax = 1E7
[]

############################
# You should not need to change any of the stuff below
############################


[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = x
  [../]
[]

[AuxVariables]
  [./density]
  [../]
[]

[AuxKernels]
  [./density_AuxK]
    type = RichardsDensityAux
    variable = density
    density_UO = density
    execute_on = timestep_begin
    pressure_var = u
  [../]
[]

[Kernels]
  [./dummy]
    type = Diffusion
    variable = u
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 0
[]

[Outputs]
  file_base = density
  [./csv]
    type = CSV
  [../]
  [./exodus]
    type = Exodus
    hide = u
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/porosity_jump/2d-rc-epsjump.i)

mu=1.1
rho=1.1
advected_interp_method='upwind'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1'
    dy = '0.5'
    ix = '30 30'
    iy = '20'
    subdomain_id = '1 2'
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = u
    v = v
    porosity = porosity
    pressure = pressure
  []
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
  []
[]

[ICs]
  inactive = 'porosity_continuous'
  [porosity_1]
    type = ConstantIC
    variable = porosity
    block = 1
    value = 1
  []
  [porosity_2]
    type = ConstantIC
    variable = porosity
    block = 2
    value = 0.5
  []
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    block = '1 2'
    function = smooth_jump
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1)))'
  []
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    pressure = pressure
    porosity = porosity
    momentum_component = 'y'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []

  [walls-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = u
    momentum_component = 'x'
  []
  [walls-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = v
    momentum_component = 'y'
  []

  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0.4
  []
[]

[Materials]
  inactive = 'smooth'
  [jump]
    type = ADPiecewiseByBlockFunctorMaterial
    prop_name = 'porosity'
    subdomain_to_prop_value = '1 1
                               2 0.5'
  []
  [smooth]
    type = ADGenericFunctionFunctorMaterial
    prop_names = 'porosity'
    prop_values = 'smooth_jump'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-10
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/pwcnsfv.i)

rho='rho'
advected_interp_method='upwind'
velocity_interp_method='rc'
gamma=1.4
R=8.3145
molar_mass=29.0e-3
R_specific=${fparse R/molar_mass}
cp=${fparse gamma*R_specific/(gamma-1)}

[GlobalParams]
  two_term_boundary_expansion = true
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = sup_vel_x
    pressure = pressure
    porosity = porosity
  []
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = INSFVPressureVariable
  []
  [sup_vel_x]
    type = PINSFVSuperficialVelocityVariable
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = INSFVEnergyVariable
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_vel_x]
    type = FunctionIC
    variable = sup_vel_x
    function = 'exact_sup_vel_x'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
  [eps]
    type = FunctionIC
    variable = porosity
    function = 'eps'
  []
[]

[FVKernels]
  [mass_advection]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = sup_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressureFlux
    variable = sup_vel_x
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
    force_boundary_execution = false
  []
  [momentum_fn]
    type = INSFVBodyForce
    variable = sup_vel_x
    functor = 'forcing_rho_ud'
    momentum_component = 'x'
  []
[]

[FVBCs]
  [mass]
    variable = pressure
    type = PINSFVFunctorBC
    boundary = 'left right'
    superficial_vel_x = sup_vel_x
    pressure = pressure
    eqn = 'mass'
    porosity = porosity
  []
  [momentum]
    variable = sup_vel_x
    type = PINSFVFunctorBC
    boundary = 'left right'
    superficial_vel_x = sup_vel_x
    pressure = pressure
    eqn = 'momentum'
    momentum_component = 'x'
    porosity = porosity
  []

  # help gradient reconstruction *and* create Dirichlet values for use in PINSFVFunctorBC
  [pressure_right]
    type = FVFunctionDirichletBC
    variable = pressure
    function = exact_p
    boundary = 'right'
  []
  [sup_vel_x_left]
    type = FVFunctionDirichletBC
    variable = sup_vel_x
    function = exact_sup_vel_x
    boundary = 'left'
  []
  [T_fluid_left]
    type = FVFunctionDirichletBC
    variable = T_fluid
    function = exact_T
    boundary = 'left'
  []
[]

[Materials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'cp'
    prop_values = '${cp}'
  []
  [rho]
    type = RhoFromPTFunctorMaterial
    fp = fp
    temperature = T_fluid
    pressure = pressure
  []
  [ins_fv]
    type = INSFVEnthalpyMaterial
    temperature = T_fluid
    rho = ${rho}
  []
[]

[Functions]
  [forcing_rho]
    type = ParsedFunction
    value = '-3.45300378856215*sin(1.1*x)'
  []
  [forcing_rho_ud]
    type = ADParsedFunction
    value = '-0.9*(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + 0.9*(10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) + 3.13909435323832*sin(x)*cos(1.1*x)^2/cos(x)^2 - 6.9060075771243*sin(1.1*x)*cos(1.1*x)/cos(x)'
  []
  [exact_T]
    type = ParsedFunction
    value = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
  []
  [exact_p]
    type = ParsedFunction
    value = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
  []
  [exact_sup_vel_x]
    type = ParsedFunction
    value = '0.9*cos(1.1*x)/cos(x)'
  []
  [eps]
    type = ParsedFunction
    value = '0.9'
  []
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_vel_x]
    variable = sup_vel_x
    function = exact_sup_vel_x
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/postprocessors/find_value_on_line/findvalueonline.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmin = 0
  xmax = 10
[]

[Variables]
  [./phi]
    [./InitialCondition]
      type = FunctionIC
      function = if(x<1,1-x,0)
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = phi
  [../]
  [./dt]
    type = TimeDerivative
    variable = phi
  [../]
[]

[BCs]
  [./influx]
    type = NeumannBC
    boundary = left
    variable = phi
    value = 1
  [../]
  [./fix]
    type = DirichletBC
    boundary = right
    variable = phi
    value = 0
  [../]
[]

[Postprocessors]
  [./pos]
    type = FindValueOnLine
    target = 0.5
    v = phi
    start_point = '0 0 0'
    end_point = '10 0 0'
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 2.5
[]

[Outputs]
  csv = true
[]

(test/tests/misc/check_error/wrong_displacement_order.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  # Mesh uses second-order elements
  elem_type = QUAD8
  displacements = 'disp_x disp_y'
  block_name = pore
  block_id = 0
[]

[Variables]
  [./temperature]
    order = SECOND
    [./InitialCondition]
      type = ConstantIC
      value = 0.0
    [../]
  [../]
[]

# We are *not* allowed to use FIRST-order displacement vars!
[AuxVariables]
  [./disp_x]
  [../]

  [./disp_y]
    [./InitialCondition]
      type = FunctionIC
      function = displ
    [../]
  [../]
[]

[Functions]
  [./displ]
    type = ParsedFunction
    value = -1/2*x*(y-0.5)
  [../]
[]

[Kernels]
  [./diffusion]
    type = Diffusion
    variable = temperature
    use_displaced_mesh = true
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 1
    use_displaced_mesh = true
  [../]
  [./right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 0
    use_displaced_mesh = true
  [../]
[]

[Preconditioning]
  [./SMP_PJFNK]
    type = SMP
    full = true
    solve_type = PJFNK
  [../]
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  line_search = none
  nl_rel_tol = 1e-6
  nl_max_its = 10
  l_tol = 1e-8
  l_max_its = 50
  num_steps = 2 # 200
  nl_abs_tol = 1e-10
  nl_rel_step_tol = 1e-10
  nl_abs_step_tol = 1e-10
  [./TimeStepper]
    type = ConstantDT
    dt = 0.001
  [../]
  dtmin = .001
[]

[Outputs]
  exodus = true
[]

(modules/fluid_properties/test/tests/water/water.i)

# Example of using Water97FluidProperties module in Region 1 by recovering the values
# in Table 5 of Revised Release on the IAPWS Industrial Formulation 1997 for the
# Thermodynamic Properties of Water and Steam

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  xmax = 3
  # This test uses ElementalVariableValue postprocessors on specific
  # elements, so element numbering needs to stay unchanged
  allow_renumbering = false
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./temperature]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./rho]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./v]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./e]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./h]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./s]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./cp]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./cv]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./c]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./mu]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./k]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Functions]
  [./tic]
    type = ParsedFunction
    value = 'if(x<2, 300, 500)'
  [../]
  [./pic]
    type = ParsedFunction
    value = 'if(x<1,3e6, if(x<2, 80e6, 3e6))'
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    function = pic
    variable = pressure
  [../]
  [./t_ic]
    type = FunctionIC
    function = tic
    variable = temperature
  [../]
[]

[AuxKernels]
  [./rho]
    type = MaterialRealAux
    variable = rho
    property = density
  [../]
  [./v]
    type = ParsedAux
    args = rho
    function = 1/rho
    variable = v
  [../]
  [./e]
    type = MaterialRealAux
    variable = e
    property = e
  [../]
  [./h]
    type = MaterialRealAux
    variable = h
    property = h
  [../]
  [./s]
    type = MaterialRealAux
    variable = s
    property = s
  [../]
  [./cp]
    type = MaterialRealAux
    variable = cp
    property = cp
  [../]
  [./cv]
    type = MaterialRealAux
    variable = cv
    property = cv
  [../]
  [./c]
    type = MaterialRealAux
    variable = c
    property = c
  [../]
  [./mu]
    type = MaterialRealAux
    variable = mu
    property = viscosity
  [../]
  [./k]
    type = MaterialRealAux
    variable = k
    property = k
  [../]
[]

[Modules]
  [./FluidProperties]
    [./water]
      type = Water97FluidProperties
    [../]
  [../]
[]

[Materials]
  [./fp_mat]
    type = FluidPropertiesMaterialPT
    pressure = pressure
    temperature = temperature
    fp = water
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[Postprocessors]
  [./density0]
    type = ElementalVariableValue
    variable = rho
    elementid = 0
  [../]
  [./density1]
    type = ElementalVariableValue
    variable = rho
    elementid = 1
  [../]
  [./density2]
    type = ElementalVariableValue
    variable = rho
    elementid = 2
  [../]
  [./v0]
    type = ElementalVariableValue
    variable = v
    elementid = 0
  [../]
  [./v1]
    type = ElementalVariableValue
    variable = v
    elementid = 1
  [../]
  [./v2]
    type = ElementalVariableValue
    variable = v
    elementid = 2
  [../]
  [./e0]
    type = ElementalVariableValue
    variable = e
    elementid = 0
  [../]
  [./e1]
    type = ElementalVariableValue
    variable = e
    elementid = 1
  [../]
  [./e2]
    type = ElementalVariableValue
    variable = e
    elementid = 2
  [../]
  [./h0]
    type = ElementalVariableValue
    variable = h
    elementid = 0
  [../]
  [./h1]
    type = ElementalVariableValue
    variable = h
    elementid = 1
  [../]
  [./h2]
    type = ElementalVariableValue
    variable = h
    elementid = 2
  [../]
  [./s0]
    type = ElementalVariableValue
    variable = s
    elementid = 0
  [../]
  [./s1]
    type = ElementalVariableValue
    variable = s
    elementid = 1
  [../]
  [./s2]
    type = ElementalVariableValue
    variable = s
    elementid = 2
  [../]
  [./cp0]
    type = ElementalVariableValue
    variable = cp
    elementid = 0
  [../]
  [./cp1]
    type = ElementalVariableValue
    variable = cp
    elementid = 1
  [../]
  [./cp2]
    type = ElementalVariableValue
    variable = cp
    elementid = 2
  [../]
  [./cv0]
    type = ElementalVariableValue
    variable = cv
    elementid = 0
  [../]
  [./cv1]
    type = ElementalVariableValue
    variable = cv
    elementid = 1
  [../]
  [./cv2]
    type = ElementalVariableValue
    variable = cv
    elementid = 2
  [../]
  [./c0]
    type = ElementalVariableValue
    variable = c
    elementid = 0
  [../]
  [./c1]
    type = ElementalVariableValue
    variable = c
    elementid = 1
  [../]
  [./c2]
    type = ElementalVariableValue
    variable = c
    elementid = 2
  [../]
  [./mu0]
    type = ElementalVariableValue
    variable = mu
    elementid = 0
  [../]
  [./mu1]
    type = ElementalVariableValue
    variable = mu
    elementid = 1
  [../]
  [./mu2]
    type = ElementalVariableValue
    variable = mu
    elementid = 2
  [../]
  [./k0]
    type = ElementalVariableValue
    variable = k
    elementid = 0
  [../]
  [./k1]
    type = ElementalVariableValue
    variable = k
    elementid = 1
  [../]
  [./k2]
    type = ElementalVariableValue
    variable = k
    elementid = 2
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/radioactive_decay/radioactive_decay01.i)

# checking radioactive decay
# 1phase, 1component, constant porosity
#
# Note that we don't get mass = mass0 * exp(-Lambda * t)
# because of the time discretisation.  We are solving
# the equation
# (mass - mass0)/dt = -Lambda * mass
# which has the solution
# mass = mass0/(1 + Lambda * dt)
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 3
  xmin = -1
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = 10
    variable = pp
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [decay]
    type = PorousFlowMassRadioactiveDecay
    fluid_component = 0
    variable = pp
    decay_rate = 2.0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [total_mass]
    type = PorousFlowFluidMass
    execute_on = 'timestep_end'
  []
  [total_mass0]
    type = PorousFlowFluidMass
    execute_on = 'timestep_begin'
  []
  [should_be_zero]
    type = FunctionValuePostprocessor
    function = should_be_0
  []
[]

[Functions]
  [should_be_0]
    type = ParsedFunction
    vars = 'm0 m rate dt'
    vals = 'total_mass0 total_mass 2.0 1'
    value = 'm-m0/(1.0+rate*dt)'
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  num_steps = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = radioactive_decay01
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/cartesian-version/2d-rc-rz-symmetry.i)

mu=1.1
rho=1.1
offset=0e0

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = ${offset}
    xmax = ${fparse 1 + offset}
    ymin = -1
    ymax = 1
    nx = 2
    ny = 2
  []
[]

[Problem]
  fv_bcs_integrity_check = false
  coord_type = 'RZ'
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  two_term_boundary_expansion = true
  advected_interp_method = 'average'
  velocity_interp_method = 'rc'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = u
    v = v
    pressure = pressure
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[ICs]
  [u]
    type = FunctionIC
    function = 'exact_u'
    variable = u
  []
  [v]
    type = FunctionIC
    function = 'exact_v'
    variable = v
  []
  [pressure]
    type = FunctionIC
    function = 'exact_p'
    variable = pressure
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = INSFVBodyForce
    variable = u
    functor = forcing_u
    momentum_component = 'x'
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = INSFVBodyForce
    variable = v
    functor = forcing_v
    momentum_component = 'y'
  []
[]

[FVBCs]
  [u_wall]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'right'
    function = 'exact_u'
  []
  [v_wall]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'right'
    function = 'exact_v'
  []
  [p]
    type = INSFVOutletPressureBC
    variable = pressure
    function = 'exact_p'
    boundary = 'top'
  []
  [inlet_u]
    type = INSFVInletVelocityBC
    variable = u
    function = 'exact_u'
    boundary = 'bottom'
  []
  [inlet_v]
    type = INSFVInletVelocityBC
    variable = v
    function = 'exact_v'
    boundary = 'bottom'
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    value = 'sin(x*pi)^2*cos(y*pi)'
  []
  [forcing_u]
    type = ADParsedFunction
    value = 'pi^2*mu*sin(x*pi)^2*cos(y*pi) - 2*pi*rho*sin(x*pi)^2*sin(y*pi)*cos(x*pi)*cos(y*pi) - pi*sin(x*pi)*cos(1.6*y) + (4*x*pi*rho*sin(x*pi)^3*cos(x*pi)*cos(y*pi)^2 + rho*sin(x*pi)^4*cos(y*pi)^2)/x - (-2*x*pi^2*mu*sin(x*pi)^2*cos(y*pi) + 2*x*pi^2*mu*cos(x*pi)^2*cos(y*pi) + 2*pi*mu*sin(x*pi)*cos(x*pi)*cos(y*pi))/x'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    value = 'cos(x*pi)*cos(y*pi)'
  []
  [forcing_v]
    type = ADParsedFunction
    value = 'pi^2*mu*cos(x*pi)*cos(y*pi) - 2*pi*rho*sin(y*pi)*cos(x*pi)^2*cos(y*pi) - 1.6*sin(1.6*y)*cos(x*pi) - (-x*pi^2*mu*cos(x*pi)*cos(y*pi) - pi*mu*sin(x*pi)*cos(y*pi))/x + (-x*pi*rho*sin(x*pi)^3*cos(y*pi)^2 + 2*x*pi*rho*sin(x*pi)*cos(x*pi)^2*cos(y*pi)^2 + rho*sin(x*pi)^2*cos(x*pi)*cos(y*pi)^2)/x'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'cos(1.6*y)*cos(x*pi)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-pi*rho*sin(y*pi)*cos(x*pi) + (2*x*pi*rho*sin(x*pi)*cos(x*pi)*cos(y*pi) + rho*sin(x*pi)^2*cos(y*pi))/x'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       NONZERO               superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = false
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [p_avg]
    type = ElementAverageValue
    variable = pressure
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/time_integrators/dirk/dirk-2d-heat.i)

#
# Testing a solution that is second order in space and first order in time.
#

[Mesh]
  type = GeneratedMesh
  dim  = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx   = 20
  ny   = 20
  elem_type = QUAD9
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = exact_fn
    [../]
  [../]
[]

[Functions]
  [./forcing_fn]
    type = ParsedFunction
    value = ((x*x)+(y*y))-(4*t)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*((x*x)+(y*y))
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  start_time = 0.0
  end_time   = 1.0
  dt         = 1.0
  nl_abs_tol=1e-13
  nl_rel_tol=1e-13

  [./TimeIntegrator]
    type = LStableDirk2
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus         = true
[]

(modules/richards/test/tests/dirac/bh08.i)

# fully-saturated
# production
# with anisotropic, but diagonal, permeability
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh02.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = 1
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 2E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 0.5
  dt = 1E-2
  solve_type = NEWTON

[]

[Outputs]
  file_base = bh08
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/richards/test/tests/buckley_leverett/bl22_lumped.i)

# two-phase version
# super-sharp front version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1E-4 1E-3 1E-2 2E-2 5E-2 6E-2 0.1 0.2'
    x = '0    1E-2 1E-1 1    5    20   40  41'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-4
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-4
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
  [./bounds_dummy]
  [../]
[]

[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsLumpedMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsLumpedMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
  [./richardsppenalty]
    type = RichardsPPenalty
    variable = pgas
    a = 1E-18
    lower_var = pwater
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_water
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_gas
  [../]
[]

[BCs]
  [./left_w]
    type = DirichletBC
    variable = pwater
    boundary = left
    value = 1E6
  [../]
  [./left_g]
    type = DirichletBC
    variable = pgas
    boundary = left
    value = 1000
  [../]
  [./right_w]
    type = DirichletBC
    variable = pwater
    boundary = right
    value = -100000
  [../]
  [./right_g]
    type = DirichletBC
    variable = pgas
    boundary = right
    value = 0
  [../]
[]


[Functions]
  [./initial_water]
    type = ParsedFunction
    value = 1000000*(1-min(x/5,1))-if(x<5,0,100000)
  [../]
  [./initial_gas]
    type = ParsedFunction
    value = 1000
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    viscosity = '1E-3 1E-6'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]

  [./standard]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-10 1E-10 20 1E-10 1E-100'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 50

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = bl22_lumped
  [./exodus]
    type = Exodus
    interval = 100000
    hide = 'pgas bounds_dummy'
    execute_on = 'initial final timestep_end'
  [../]
[]

(modules/level_set/examples/rotating_circle/circle_rotate_supg.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 32
  ny = 32
  uniform_refine = 2
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[Variables]
  [./phi]
  [../]
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '4*y'
    value_y = '-4*x'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
  [./advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = phi
  [../]
  [./time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1.570796
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/richards/test/tests/uo_egs/seff2.i)

# Outputs a 2phase effective saturation relationship into an exodus file
# and into a CSV file.
# In the exodus file, the Seff will be a function of "x", and
# this "x" is actually the difference in porepressures,
# say P_gas - P_water (so "x" should be positive).
# In the CSV file you will find the Seff at the "x" point
# specified by you below.
#
# You may specify:
#  - the "type" of Seff in the UserObjects block
#  - the parameters of this Seff function in the UserObjects block
#  - the "x" point (which is del_porepressure) that you want to extract
#       the Seff at, if you want a value at a particular point
#  - the range of "x" values (which is porepressure values) may be
#       changed in the Mesh block, below


[UserObjects]
  [./seff]
    type = RichardsSeff2waterVG
    al = 1E-6
    m = 0.8
  [../]
[]

[Postprocessors]
  [./point_val]
    type = PointValue
    execute_on = timestep_begin
    # note this point must lie inside the mesh below
    point = '1 0 0'
    variable = seff
  [../]
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  # the following specify the range of porepressure
  xmin = 0
  xmax = 3E6
[]

############################
# You should not need to change any of the stuff below
############################


[Variables]
  [./u]
  [../]
  [./v]
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = x
  [../]
  [./v_init]
    type = ConstantIC
    variable = v
    value = 0
  [../]
[]

[AuxVariables]
  [./seff]
  [../]
[]

[AuxKernels]
  [./seff_AuxK]
    type = RichardsSeffAux
    variable = seff
    seff_UO = seff
    execute_on = timestep_begin
    pressure_vars = 'v u'
  [../]
[]

[Kernels]
  [./dummy_u]
    type = Diffusion
    variable = u
  [../]
  [./dummy_v]
    type = Diffusion
    variable = v
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 0
[]

[Outputs]
  file_base = seff2
  [./csv]
    type = CSV
  [../]
  [./exodus]
    type = Exodus
    hide = 'u v'
  [../]
[]

(modules/porous_flow/test/tests/basic_advection/2phase.i)

# Basic advection of u in a 2-phase situation
#
# grad(P) = -2
# density * gravity = 4 * 0.25
# grad(P) - density * gravity = -3
# permeability = 10
# relative permeability = 0.5
# viscosity = 150
# so Darcy velocity = 0.1
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P0]
  []
  [P1]
  []
[]

[ICs]
  [P0]
    type = FunctionIC
    variable = P0
    function = '0'
  []
  [P1]
    type = FunctionIC
    variable = P1
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 2
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      density0 = 32
      viscosity = 123
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 4
      thermal_expansion = 0
      viscosity = 150.0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = P0
    phase1_porepressure = P1
    capillary_pressure = pc
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '10 0 0 0 10 0 0 0 10'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityConst
    kr = 0.5
    phase = 1
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/combined/examples/mortar/mortar_gradient.i)

#
# Compare a diffusion equation with (c) and without (v) periodic gradient
# constraints and a ramped sloped initial condition and value-periodic diffusion (p)
# without a slope.
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 40
  []
  [secondary_x]
    input = gen
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10
    new_block_name = "secondary_x"
  []
  [primary_x]
    input = secondary_x
    type = LowerDBlockFromSidesetGenerator
    sidesets = '1'
    new_block_id = 12
    new_block_name = "primary_x"
  []
  [secondary_y]
    input = primary_x
    type = LowerDBlockFromSidesetGenerator
    sidesets = '0'
    new_block_id = 11
    new_block_name = "secondary_y"
  []
  [primary_y]
    input = secondary_y
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 13
    new_block_name = "primary_y"
  []
[]

[Functions]
  [./init_slope]
    # slope with a concentration spike close to the lower interface
    type = ParsedFunction
    value = 'if(x>0.4 & x<0.6 & y>0.1 & y<0.3, 3+y, y)'
  [../]
  [./init_flat]
    # no-slope and the same spike
    type = ParsedFunction
    value = 'if(x>0.4 & x<0.6 & y>0.1 & y<0.3, 3, 0)'
  [../]
[]

[Variables]
  # gradient constrained concentration
  [./c]
    order = FIRST
    family = LAGRANGE
    block = 0
    [./InitialCondition]
      type = FunctionIC
      function = init_slope
    [../]
  [../]

  # unconstrained concentrarion
  [./v]
    order = FIRST
    family = LAGRANGE
    block = 0
    [./InitialCondition]
      type = FunctionIC
      function = init_slope
    [../]
  [../]

  # flat value periodic diffusion
  [./p]
    order = FIRST
    family = LAGRANGE
    block = 0
    [./InitialCondition]
      type = FunctionIC
      function = init_flat
    [../]
  [../]

  # Lagrange multipliers for gradient component in the horizontal directon
  [./lm_left_right_x]
    order = FIRST
    family = LAGRANGE
    block = "secondary_x"
  [../]
  [./lm_left_right_y]
    order = FIRST
    family = LAGRANGE
    block = "secondary_x"
  [../]

  # Lagrange multipliers for gradient component in the vertical directon
  [./lm_up_down_x]
    order = FIRST
    family = LAGRANGE
    block = "secondary_y"
  [../]
  [./lm_up_down_y]
    order = FIRST
    family = LAGRANGE
    block = "secondary_y"
  [../]
[]

[Kernels]
  # the gradient constrained concentration
  [./diff]
    type = Diffusion
    variable = c
    block = 0
  [../]
  [./dt]
    type = TimeDerivative
    variable = c
    block = 0
  [../]

  # the un-constrained concentration
  [./diff2]
    type = Diffusion
    variable = v
    block = 0
  [../]
  [./dt2]
    type = TimeDerivative
    variable = v
    block = 0
  [../]

  # the value periodic concentration
  [./diff3]
    type = Diffusion
    variable = p
    block = 0
  [../]
  [./dt3]
    type = TimeDerivative
    variable = p
    block = 0
  [../]
[]

[Constraints]
  [./equaly_grad_x]
    type = EqualGradientConstraint
    variable = lm_up_down_x
    component = 0
    secondary_variable = c
    secondary_boundary = bottom
    primary_boundary = top
    secondary_subdomain = secondary_y
    primary_subdomain = primary_y
    periodic = true
  [../]
  [./equaly_grad_y]
    type = EqualGradientConstraint
    variable = lm_up_down_y
    component = 1
    secondary_variable = c
    secondary_boundary = bottom
    primary_boundary = top
    secondary_subdomain = secondary_y
    primary_subdomain = primary_y
    periodic = true
  [../]

  [./equalx_grad_x]
    type = EqualGradientConstraint
    variable = lm_left_right_x
    component = 0
    secondary_variable = c
    secondary_boundary = left
    primary_boundary = right
    secondary_subdomain = secondary_x
    primary_subdomain = primary_x
    periodic = true
  [../]
  [./equalx_grad_y]
    type = EqualGradientConstraint
    variable = lm_left_right_y
    component = 1
    secondary_variable = c
    secondary_boundary = left
    primary_boundary = right
    secondary_subdomain = secondary_x
    primary_subdomain = primary_x
    periodic = true
  [../]
[]

[BCs]
  # DiffusionFluxBC is the surface term in the weak form of the Diffusion equation
  [./surface]
    type = DiffusionFluxBC
    boundary = 'top bottom left right'
    variable = c
  [../]
  [./surface2]
    type = DiffusionFluxBC
    boundary = 'top bottom left right'
    variable = v
  [../]

  # for the value periodic diffusion we skip the surface term and apply value PBCs
  [./Periodic]
    [./up_down]
      variable = p
      primary = 0
      secondary = 2
      translation = '0 1 0'
    [../]
    [./left_right]
      variable = p
      primary = 1
      secondary = 3
      translation = '-1 0 0'
    [../]
  [../]
[]

[AuxVariables]
  [./diff_constraint]
    block = 0
  [../]
  [./diff_periodic]
    block = 0
  [../]
  [./diff_slope]
    block = 0
  [../]
  [./slope]
    block = 0
    [./InitialCondition]
      type = FunctionIC
      function = y
    [../]
  [../]
[]

[AuxKernels]
  # difference between the constrained and unconstrained sloped diffusions
  [./diff_constraint]
    type = ParsedAux
    variable = diff_constraint
    function = 'c-v'
    args = 'c v'
    block = 0
  [../]

  # difference between the periodic gradient constrained diffusion and the flat
  # value period diffusien with a constant slope added. This should be the same,
  # but they aren't quite because the gradient constraint affects the gradient in
  # the entire elements (i.e. a larger volume is affected by the gradient constraint
  # compared to the nodal value periodicity)
  [./diff_periodic]
    type = ParsedAux
    variable = diff_periodic
    function = 'c-p-slope'
    args = 'c p slope'
    block = 0
  [../]

  # subtract the constant slope from the gradient periodic simulation (should yield
  # almost p - per the argument above)
  [./diff_slope]
    type = ParsedAux
    variable = diff_slope
    function = 'c-slope'
    args = 'c slope'
    block = 0
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON

  # the shift is necessary to facilitate the solve. The Lagrange multipliers
  # introduce zero-on diaginal blocks, which make the matrix hard to invert.
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       NONZERO               1e-10'

  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-10
  l_tol = 1e-10
  dt = 0.01
  num_steps = 20
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/mass_conservation/mass02.i)

# checking that the mass postprocessor correctly calculates the mass
# 1phase, 2component, constant porosity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 3
  xmin = -1
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [mass_frac_comp0]
  []
[]

[ICs]
  [pinit]
    type = FunctionIC
    function = x
    variable = pp
  []
  [minit]
    type = FunctionIC
    function = 'x*x'
    variable = mass_frac_comp0
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = mass_frac_comp0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp mass_frac_comp0'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'mass_frac_comp0'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [total_mass_0]
    type = PorousFlowFluidMass
  []
  [total_mass_1]
    type = PorousFlowFluidMass
    fluid_component = 1
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = mass02
  csv = true
[]

(test/tests/time_integrators/explicit-euler/ee-2d-linear.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = (x+y)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*(x+y)
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    lumping = true
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[BCs]
  active = 'all'

  [./all]
    type = FunctionDirichletBC
    variable = u
    preset = false
    boundary = '0 1 2 3'
    function = exact_fn
    implicit = true
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'explicit-euler'
  solve_type = 'LINEAR'

  start_time = 0.0
  num_steps = 20
  dt = 0.00005
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/richards/test/tests/dirac/bh_fu_02.i)

# fully-saturated
# production
# fullyupwind
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh02.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = 1
    fully_upwind = true
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 0.5
  dt = 1E-2
  solve_type = NEWTON

[]

[Outputs]
  file_base = bh_fu_02
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/combined/doc/richards/user/excav/ex01.i)

###########################################
#                                         #
#   THIS EXAMPLE CONTAINS AN EXCAVATION   #
#                                         #
###########################################


# Easiest way of figuring out what's happening:
# Run this example, load into paraview, take
# a slice through (0,0,0) with normal (0,0,1),
# colour by pressure and play the animation.


# This mesh has an interior sideset called excav_bdy
[Mesh]
  type = FileMesh
  file = ex01_input.e
[]



# This is a boundary condition acting on excav_bdy
# All it does is to set the pressure to p_excav=0
# at places on excav_bdy wherever excav_fcn tells it to.
[BCs]
  [./excav_bdy]
    type = RichardsExcav
    boundary = excav_bdy
    p_excav = 0.0
    variable = pressure
    excav_geom_function = excav_fcn
  [../]
[]



[Functions]
# excav_fcn controls where to set pressure=p_excav
# You supply start and end positions and times and
# by a linear interpolation these define the position
# of the coal face at all times
  [./excav_fcn]
    type = RichardsExcavGeom
    start_posn = '0 -500 0'
    start_time = 0
    end_posn = '0 500 0'
    end_time = 3E7
  [../]

# mass_bal_fcn calculates the mass balance
  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-fout-mf)/2/(mi+mf))
    vars = 'mi mf fout'
    vals = 'mass_init mass_final flux_out'
  [../]

# initial pressure - unimportant in this example
  [./initial_pressure]
    type = ParsedFunction
    value = -10000*(z-100)
  [../]
[]




# following is needed by postprocessors, kernels, etc
# unimportant in this example
[GlobalParams]
  porepressureNames_UO = PPNames
[]




# following does the calculation of relevant
# masses and mass-flux to the excavation
[Postprocessors]

# note that this is calculated at beginning of timestep
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

# note this is calculated at end of timestep
  [./mass_final]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

# this is what calculates the mass flux to the excavation
# it is calculating it for boundary=excav_bdy, and the
# excavation time-dependence is set through the excav_fcn
  [./flux_out]
    type = RichardsExcavFlow
    boundary = excav_bdy
    variable = pressure
    excav_geom_function = excav_fcn
  [../]

# mass_bal just outputs the result to screen
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]




######################################
#                                    #
#  THE FOLLOWING STUFF IS STANDARD   #
#                                    #
######################################


[UserObjects]
  [./PPNames]
    type = RichardsPorepressureNames
    porepressure_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E+2
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = '1 2 3 4'
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-15 0 0  0 1E-15 0  0 0 1E-15'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 -10'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 6E6
  dt = 3E6
  solve_type = NEWTON
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = ex01
  exodus = true
  csv = true
[]

(modules/richards/test/tests/dirac/bh03.i)

# fully-saturated
# injection
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 1E7
    point_file = bh03.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = -1
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 0
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]

[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 0.5
  dt = 1E-2
  solve_type = NEWTON

[]

[Outputs]
  file_base = bh03
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/relperm/brooks_corey2.i)

# Test Brooks-Corey relative permeability curve by varying saturation over the mesh
# Exponent lambda = 2 for both phases
# Residual saturation of phase 0: s0r = 0.2
# Residual saturation of phase 1: s1r = 0.3

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityBC
    phase = 0
    lambda = 2
    s_res = 0.2
    sum_s_res = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityBC
    phase = 1
    lambda = 2
    nw_phase = true
    s_res = 0.3
    sum_s_res = 0.5
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(test/tests/functions/piecewise_constant_from_csv/piecewise_constant.i)

[Mesh]
  allow_renumbering = false
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1.5 2.4 0.1'
    dy = '1.3 0.9'
    ix = '2 1 1'
    iy = '1 3'
    subdomain_id = '0 1 1
                    2 2 2'
  []
[]

[Variables]
  [u]
  []
[]

[UserObjects]
  [reader_element]
    type = PropertyReadFile
    prop_file_name = 'data_element.csv'
    read_type = 'element'
    nprop = 3  # number of columns in CSV
  []
  [reader_node]
    type = PropertyReadFile
    prop_file_name = 'data_node.csv'
    read_type = 'node'
    nprop = 3  # number of columns in CSV
  []
  [reader_nearest]
    type = PropertyReadFile
    prop_file_name = 'data_nearest.csv'
    read_type = 'voronoi'
    nprop = 3
    nvoronoi = 3
  []
  [reader_block]
    type = PropertyReadFile
    prop_file_name = 'data_nearest.csv'
    read_type = 'block'
    nprop = 3
    nblock = 3
  []
[]

[Functions]
  [element]
    type = PiecewiseConstantFromCSV
    read_prop_user_object = 'reader_element'
    read_type = 'element'
    column_number = '2'
  []
  [node]
    type = PiecewiseConstantFromCSV
    read_prop_user_object = 'reader_node'
    read_type = 'node'
    column_number = '2'
  []
  [nearest]
    type = PiecewiseConstantFromCSV
    read_prop_user_object = 'reader_nearest'
    read_type = 'voronoi'
    column_number = '2'
  []
  [block]
    type = PiecewiseConstantFromCSV
    read_prop_user_object = 'reader_block'
    read_type = 'block'
    column_number = '2'
  []
[]

[ICs]
  active = 'element'
  [element]
    type = FunctionIC
    variable = 'u'
    function = 'element'
  []
  [node]
    type = FunctionIC
    variable = 'u'
    function = 'node'
  []
  [nearest]
    type = FunctionIC
    variable = 'u'
    function = 'nearest'
  []
  [block]
    type = FunctionIC
    variable = 'u'
    function = 'block'
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
[]

[BCs]
  [unity]
    type = DirichletBC
    variable = u
    boundary = 'left bottom'
    value = 1
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Transient
  end_time = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/numerical_diffusion/fltvd_no_antidiffusion.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, but without any antidiffusion
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = none
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-1
  nl_abs_tol = 1E-8
  nl_max_its = 500
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/porous_flow/examples/groundwater/ex01.i)

# Groundwater extraction example.
# System consists of two confined aquifers separated by an aquitard
# There is a hydraulic gradient in the upper aquifer
# A well extracts water from the lower aquifer, and the impact on the upper aquifer is observed
# In the center of the model, the roof of the upper aquifer sits 70m below the local water table

[Mesh]
  [basic_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -50
    xmax = 50
    nx = 20
    ymin = -25
    ymax = 25
    ny = 10
    zmin = -100
    zmax = -70
    nz = 3
  []
  [lower_aquifer]
    type = SubdomainBoundingBoxGenerator
    input = basic_mesh
    block_id = 1
    block_name = lower_aquifer
    bottom_left = '-1000 -500 -100'
    top_right = '1000 500 -90'
  []
  [aquitard]
    type = SubdomainBoundingBoxGenerator
    input = lower_aquifer
    block_id = 2
    block_name = aquitard
    bottom_left = '-1000 -500 -90'
    top_right = '1000 500 -80'
  []
  [upper_aquifer]
    type = SubdomainBoundingBoxGenerator
    input = aquitard
    block_id = 3
    block_name = upper_aquifer
    bottom_left = '-1000 -500 -80'
    top_right = '1000 500 -70'
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = insitu_pp
  []
[]

[BCs]
  [pp]
    type = FunctionDirichletBC
    variable = pp
    function = insitu_pp
    boundary = 'left right top bottom front back'
  []
[]

[Functions]
  [upper_aquifer_head]
    type = ParsedFunction
    value = '10 + x / 200'
  []
  [lower_aquifer_head]
    type = ParsedFunction
    value = '20'
  []
  [insitu_head]
    type = ParsedFunction
    vals = 'lower_aquifer_head upper_aquifer_head'
    vars = 'low up'
    value = 'if(z <= -90, low, if(z >= -80, up, (up * (z + 90) - low * (z + 80)) / (10.0)))'
  []
  [insitu_pp]
    type = ParsedFunction
    vals = 'insitu_head'
    vars = 'h'
    value = '(h - z) * 1E4'
  []
  [l_rate]
    type = ParsedFunction
    vals = 'm3_produced dt'
    vars = 'm3_produced dt'
    value = '1000 * m3_produced / dt'
  []
[]

[AuxVariables]
  [insitu_head]
  []
  [head_change]
  []
[]

[AuxKernels]
  [insitu_head]
    type = FunctionAux
    variable = insitu_head
    function = insitu_head
  []
  [head_change]
    type = ParsedAux
    args = 'pp insitu_head'
    use_xyzt = true
    function = 'pp / 1E4 + z - insitu_head'
    variable = head_change
  []
[]

[Postprocessors]
  [m3_produced]
    type = PorousFlowPlotQuantity
    uo = volume_extracted
    outputs = 'none'
  []
  [dt]
    type = TimestepSize
    outputs = 'none'
  []
  [l_per_s]
    type = FunctionValuePostprocessor
    function = l_rate
  []
[]

[VectorPostprocessors]
  [drawdown]
    type = LineValueSampler
    variable = head_change
    start_point = '-50 0 -75'
    end_point = '50 0 -75'
    num_points = 101
    sort_by = x
  []
[]

[PorousFlowBasicTHM]
  fp = simple_fluid
  gravity = '0 0 -10'
  porepressure = pp
  multiply_by_density = false
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      # the following mean that density = 1000 * exp(P / 1E15) ~ 1000
      thermal_expansion = 0
      bulk_modulus = 1E15
    []
  []
[]

[Materials]
  [porosity_aquifers]
    type = PorousFlowPorosityConst
    porosity = 0.05
    block = 'upper_aquifer lower_aquifer'
  []
  [porosity_aquitard]
    type = PorousFlowPorosityConst
    porosity = 0.2
    block = aquitard
  []
  [biot_mod]
    type = PorousFlowConstantBiotModulus
    fluid_bulk_modulus = 2E9
    biot_coefficient = 1.0
  []
  [permeability_aquifers]
    type = PorousFlowPermeabilityConst
    permeability = '1E-12 0 0 0 1E-12 0 0 0 1E-12'
    block = 'upper_aquifer lower_aquifer'
  []
  [permeability_aquitard]
    type = PorousFlowPermeabilityConst
    permeability = '1E-16 0 0 0 1E-16 0 0 0 1E-17'
    block = aquitard
  []
[]

[DiracKernels]
  [sink]
    type = PorousFlowPolyLineSink
    SumQuantityUO = volume_extracted
    point_file = ex01.bh_lower
    line_length = 10
    variable = pp
    # following produces a flux of 0 m^3(water)/m(borehole length)/s if porepressure = 0, and a flux of 1 m^3/m/s if porepressure = 1E9
    p_or_t_vals = '0 1E9'
    fluxes = '0 1'
  []
[]

[UserObjects]
  [volume_extracted]
    type = PorousFlowSumQuantity
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  [TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 1.1E5
  []
  end_time = 3.456E5 # 4 days
  nl_abs_tol = 1E-13
[]

[Outputs]
  [csv]
    type = CSV
    file_base = ex01_lower_extraction
    execute_on = final
  []
[]

(modules/phase_field/examples/multiphase/DerivativeMultiPhaseMaterial.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 40
  ny = 40
  nz = 0
  xmin = -12
  xmax = 12
  ymin = -12
  ymax = 12
  elem_type = QUAD4
[]

[GlobalParams]
  # let's output all material properties for demonstration purposes
  outputs = exodus

  # prefactor on the penalty function kernels. The higher this value is, the
  # more rigorously the constraint is enforced
  penalty = 1e3
[]

#
# These AuxVariables hold the directly calculated free energy density in the
# simulation cell. They are provided for visualization purposes.
#
[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./cross_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./local_free_energy]
    type = TotalFreeEnergy
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
    additional_free_energy = cross_energy
  [../]

  #
  # Helper kernel to cpompute the gradient contribution from interfaces of order
  # parameters evolved using the ACMultiInterface kernel
  #
  [./cross_terms]
    type = CrossTermGradientFreeEnergy
    variable = cross_energy
    interfacial_vars = 'eta1 eta2 eta3'
    #
    # The interface coefficient matrix. This should be symmetrical!
    #
    kappa_names = 'kappa11 kappa12 kappa13
                   kappa21 kappa22 kappa23
                   kappa31 kappa32 kappa33'
  [../]
[]

[Variables]
  [./c]
    order = FIRST
    family = LAGRANGE
    #
    # We set up a smooth cradial concentrtaion gradient
    # The concentration will quickly change to adapt to the preset order
    # parameters eta1, eta2, and eta3
    #
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = 0.0
      y1 = 0.0
      radius = 5.0
      invalue = 1.0
      outvalue = 0.01
      int_width = 10.0
    [../]
  [../]

  [./eta1]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      #
      # Note: this initial conditions sets up a _sharp_ interface. Ideally
      # we should start with a smooth interface with a width consistent
      # with the kappa parameter supplied for the given interface.
      #
      function = 'r:=sqrt(x^2+y^2);if(r<=4,1,0)'
    [../]
  [../]
  [./eta2]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt(x^2+y^2);if(r>4&r<=7,1,0)'
    [../]
  [../]
  [./eta3]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt(x^2+y^2);if(r>7,1,0)'
    [../]
  [../]
[]

[Kernels]
  #
  # Cahn-Hilliard kernel for the concentration variable.
  # Note that we are not using an interfcae kernel on this variable, but rather
  # rely on the interface width enforced on the order parameters. This allows us
  # to use a direct solve using the CahnHilliard kernel _despite_ only using first
  # order elements.
  #
  [./c_res]
    type = CahnHilliard
    variable = c
    f_name = F
    args = 'eta1 eta2 eta3'
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]

  #
  # Order parameter eta1
  # Each order parameter is acted on by 4 kernels:
  #  1. The stock time derivative deta_i/dt kernel
  #  2. The Allen-Cahn kernel that takes a Dervative Material for the free energy
  #  3. A gradient interface kernel that includes cross terms
  #     see http://mooseframework.org/wiki/PhysicsModules/PhaseField/DevelopingModels/MultiPhaseModels/ACMultiInterface/
  #  4. A penalty contribution that forces the interface contributions h(eta)
  #     to sum up to unity
  #
  [./deta1dt]
    type = TimeDerivative
    variable = eta1
  [../]
  [./ACBulk1]
    type = AllenCahn
    variable = eta1
    args = 'eta2 eta3 c'
    mob_name = L1
    f_name = F
  [../]
  [./ACInterface1]
    type = ACMultiInterface
    variable = eta1
    etas = 'eta1 eta2 eta3'
    mob_name = L1
    kappa_names = 'kappa11 kappa12 kappa13'
  [../]
  [./penalty1]
    type = SwitchingFunctionPenalty
    variable = eta1
    etas    = 'eta1 eta2 eta3'
    h_names = 'h1   h2   h3'
  [../]

  #
  # Order parameter eta2
  #
  [./deta2dt]
    type = TimeDerivative
    variable = eta2
  [../]
  [./ACBulk2]
    type = AllenCahn
    variable = eta2
    args = 'eta1 eta3 c'
    mob_name = L2
    f_name = F
  [../]
  [./ACInterface2]
    type = ACMultiInterface
    variable = eta2
    etas = 'eta1 eta2 eta3'
    mob_name = L2
    kappa_names = 'kappa21 kappa22 kappa23'
  [../]
  [./penalty2]
    type = SwitchingFunctionPenalty
    variable = eta2
    etas    = 'eta1 eta2 eta3'
    h_names = 'h1   h2   h3'
  [../]

  #
  # Order parameter eta3
  #
  [./deta3dt]
    type = TimeDerivative
    variable = eta3
  [../]
  [./ACBulk3]
    type = AllenCahn
    variable = eta3
    args = 'eta1 eta2 c'
    mob_name = L3
    f_name = F
  [../]
  [./ACInterface3]
    type = ACMultiInterface
    variable = eta3
    etas = 'eta1 eta2 eta3'
    mob_name = L3
    kappa_names = 'kappa31 kappa32 kappa33'
  [../]
  [./penalty3]
    type = SwitchingFunctionPenalty
    variable = eta3
    etas    = 'eta1 eta2 eta3'
    h_names = 'h1   h2   h3'
  [../]
[]

[BCs]
  [./Periodic]
    [./All]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Materials]
  # here we declare some of the model parameters: the mobilities and interface
  # gradient prefactors. For this example we use arbitrary numbers. In an actual simulation
  # physical mobilities would be used, and the interface gradient prefactors would
  # be readjusted to the free energy magnitudes.
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M   kappa_c L1 L2 L3  kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
    prop_values = '0.2 0.75    1  1  1   0.75    0.75    0.75    0.75    0.75    0.75    0.75    0.75    0.75   '
  [../]

  # This material sums up the individual phase contributions. It is written to the output file
  # (see GlobalParams section above) and can be used to check the constraint enforcement.
  [./etasummat]
    type = ParsedMaterial
    f_name = etasum
    args = 'eta1 eta2 eta3'
    material_property_names = 'h1 h2 h3'
    function = 'h1+h2+h3'
  [../]

  # The phase contribution factors for each material point are computed using the
  # SwitchingFunctionMaterials. Each phase with an order parameter eta contributes h(eta)
  # to the global free energy density. h is a function that switches smoothly from 0 to 1
  [./switching1]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
    h_order = SIMPLE
  [../]
  [./switching2]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
    h_order = SIMPLE
  [../]
  [./switching3]
    type = SwitchingFunctionMaterial
    function_name = h3
    eta = eta3
    h_order = SIMPLE
  [../]

  # The barrier function adds a phase transformation energy barrier. It also
  # Drives order parameters toward the [0:1] interval to avoid negative or larger than 1
  # order parameters (these are set to 0 and 1 contribution by the switching functions
  # above)
  [./barrier]
    type = MultiBarrierFunctionMaterial
    etas = 'eta1 eta2 eta3'
  [../]

  # We use DerivativeParsedMaterials to specify three (very) simple free energy
  # expressions for the three phases. All necessary derivatives are built automatically.
  # In a real problem these expressions can be arbitrarily complex (or even provided
  # by custom kernels).
  [./phase_free_energy_1]
    type = DerivativeParsedMaterial
    f_name = F1
    function = '(c-1)^2'
    args = 'c'
  [../]
  [./phase_free_energy_2]
    type = DerivativeParsedMaterial
    f_name = F2
    function = '(c-0.5)^2'
    args = 'c'
  [../]
  [./phase_free_energy_3]
    type = DerivativeParsedMaterial
    f_name = F3
    function = 'c^2'
    args = 'c'
  [../]

  # The DerivativeMultiPhaseMaterial ties the phase free energies together into a global free energy.
  # http://mooseframework.org/wiki/PhysicsModules/PhaseField/DevelopingModels/MultiPhaseModels/
  [./free_energy]
    type = DerivativeMultiPhaseMaterial
    f_name = F
    # we use a constant free energy (GeneriConstantmaterial property Fx)
    fi_names = 'F1  F2  F3'
    hi_names = 'h1  h2  h3'
    etas     = 'eta1 eta2 eta3'
    args = 'c'
    W = 1
  [../]
[]

[Postprocessors]
  # The total free energy of the simulation cell to observe the energy reduction.
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    variable = local_energy
  [../]

  # for testing we also monitor the total solute amount, which should be conserved.
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    variable = c
  [../]
[]

[Preconditioning]
  # This preconditioner makes sure the Jacobian Matrix is fully populated. Our
  # kernels compute all Jacobian matrix entries.
  # This allows us to use the Newton solver below.
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'

  # Automatic differentiation provedes a _full_ Jacobian in this example
  # so we can safely use NEWTON for a fast solve
  solve_type = 'NEWTON'

  l_max_its = 15
  l_tol = 1.0e-6

  nl_max_its = 50
  nl_rel_tol = 1.0e-6
  nl_abs_tol = 1.0e-6

  start_time = 0.0
  end_time   = 150.0

  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.1
  [../]
[]

[Debug]
  # show_var_residual_norms = true
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

(modules/richards/test/tests/dirac/bh_fu_05.i)

# unsaturated
# injection
# fullyupwind
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '500 500 1E1'
    x = '4000 5000 6500'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh03.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = -1
    fully_upwind = true
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = -2E5
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]

[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 6500
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  file_base = bh_fu_05
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(test/tests/time_integrators/rk-2/1d-linear.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 20
  elem_type = EDGE2
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = ExplicitMidpoint
  [../]
  solve_type = 'LINEAR'

  start_time = 0.0
  num_steps = 10
  dt = 0.001
  l_tol = 1e-15
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(test/tests/materials/derivative_material_interface/construction_order.i)

#
# Test the the getDefaultMaterialProperty in DerivativeMaterialInterface.
# This test should only pass, if the construction order of the Materials
# using this interface does not influence the outcome.
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 0.1
  elem_type = QUAD4
[]

[GlobalParams]
  derivative_order = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
[]

[Kernels]
  [./dummy1]
    type = Diffusion
    variable = c
  [../]
  [./dummy2]
    type = TimeDerivative
    variable = c
  [../]
[]

[Materials]
  # derivatives used both before and after being declared
  [./sum_a_1]
    type = DerivativeSumMaterial
    f_name = Fa1
    sum_materials = 'Fa'
    args = 'c'
    outputs = exodus
  [../]
  [./free_energy_a]
    type = DerivativeParsedMaterial
    f_name = Fa
    args = 'c'
    function = 'c^4'
  [../]
  [./sum_a_2]
    type = DerivativeSumMaterial
    f_name = Fa2
    sum_materials = 'Fa'
    args = 'c'
    outputs = exodus
  [../]

  # derivatives declared after being used
  [./sum_b_1]
    type = DerivativeSumMaterial
    f_name = Fb1
    sum_materials = 'Fb'
    args = 'c'
    outputs = exodus
  [../]
  [./free_energy_b]
    type = DerivativeParsedMaterial
    f_name = Fb
    args = 'c'
    function = 'c^4'
  [../]

  # derivatives declared before being used
  [./free_energy_c]
    type = DerivativeParsedMaterial
    f_name = Fc
    args = 'c'
    function = 'c^4'
  [../]
  [./sum_c_2]
    type = DerivativeSumMaterial
    f_name = Fc2
    sum_materials = 'Fc'
    args = 'c'
    outputs = exodus
  [../]

  # non-existing derivatives
  [./free_energy_d]
    type = ParsedMaterial
    f_name = Fd
    args = 'c'
    function = 'c^4'
  [../]
  [./sum_d_1]
    type = DerivativeSumMaterial
    f_name = Fd1
    sum_materials = 'Fd'
    args = 'c'
    outputs = exodus
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2

  solve_type = 'NEWTON'
  num_steps = 1
  dt = 1e-5
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(modules/phase_field/test/tests/misc/interface_grad.i)

#
# Test a gradient continuity interfacekernel
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    ymax = 0.5
  []
  [./box1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.51 1 0'
    input = gen
  [../]
  [./box2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.49 0 0'
    top_right = '1 1 0'
    input = box1
  [../]
  [./iface_u]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = 10
    input = box2
  [../]
  [./iface_v]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 2
    paired_block = 1
    new_boundary = 11
    input = iface_u
  [../]
[]

[Variables]
  [./u]
    block = 1
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.4)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
  [./v]
    block = 2
    initial_condition = 0.8
  [../]
[]

[Kernels]
  [./u_diff]
    type = Diffusion
    variable = u
    block = 1
  [../]
  [./u_dt]
    type = TimeDerivative
    variable = u
    block = 1
  [../]
  [./v_diff]
    type = Diffusion
    variable = v
    block = 2
  [../]
  [./v_dt]
    type = TimeDerivative
    variable = v
    block = 2
  [../]
[]

[InterfaceKernels]
  [./iface]
    type = InterfaceDiffusionFluxMatch
    variable = u
    boundary = 10
    neighbor_var = v
  [../]
[]

[BCs]
  [./u_boundary_term]
    type = DiffusionFluxBC
    variable = u
    boundary = 10
  [../]
  [./v_boundary_term]
    type = DiffusionFluxBC
    variable = v
    boundary = 11
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.002
  num_steps = 10
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(test/tests/materials/functor_properties/1d_dirichlet.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmax = 2
[]

[Variables]
  [v]
    type = MooseVariableFVReal
  []
[]

[AuxVariables]
  [sink]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [sink]
    type = FunctionIC
    variable = sink
    function = 'x^3'
  []
[]


[FVKernels]
  [diff]
    type = FVDiffusion
    variable = v
    coeff = 1
  []
  [sink]
    type = FVFunctorElementalKernel
    variable = v
    functor_name = 'sink_mat'
  []
[]

[FVBCs]
  [bounds]
    type = FVDirichletBC
    variable = v
    boundary = 'left right'
    value = 0
  []
[]

[Materials]
  active = 'functor'
  [functor]
    type = ADGenericFunctorMaterial
    prop_names = sink_mat
    prop_values = sink
  []
  [overlapping_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'sink_mat'
    prop_values = v
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/relperm/corey4.i)

# Test Corey relative permeability curve by varying saturation over the mesh
# Residual saturation of phase 0: s0r = 0.2
# Residual saturation of phase 1: s1r = 0.3

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [p0]
    initial_condition = 1e6
  []
  [s1]
    family = LAGRANGE
    order = FIRST
  []
[]

[AuxVariables]
  [s0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [s1aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr0aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [kr1aux]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  []
  [s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  []
  [kr0]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 0
    variable = kr0aux
  []
  [kr1]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = kr1aux
  []
[]

[Functions]
  [s1]
    type = ParsedFunction
    value = x
  []
[]

[ICs]
  [s1]
    type = FunctionIC
    variable = s1
    function = s1
  []
[]

[Kernels]
  [p0]
    type = Diffusion
    variable = p0
  []
  [s1]
    type = Diffusion
    variable = s1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  []
  [kr0]
    type = PorousFlowRelativePermeabilityCorey
    scaling = 0.1
    phase = 0
    n = 2
    s_res = 0.2
    sum_s_res = 0.5
  []
  [kr1]
    type = PorousFlowRelativePermeabilityCorey
    scaling = 10.0
    phase = 1
    n = 2
    s_res = 0.3
    sum_s_res = 0.5
  []
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    variable = 's0aux s1aux kr0aux kr1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 20
    sort_by = id
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-8
[]

[BCs]
  [sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  []
  [sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/hysteresis/hys_sat_01.i)

# 1-phase hysteresis.  Saturation calculation.  Primary drying curve with low_extension_type = none
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 10
    nx = 100
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = pp
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1 - x'
  []
[]

[BCs]
  [pp]
    type = FunctionDirichletBC
    variable = pp
    function = '1 - x'
    boundary = 'left right'
  []
[]

[Kernels]
  [dummy]
    type = Diffusion
    variable = pp
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
  []
  [saturation_calculator]
    type = PorousFlow1PhaseHysP
    alpha_d = 10.0
    alpha_w = 10.0
    n_d = 1.1
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 7.0
    low_extension_type = none
    porepressure = pp
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [saturation]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [saturation]
    type = PorousFlowPropertyAux
    variable = saturation
    property = saturation
    phase = 0
  []
[]

[VectorPostprocessors]
  [sat]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0.5 0 0'
    end_point = '9.5 0 0'
    num_points = 10
    sort_by = x
    variable = 'saturation pp'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/hysteresis/hys_sat_02.i)

# 1-phase hysteresis.  Saturation calculation.  Primary drying curve with low_extension_type = quadratic
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 10
    nx = 100
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = pp
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1 - x'
  []
[]

[BCs]
  [pp]
    type = FunctionDirichletBC
    variable = pp
    function = '1 - x'
    boundary = 'left right'
  []
[]

[Kernels]
  [dummy]
    type = Diffusion
    variable = pp
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
  []
  [saturation_calculator]
    type = PorousFlow1PhaseHysP
    alpha_d = 10.0
    alpha_w = 10.0
    n_d = 1.1
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 7.0
    low_extension_type = quadratic
    porepressure = pp
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [saturation]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [saturation]
    type = PorousFlowPropertyAux
    variable = saturation
    property = saturation
    phase = 0
  []
[]

[VectorPostprocessors]
  [sat]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0.5 0 0'
    end_point = '9.5 0 0'
    num_points = 10
    sort_by = x
    variable = 'saturation pp'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(test/tests/scaling/residual-based/residual-based-two-var.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = '1000 * (1 - x)'
  []
  [v]
    type = FunctionIC
    variable = v
    function = '1e-3 * (1 - x)'
  []
[]

[Variables]
  [u][]
  [v][]
[]

[Problem]
  type = ReferenceResidualProblem
  extra_tag_vectors = 'ref'
  reference_vector = 'ref'
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
    extra_vector_tags = 'ref'
  [../]
  [rxn]
    type = PReaction
    power = 2
    variable = u
    extra_vector_tags = 'ref'
  []
  [./diff_v]
    type = Diffusion
    variable = v
    extra_vector_tags = 'ref'
  [../]
  [rxn_v]
    type = PReaction
    power = 2
    variable = v
    extra_vector_tags = 'ref'
  []
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 1000
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 0
  [../]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1e-3
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  verbose = true
  automatic_scaling = true
  resid_vs_jac_scaling_param = 1
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialMultiphase.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  xmin = -20
  xmax = 20
  ymin = -20
  ymax = 20
[]

[GlobalParams]
  op_num = 2
  var_name_base = etab
[]

[Variables]
  [./w]
  [../]
  [./etaa0]
  [../]
  [./etab0]
  [../]
  [./etab1]
  [../]
[]

[AuxVariables]
  [./bnds]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]

  [./IC_etaa0]
    type = FunctionIC
    variable = etaa0
    function = ic_func_etaa0
  [../]
  [./IC_etab0]
    type = FunctionIC
    variable = etab0
    function = ic_func_etab0
  [../]
  [./IC_etab1]
    type = FunctionIC
    variable = etab1
    function = ic_func_etab1
  [../]
  [./IC_w]
    type = ConstantIC
    value = -0.05
    variable = w
  [../]
[]

[Functions]
  [./ic_func_etaa0]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2);0.5*(1.0-tanh((r-10.0)/sqrt(2.0)))'
  [../]
  [./ic_func_etab0]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2);0.5*(1.0+tanh((r-10)/sqrt(2.0)))*0.5*(1.0+tanh((y)/sqrt(2.0)))'
  [../]
  [./ic_func_etab1]
    type = ParsedFunction
    value = 'r:=sqrt(x^2+y^2);0.5*(1.0+tanh((r-10)/sqrt(2.0)))*0.5*(1.0-tanh((y)/sqrt(2.0)))'
  [../]
[]


[BCs]
[]

[Kernels]
# Order parameter eta_alpha0
  [./ACa0_bulk]
    type = ACGrGrMulti
    variable = etaa0
    v =           'etab0 etab1'
    gamma_names = 'gab   gab'
  [../]
  [./ACa0_sw]
    type = ACSwitching
    variable = etaa0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etab0 etab1 w'
  [../]
  [./ACa0_int]
    type = ACInterface
    variable = etaa0
    kappa_name = kappa
  [../]
  [./ea0_dot]
    type = TimeDerivative
    variable = etaa0
  [../]
# Order parameter eta_beta0
  [./ACb0_bulk]
    type = ACGrGrMulti
    variable = etab0
    v =           'etaa0 etab1'
    gamma_names = 'gab   gbb'
  [../]
  [./ACb0_sw]
    type = ACSwitching
    variable = etab0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etaa0 etab1 w'
  [../]
  [./ACb0_int]
    type = ACInterface
    variable = etab0
    kappa_name = kappa
  [../]
  [./eb0_dot]
    type = TimeDerivative
    variable = etab0
  [../]
# Order parameter eta_beta1
  [./ACb1_bulk]
    type = ACGrGrMulti
    variable = etab1
    v =           'etaa0 etab0'
    gamma_names = 'gab   gbb'
  [../]
  [./ACb1_sw]
    type = ACSwitching
    variable = etab1
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etaa0 etab0 w'
  [../]
  [./ACb1_int]
    type = ACInterface
    variable = etab1
    kappa_name = kappa
  [../]
  [./eb1_dot]
    type = TimeDerivative
    variable = etab1
  [../]
#Chemical potential
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
    args = '' # in this case chi (the susceptibility) is simply a constant
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = Dchi
    args = ''
  [../]
  [./coupled_etaa0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etaa0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0 etab1'
  [../]
  [./coupled_etab0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0 etab1'
  [../]
  [./coupled_etab1dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab1
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0 etab1'
  [../]
[]

[AuxKernels]
  [./BndsCalc]
    type = BndsCalcAux
    variable = bnds
    execute_on = timestep_end
  [../]
[]

# enable_jit set to false in many materials to make this test start up faster.
# It is recommended to set enable_jit = true or just remove these lines for
# production runs with this model
[Materials]
  [./ha]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = ha
    all_etas = 'etaa0 etab0 etab1'
    phase_etas = 'etaa0'
  [../]
  [./hb]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hb
    all_etas = 'etaa0 etab0 etab1'
    phase_etas = 'etab0 etab1'
  [../]
  [./omegaa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegaa
    material_property_names = 'Vm ka caeq'
    function = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
    derivative_order = 2
    enable_jit = false
  [../]
  [./omegab]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegab
    material_property_names = 'Vm kb cbeq'
    function = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
    derivative_order = 2
    enable_jit = false
  [../]
  [./rhoa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhoa
    material_property_names = 'Vm ka caeq'
    function = 'w/Vm^2/ka + caeq/Vm'
    derivative_order = 2
    enable_jit = false
  [../]
  [./rhob]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhob
    material_property_names = 'Vm kb cbeq'
    function = 'w/Vm^2/kb + cbeq/Vm'
    derivative_order = 2
    enable_jit = false
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'kappa_c  kappa   L   D    chi  Vm   ka    caeq kb    cbeq  gab gbb mu'
    prop_values = '0        1       1.0 1.0  1.0  1.0  10.0  0.1  10.0  0.9   4.5 1.5 1.0'
  [../]
  [./Mobility]
    type = DerivativeParsedMaterial
    f_name = Dchi
    material_property_names = 'D chi'
    function = 'D*chi'
    derivative_order = 2
    enable_jit = false
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  lu           1'
  l_tol = 1.0e-3
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1e-8
  num_steps = 2
  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.1
  [../]

[]

[Outputs]
  exodus = true
[]

(test/tests/time_integrators/tvdrk2/1d-linear.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 20
  elem_type = EDGE2
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = x
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*x
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = ic
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = ExplicitTVDRK2
  [../]
  solve_type = 'LINEAR'

  start_time = 0.0
  num_steps = 10
  dt = 0.001
  l_tol = 1e-15
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(test/tests/restart/restart_subapp_not_master/complete_solve_no_subapp.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./average]
    type = ElementAverageValue
    variable = u
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0.0
  end_time = 4.0
  dt = 1.0
[]

[Outputs]
  file_base = complete_solve_no_subapp
  exodus = true
[]

(modules/geochemistry/test/tests/kernels/advection_1.i)

# A step-like initial concentration is advected to the right using a constant velocity.
# Because of the Dirichlet BC on the left, the step-like concentration profile is maintained (up to the usual numerical diffusion)
# Because upwinding_type=full in the ConservativeAdvection Kernel, there are no overshoots and undershoots
# The total amount of "conc" should increase by dt * velocity every timestep, as recorded by the front_position Postprocessor
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
[]

[Variables]
  [conc]
  []
[]

[ICs]
  [conc]
    type = FunctionIC
    function = 'if(x<=0.25, 1, 0)'
    variable = conc
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1.0
    variable = conc
  []
[]

[Kernels]
  [dot]
    type = GeochemistryTimeDerivative
    variable = conc
  []
  [adv]
    type = ConservativeAdvection
    velocity = velocity
    upwinding_type = full
    variable = conc
  []
[]

[AuxVariables]
  [velocity]
    family = MONOMIAL_VEC
    order = CONSTANT
  []
[]

[AuxKernels]
  [velocity]
    type = VectorFunctionAux
    function = vel_fcn
    variable = velocity
  []
[]

[Functions]
  [vel_fcn]
    type = ParsedVectorFunction
    value_x = 1
    value_y = 0
    value_z = 0
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.01
  end_time = 0.1
[]

[Postprocessors]
  [front_position]
    type = ElementIntegralVariablePostprocessor
    variable = conc
  []
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/examples/restart/gravityeq.i)

# Initial run to establish gravity equilibrium. As only brine is present (no gas),
# we can use the single phase equation of state and kernels, reducing the computational
# cost. An estimate of the hydrostatic pressure gradient is used as the initial condition
# using an approximate brine density of 1060 kg/m^3.
# The end time is set to a large value (~100 years) to allow the pressure to reach
# equilibrium. Steady state detection is used to halt the run when a steady state is reached.

[Mesh]
  type = GeneratedMesh
  dim = 2
  ny = 10
  nx = 10
  ymax = 100
  xmax = 5000
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -9.81 0'
  temperature_unit = Celsius
[]

[Variables]
  [porepressure]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    function = ppic
    variable = porepressure
  []
[]

[Functions]
  [ppic]
    type = ParsedFunction
    value = '10e6 + 1060*9.81*(100-y)'
  []
[]

[BCs]
  [top]
    type = DirichletBC
    variable = porepressure
    value = 10e6
    boundary = top
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 50
  []
  [xnacl]
    initial_condition = 0.1
  []
  [brine_density]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = porepressure
  []
  [flux0]
    type = PorousFlowFullySaturatedDarcyFlow
    variable = porepressure
  []
[]

[AuxKernels]
  [brine_density]
    type = PorousFlowPropertyAux
    property = density
    variable = brine_density
    execute_on = 'initial timestep_end'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = porepressure
    number_fluid_phases = 1
    number_fluid_components = 1
  []
[]

[Modules]
  [FluidProperties]
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [ps]
    type = PorousFlow1PhaseFullySaturated
    porepressure = porepressure
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [brine]
    type = PorousFlowBrine
    compute_enthalpy = false
    compute_internal_energy = false
    xnacl = xnacl
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-13 0 0 0 1e-13 0  0 0 1e-13'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 3e9
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-06
  steady_state_detection = true
  steady_state_tolerance = 1e-12
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e1
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  perf_graph = true
[]

(modules/phase_field/test/tests/functions/fourier_noise.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [./c]
  [../]
[]

[Functions]
  [./fn]
    type = FourierNoise
    lambda = 0.2
  [../]
[]

[ICs]
  [./c]
    type = FunctionIC
    variable = c
    function = fn
  [../]
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(test/tests/userobjects/shape_element_user_object/jacobian_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  parallel_type = replicated
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = (x-0.5)^2
    [../]
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = (x-0.5)^2
    [../]
  [../]
  [./w]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = (x-0.5)^2
    [../]
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./shape_w]
    type = ExampleShapeElementKernel2
    user_object = example_uo
    v = v
    u = u
    variable = w
  [../]
  [./time_w]
    type = TimeDerivative
    variable = w
  [../]
  [./time_u]
    type = TimeDerivative
    variable = u
  [../]
  [./time_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[UserObjects]
  [./example_uo]
    type = ExampleShapeElementUserObject
    u = u
    v = v
    # as this userobject computes quantities for both the residual AND the jacobian
    # it needs to have these execute_on flags set.
    execute_on = 'linear nonlinear'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    #off_diag_row =    'w w'
    #off_diag_column = 'v u'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options = '-snes_test_display'
  petsc_options_iname = '-snes_type'
  petsc_options_value = 'test'
  dt = 0.1
  num_steps = 2
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/richards/test/tests/dirac/bh_lumped_07.i)

[Mesh]
  type = FileMesh
  file = bh07_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1000 10000'
    x = '100 1000'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[BCs]
  [./fix_outer]
    type = DirichletBC
    boundary = perimeter
    variable = pressure
    value = 1E7
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsLumpedMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh07.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    re_constant = 0.1594
    character = 2
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
    execute_on = 'initial timestep_end'
  [../]

  [./fluid_mass]
    type = RichardsMass
    variable = pressure
    execute_on = 'initial timestep_end'
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-11 0 0  0 1E-11 0  0 0 1E-11'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1000
  solve_type = NEWTON

  [./TimeStepper]
    # get only marginally better results for smaller time steps
    type = FunctionDT
    function = dts
  [../]

[]

[Outputs]
  file_base = bh_lumped_07
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
[]

(modules/richards/test/tests/buckley_leverett/bl22_lumped_fu.i)

# two-phase version
# super-sharp front version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1E-4 1E-3 1E-2 2E-2 5E-2 6E-2 0.1 0.2'
    x = '0    1E-2 1E-1 1    5    20   40  41'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-4
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-4
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
  [./bounds_dummy]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsLumpedMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFullyUpwindFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsLumpedMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFullyUpwindFlux
    variable = pgas
  [../]
  [./richardsppenalty]
    type = RichardsPPenalty
    variable = pgas
    a = 1E-18
    lower_var = pwater
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_water
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_gas
  [../]
[]

[BCs]
  [./left_w]
    type = DirichletBC
    variable = pwater
    boundary = left
    value = 1E6
  [../]
  [./left_g]
    type = DirichletBC
    variable = pgas
    boundary = left
    value = 1000
  [../]
  [./right_w]
    type = DirichletBC
    variable = pwater
    boundary = right
    value = -100000
  [../]
  [./right_g]
    type = DirichletBC
    variable = pgas
    boundary = right
    value = 0
  [../]
[]


[Functions]
  [./initial_water]
    type = ParsedFunction
    value = 1000000*(1-min(x/5,1))-if(x<5,0,100000)
  [../]
  [./initial_gas]
    type = ParsedFunction
    value = 1000
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    viscosity = '1E-3 1E-6'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]

  [./standard]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-10 1E-10 20 1E-10 1E-100'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 50

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = bl22_lumped_fu
  [./exodus]
    type = Exodus
    interval = 100000
    hide = 'pgas bounds_dummy'
    execute_on = 'initial final timestep_end'
  [../]
[]

(modules/porous_flow/test/tests/hysteresis/hys_pc_1.i)

# Capillary-pressure calculation.  First-order wetting curve
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
# Also, when using info_required=sat, remember that: (1) the hysteretic capillary pressure is not invertible if no high extension is used; (2) if saturation exceeds the turning point (eg sat <= 0.1) then the drying curve will be used
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 100
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = ''
  []
[]

[Variables]
  [sat]
  []
[]

[ICs]
  [sat]
    type = FunctionIC
    variable = sat
    function = 'x'
  []
[]

[BCs]
  [sat]
    type = FunctionDirichletBC
    variable = sat
    function = 'x'
    boundary = 'left right'
  []
[]


[Kernels]
  [dummy]
    type = Diffusion
    variable = sat
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
    initial_order = 1
    previous_turning_points = 0.1
  []
  [pc_calculator]
    type = PorousFlowHystereticInfo
    alpha_d = 10.0
    alpha_w = 7.0
    n_d = 1.5
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 12.0
    high_ratio = 0.9
    low_extension_type = none
    high_extension_type = none
    sat_var = sat
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [pc]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [pc]
    type = PorousFlowPropertyAux
    variable = pc
    property = hysteretic_info
  []
[]

[VectorPostprocessors]
  [pc]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 10
    sort_by = x
    variable = 'sat pc'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/richards/test/tests/newton_cooling/nc02.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1000
  ny = 1
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 1.0E6
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGnone]
    type = RichardsSUPGnone
  [../]
[]




[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Functions]
  active = 'initial_pressure'
  [./initial_pressure]
    type = ParsedFunction
    value = 2000000-x*1000000/100
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 2E6
  [../]
  [./newton]
    type = RichardsPiecewiseLinearSink
    variable = pressure
    boundary = right
    pressures = '0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000 1100000 1200000 1300000 1400000 1500000 1600000 1700000 1800000 1900000 2000000'
    bare_fluxes = '0. 5.6677197748570516e-6 0.000011931518841831313 0.00001885408740732065 0.000026504708864284114 0.000034959953203725676 0.000044304443352900224 0.00005463170211001232 0.00006604508815181467 0.00007865883048198513 0.00009259917167338928 0.00010800563134618119 0.00012503240252705603 0.00014384989486488752 0.00016464644014777016 0.00018763017719085535 0.0002130311349595711 0.00024110353477682344 0.00027212833465544285 0.00030641604122040985 0.00034430981736352295'
    use_mobility = false
    use_relperm = false
  [../]
[]

[Kernels]
  active = 'richardsf'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]



[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-15 0 0  0 1E-15 0  0 0 1E-15'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGnone
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'andy'
  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-15 10000'
  [../]


[]

[Executioner]
  type = Steady
  snesmf_reuse_base = false
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = nc02
  exodus = true
[]

(modules/porous_flow/test/tests/poroperm/poro_thm.i)

# Test that porosity is correctly calculated.
# Porosity = biot + (phi0 - biot) * exp(-vol_strain + (biot - 1) / solid_bulk * (porepressure - ref_pressure) + thermal_exp_coeff * (temperature - ref_temperature))
# The parameters used are:
# biot = 0.7
# phi0 = 0.5
# vol_strain = 0.5
# solid_bulk = 0.3
# porepressure = 2
# ref_pressure = 3
# thermal_exp_coeff = 0.5
# temperature = 4
# ref_temperature = 3.5
# which yield porosity = 0.276599996677
[Mesh]
  type = GeneratedMesh
  dim = 3
[]

[GlobalParams]
  PorousFlowDictator = dictator
  displacements = 'disp_x disp_y disp_z'
  biot_coefficient = 0.7
[]

[Variables]
  [porepressure]
    initial_condition = 2
  []
  [temperature]
    initial_condition = 4
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[ICs]
  [disp_x]
    type = FunctionIC
    function = '0.5 * x'
    variable = disp_x
  []
[]

[Kernels]
  [dummy_p]
    type = TimeDerivative
    variable = porepressure
  []
  [dummy_t]
    type = TimeDerivative
    variable = temperature
  []
  [dummy_x]
    type = TimeDerivative
    variable = disp_x
  []
  [dummy_y]
    type = TimeDerivative
    variable = disp_y
  []
  [dummy_z]
    type = TimeDerivative
    variable = disp_z
  []
[]

[AuxVariables]
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [porosity]
    type = PorousFlowPropertyAux
    property = porosity
    variable = porosity
  []
[]

[Postprocessors]
  [porosity]
    type = PointValue
    variable = porosity
    point = '0 0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure temperature'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [eff_fluid_pressure]
    type = PorousFlowEffectiveFluidPressure
  []
  [total_strain]
    type = ComputeSmallStrain
  []
  [vol_strain]
    type = PorousFlowVolumetricStrain
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [porosity]
    type = PorousFlowPorosity
    mechanical = true
    fluid = true
    thermal = true
    ensure_positive = false
    porosity_zero = 0.5
    solid_bulk = 0.3
    thermal_expansion_coeff = 0.5
    reference_porepressure = 3
    reference_temperature = 3.5
  []
[]

[Executioner]
  solve_type = Newton
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/jacobian/fflux10.i)

# 1phase, 3components, constant viscosity, constant insitu permeability
# density with constant bulk, BW relative perm, nonzero gravity, unsaturated with BW
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  xmin = 0
  xmax = 1
  ny = 1
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [massfrac0]
  []
  [massfrac1]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = -0.7+x+y
  []
  [massfrac0]
    type = RandomIC
    variable = massfrac0
    min = 0
    max = 0.3
  []
  [massfrac1]
    type = RandomIC
    variable = massfrac1
    min = 0
    max = 0.4
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
    gravity = '-1 -0.1 0'
  []
  [flux2]
    type = PorousFlowAdvectiveFlux
    fluid_component = 2
    variable = massfrac1
    gravity = '-1 -0.1 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0 massfrac1'
    number_fluid_phases = 1
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureBW
    Sn = 0.05
    Ss = 0.9
    las = 2.2
    C = 1.5
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      density0 = 1
      thermal_expansion = 0
      viscosity = 1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac0 massfrac1'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0 0 2 0 0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityBW
    Sn = 0.05
    Ss = 0.9
    Kn = 0.02
    Ks = 0.95
    C = 1.5
    phase = 0
  []
[]

[Preconditioning]
  active = check
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000'
  []
  [check]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  exodus = false
[]

(modules/richards/test/tests/sinks/s_fu_01.i)

# with fully_upwind sink
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  SUPG_UO = SUPGstandard
  sat_UO = Saturation
  seff_UO = SeffVG
  fully_upwind = true
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1 # same deal with PETSc constant state
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 2
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-lfout-rfout-mf)/2/(mi+mf))
    vars = 'mi mf lfout rfout'
    vals = 'mass_init mass_fin left_flux_out right_flux_out'
  [../]
[]

[Postprocessors]
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]
  [./mass_fin]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]
  [./left_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = left
    variable = pressure
    pressures = '0 1'
    bare_fluxes = '1 2'
    use_mobility = false
    use_relperm = false
  [../]
  [./right_flux_out]
    type = RichardsPiecewiseLinearSinkFlux
    boundary = right
    variable = pressure
    pressures = '0 1'
    bare_fluxes = '1 2'
    use_mobility = false
    use_relperm = false
  [../]
  [./p0]
    type = PointValue
    point = '0 0 0'
    variable = pressure
  [../]
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]

[BCs]
  [./left_flux]
    type = RichardsPiecewiseLinearSink
    boundary = left
    pressures = '0 1'
    bare_fluxes = '1 2'
    variable = pressure
    use_mobility = false
    use_relperm = false
  [../]
  [./right_flux]
    type = RichardsPiecewiseLinearSink
    boundary = right
    pressures = '0 1'
    bare_fluxes = '1 2'
    variable = pressure
    use_mobility = false
    use_relperm = false
  [../]
[]

[Kernels]
  active = 'richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'andy'
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2E-3
  end_time = 0.2
  nl_abs_tol = 1E-12
  nl_rel_tol = 1E-10
[]

[Outputs]
  file_base = s_fu_01
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/basic_advection/except1.i)

# phase number is too high in PorousFlowBasicAdvection
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [P]
  []
[]

[ICs]
  [P]
    type = FunctionIC
    variable = P
    function = '2*(1-x)'
  []
  [u]
    type = FunctionIC
    variable = u
    function = 'if(x<0.1,1,0)'
  []
[]

[Kernels]
  [u_dot]
    type = TimeDerivative
    variable = u
  []
  [u_advection]
    type = PorousFlowBasicAdvection
    variable = u
    phase = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = ''
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 4
      thermal_expansion = 0
      viscosity = 150.0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = P
    capillary_pressure = pc
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '5 0 0 0 5 0 0 0 5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 0
    phase = 0
  []
  [darcy_velocity]
    type = PorousFlowDarcyVelocityMaterial
    gravity = '0.25 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 1
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -snes_rtol'
    petsc_options_value = ' lu       1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 5
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(test/tests/kernels/mass_lumping/mass_lumping.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = -1
  xmax = 1
  nx = 2
[]

[Variables]
  [./u]
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = init_f
  [../]
[]

[Kernels]
  [./time_deriv]
    type = MassLumpedTimeDerivative
    variable = u
  [../]
  [./diff]
    type = FuncCoefDiffusion
    variable = u
    coef = diff_f
  [../]
[]

[Functions]
  [./init_f]
    type = ParsedFunction
    value = max(x,0) #(x>0)
  [../]
  [./diff_f]
    type = ParsedFunction
    value = max(x,0)
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(test/tests/postprocessors/element_l1_error/element_l1_error.i)

# Tests the ElementL1Error post-processor.
#
# The Element L1 error is defined as follows:
#   \sum\limits_i = int\limits_{\Omega_i} |y_{h,i} - y(x)| d\Omega
# where i is the element index and y_h is the approximate solution.
#
# This example uses 2 uniform elements on (0,10) with the following values:
#   (0,5):  y = 3, y_h = 5
#   (5,10): y = 2, y_h = 6
# Thus the gold value is
#   gold = 5*(5-3) + 5*(6-2) = 10 + 20 = 30

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  xmin = 0
  xmax = 10
[]

[Variables]
  [u]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    variable = u
    function = u_ic_fn
  []
[]

[Functions]
  [u_ic_fn]
    type = ParsedFunction
    value = 'if(x<5,5,6)'
  []

  [u_exact_fn]
    type = ParsedFunction
    value = 'if(x<5,3,2)'
  []
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[]

[Postprocessors]
  [err]
    type = ElementL1Error
    variable = u
    function = u_exact_fn
    execute_on = 'initial'
  []
[]

[Outputs]
  csv = true
  execute_on = 'initial'
[]

(test/tests/nodalkernels/constraint_enforcement/vi-bounding.i)

l=10
nx=100
num_steps=10

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [bounds][]
[]

[Bounds]
  [./u_upper_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = upper
    bound_value = ${l}
  [../]
  [./u_lower_bounds]
    type = ConstantBoundsAux
    variable = bounds
    bounded_variable = u
    bound_type = lower
    bound_value = 0
  [../]
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type -snes_type'
  petsc_options_value = '0                           30          asm      16                    basic                 vinewtonrsls'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

(modules/richards/test/tests/user_objects/uo2.i)

# Density User objects give the correct value
#
# If you want to add another test for another UserObject
# then add the UserObject, add a Function defining the expected result,
# add an AuxVariable and AuxKernel that will record the UserObjects value
# and finally add a NodalL2Error that compares this with the Function

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityIdeal]
    type = RichardsDensityIdeal
    p0 = 33333
    slope = 1.1E-2
  [../]
  [./DensityMethane20degC]
    type = RichardsDensityMethane20degC
  [../]
  [./DensityVDW]
    type = RichardsDensityVDW
    a = 0.2303
    b = 4.31E-4
    temperature = 293
    molar_mass = 16.04246E-3
    infinity_ratio = 10
  [../]
  [./DensityConstBulkCut]
    type = RichardsDensityConstBulkCut
    dens0 = 1000
    bulk_mod = 2E6
    cut_limit = 1E6
    zero_point = -1E6
  [../]

  # following are unimportant in this test
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-6
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.10101
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.054321
    sum_s_res = 0.054321
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E5
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = x
  [../]
  [./answer_DensityConstBulk]
    type = ParsedFunction
    value = dens0*exp(x/bulk_mod)
    vars = 'dens0 bulk_mod'
    vals = '1000 2E6'
  [../]
  [./answer_dDensityConstBulk]
    type = GradParsedFunction
    direction = '1 0 0'
    value = dens0*exp(x/bulk_mod)
    vars = 'dens0 bulk_mod'
    vals = '1000 2E6'
  [../]
  [./answer_d2DensityConstBulk]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = dens0*exp(x/bulk_mod)
    vars = 'dens0 bulk_mod'
    vals = '1000 2E6'
  [../]

  [./answer_DensityIdeal]
    type = ParsedFunction
    value = slope*(x-p0)
    vars = 'p0 slope'
    vals = '33333 1.1E-2'
  [../]
  [./answer_dDensityIdeal]
    type = GradParsedFunction
    direction = '1 0 0'
    value = slope*(x-p0)
    vars = 'p0 slope'
    vals = '33333 1.1E-2'
  [../]
  [./answer_d2DensityIdeal]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = slope*(x-p0)
    vars = 'p0 slope'
    vals = '33333 1.1E-2'
  [../]

  [./answer_DensityMethane20degC]
    type = ParsedFunction
    value = if(x>0,(0.00654576947608E-3*x+1.04357716547E-13*x^2),0)+if(x<0,0.1*(e^(6.54576947608E-5*x)-1),0)
  [../]
  [./answer_dDensityMethane20degC]
    type = GradParsedFunction
    direction = '1 0 0'
    value = if(x>0,(0.00654576947608E-3*x+1.04357716547E-13*x^2),0)+if(x<0,0.1*(e^(6.54576947608E-5*x)-1),0)
  [../]
  [./answer_d2DensityMethane20degC]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = if(x>0,(0.00654576947608E-3*x+1.04357716547E-13*x^2),0)+if(x<0,0.1*(e^(6.54576947608E-5*x)-1),0)
  [../]

  [./answer_DensityVDW]
    type = ParsedFunction
    value = if(x>0,-(molar_mass*(-2+(2*pow(2,0.3333333333333333)*(a-3*b*(b*x+rt)))/pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*x+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*x-rt),2)-4*pow(a-3*b*(b*x+rt),3)),0.5),0.3333333333333333)+(pow(2,0.6666666666666666)*pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*x+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*x-rt),2)-4*pow(a-3*b*(b*x+rt),3)),0.5),0.3333333333333333))/a))/(6.*b)+(molar_mass*(-2+(2*pow(2,0.3333333333333333)*(a-3*b*(b*0+rt)))/pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*0+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*0-rt),2)-4*pow(a-3*b*(b*0+rt),3)),0.5),0.3333333333333333)+(pow(2,0.6666666666666666)*pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*0+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*0-rt),2)-4*pow(a-3*b*(b*0+rt),3)),0.5),0.3333333333333333))/a))/(6.*b),infinityratio*molar_mass*(e^(slope0*x)-1))
    vars = 'a b rt molar_mass infinityratio slope0'
    vals = '0.2303 0.000431 2436.1403 0.01604246 10 4.10485e-05'
  [../]
  [./answer_dDensityVDW]
    type = GradParsedFunction
    direction = '1 0 0'
    value = if(x>0,-(molar_mass*(-2+(2*pow(2,0.3333333333333333)*(a-3*b*(b*x+rt)))/pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*x+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*x-rt),2)-4*pow(a-3*b*(b*x+rt),3)),0.5),0.3333333333333333)+(pow(2,0.6666666666666666)*pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*x+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*x-rt),2)-4*pow(a-3*b*(b*x+rt),3)),0.5),0.3333333333333333))/a))/(6.*b),infinityratio*molar_mass*(e^(slope0*x)-1))
    vars = 'a b rt molar_mass infinityratio slope0'
    vals = '0.2303 0.000431 2436.1403 0.01604246 10 4.10485e-05'
  [../]
  [./answer_d2DensityVDW]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = if(x>0,-(molar_mass*(-2+(2*pow(2,0.3333333333333333)*(a-3*b*(b*x+rt)))/pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*x+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*x-rt),2)-4*pow(a-3*b*(b*x+rt),3)),0.5),0.3333333333333333)+(pow(2,0.6666666666666666)*pow(-2*pow(a,3)+9*pow(a,2)*b*(-2*b*x+rt)+pow(pow(a,3)*(a*pow(2*a+9*b*(2*b*x-rt),2)-4*pow(a-3*b*(b*x+rt),3)),0.5),0.3333333333333333))/a))/(6.*b),infinityratio*molar_mass*(e^(slope0*x)-1))
    vars = 'a b rt molar_mass infinityratio slope0'
    vals = '0.2303 0.000431 2436.1403 0.01604246 10 4.10485e-05'
  [../]

  [./answer_DensityConstBulkCut]
    type = ParsedFunction
    value = if(x<zero_pt,0,if(x>cut_limit,dens0*exp(x/bulk_mod),(3*cut_limit-2*x-zero_pt)*(x-zero_pt)*(x-zero_pt)*dens0*exp(x/bulk_mod)/(cut_limit-zero_pt)/(cut_limit-zero_pt)/(cut_limit-zero_pt)))
    vars = 'dens0 bulk_mod zero_pt cut_limit'
    vals = '1000 2E6 -1E6 1E6'
  [../]
  [./answer_dDensityConstBulkCut]
    type = GradParsedFunction
    direction = '1 0 0'
    value = if(x<zero_pt,0,if(x>cut_limit,dens0*exp(x/bulk_mod),(3*cut_limit-2*x-zero_pt)*(x-zero_pt)*(x-zero_pt)*dens0*exp(x/bulk_mod)/(cut_limit-zero_pt)/(cut_limit-zero_pt)/(cut_limit-zero_pt)))
    vars = 'dens0 bulk_mod zero_pt cut_limit'
    vals = '1000 2E6 -1E6 1E6'
  [../]
  [./answer_d2DensityConstBulkCut]
    type = Grad2ParsedFunction
    direction = '1 0 0'
    value = if(x<zero_pt,0,if(x>cut_limit,dens0*exp(x/bulk_mod),(3*cut_limit-2*x-zero_pt)*(x-zero_pt)*(x-zero_pt)*dens0*exp(x/bulk_mod)/(cut_limit-zero_pt)/(cut_limit-zero_pt)/(cut_limit-zero_pt)))
    vars = 'dens0 bulk_mod zero_pt cut_limit'
    vals = '1000 2E6 -1E6 1E6'
  [../]
[]

[AuxVariables]
  [./DensityConstBulk_Aux]
  [../]
  [./dDensityConstBulk_Aux]
  [../]
  [./d2DensityConstBulk_Aux]
  [../]

  [./DensityIdeal_Aux]
  [../]
  [./dDensityIdeal_Aux]
  [../]
  [./d2DensityIdeal_Aux]
  [../]

  [./DensityMethane20degC_Aux]
  [../]
  [./dDensityMethane20degC_Aux]
  [../]
  [./d2DensityMethane20degC_Aux]
  [../]

  [./DensityVDW_Aux]
  [../]
  [./dDensityVDW_Aux]
  [../]
  [./d2DensityVDW_Aux]
  [../]

  [./DensityConstBulkCut_Aux]
  [../]
  [./dDensityConstBulkCut_Aux]
  [../]
  [./d2DensityConstBulkCut_Aux]
  [../]

  [./check_Aux]
  [../]
[]

[AuxKernels]
  [./DensityConstBulk_AuxK]
    type = RichardsDensityAux
    variable = DensityConstBulk_Aux
    density_UO = DensityConstBulk
    pressure_var = pressure
  [../]
  [./dDensityConstBulk_AuxK]
    type = RichardsDensityPrimeAux
    variable = dDensityConstBulk_Aux
    density_UO = DensityConstBulk
    pressure_var = pressure
  [../]
  [./d2DensityConstBulk_AuxK]
    type = RichardsDensityPrimePrimeAux
    variable = d2DensityConstBulk_Aux
    density_UO = DensityConstBulk
    pressure_var = pressure
  [../]

  [./DensityIdeal_AuxK]
    type = RichardsDensityAux
    variable = DensityIdeal_Aux
    density_UO = DensityIdeal
    pressure_var = pressure
  [../]
  [./dDensityIdeal_AuxK]
    type = RichardsDensityPrimeAux
    variable = dDensityIdeal_Aux
    density_UO = DensityIdeal
    pressure_var = pressure
  [../]
  [./d2DensityIdeal_AuxK]
    type = RichardsDensityPrimePrimeAux
    variable = d2DensityIdeal_Aux
    density_UO = DensityIdeal
    pressure_var = pressure
  [../]

  [./DensityMethane20degC_AuxK]
    type = RichardsDensityAux
    variable = DensityMethane20degC_Aux
    density_UO = DensityMethane20degC
    pressure_var = pressure
  [../]
  [./dDensityMethane20degC_AuxK]
    type = RichardsDensityPrimeAux
    variable = dDensityMethane20degC_Aux
    density_UO = DensityMethane20degC
    pressure_var = pressure
  [../]
  [./d2DensityMethane20degC_AuxK]
    type = RichardsDensityPrimePrimeAux
    variable = d2DensityMethane20degC_Aux
    density_UO = DensityMethane20degC
    pressure_var = pressure
  [../]

  [./DensityVDW_AuxK]
    type = RichardsDensityAux
    variable = DensityVDW_Aux
    density_UO = DensityVDW
    pressure_var = pressure
  [../]
  [./dDensityVDW_AuxK]
    type = RichardsDensityPrimeAux
    variable = dDensityVDW_Aux
    density_UO = DensityVDW
    pressure_var = pressure
  [../]
  [./d2DensityVDW_AuxK]
    type = RichardsDensityPrimePrimeAux
    variable = d2DensityVDW_Aux
    density_UO = DensityVDW
    pressure_var = pressure
  [../]

  [./DensityConstBulkCut_AuxK]
    type = RichardsDensityAux
    variable = DensityConstBulkCut_Aux
    density_UO = DensityConstBulkCut
    pressure_var = pressure
  [../]
  [./dDensityConstBulkCut_AuxK]
    type = RichardsDensityPrimeAux
    variable = dDensityConstBulkCut_Aux
    density_UO = DensityConstBulkCut
    pressure_var = pressure
  [../]
  [./d2DensityConstBulkCut_AuxK]
    type = RichardsDensityPrimePrimeAux
    variable = d2DensityConstBulkCut_Aux
    density_UO = DensityConstBulkCut
    pressure_var = pressure
  [../]

  [./check_AuxK]
    type = FunctionAux
    variable = check_Aux
    function = answer_d2DensityConstBulkCut
  [../]
[]

[Postprocessors]
  [./cf_DensityConstBulk]
    type = NodalL2Error
    function = answer_DensityConstBulk
    variable = DensityConstBulk_Aux
  [../]
  [./cf_dDensityConstBulk]
    type = NodalL2Error
    function = answer_dDensityConstBulk
    variable = dDensityConstBulk_Aux
  [../]
  [./cf_d2DensityConstBulk]
    type = NodalL2Error
    function = answer_d2DensityConstBulk
    variable = d2DensityConstBulk_Aux
  [../]

  [./cf_DensityIdeal]
    type = NodalL2Error
    function = answer_DensityIdeal
    variable = DensityIdeal_Aux
  [../]
  [./cf_dDensityIdeal]
    type = NodalL2Error
    function = answer_dDensityIdeal
    variable = dDensityIdeal_Aux
  [../]
  [./cf_d2DensityIdeal]
    type = NodalL2Error
    function = answer_d2DensityIdeal
    variable = d2DensityIdeal_Aux
  [../]

  [./cf_DensityMethane20degC]
    type = NodalL2Error
    function = answer_DensityMethane20degC
    variable = DensityMethane20degC_Aux
  [../]
  [./cf_dDensityMethane20degC]
    type = NodalL2Error
    function = answer_dDensityMethane20degC
    variable = dDensityMethane20degC_Aux
  [../]
  [./cf_d2DensityMethane20degC]
    type = NodalL2Error
    function = answer_d2DensityMethane20degC
    variable = d2DensityMethane20degC_Aux
  [../]

  [./cf_DensityVDW]
    type = NodalL2Error
    function = answer_DensityVDW
    variable = DensityVDW_Aux
  [../]
  [./cf_dDensityVDW]
    type = NodalL2Error
    function = answer_dDensityVDW
    variable = dDensityVDW_Aux
  [../]
  [./cf_d2DensityVDW]
    type = NodalL2Error
    function = answer_d2DensityVDW
    variable = d2DensityVDW_Aux
  [../]

  [./cf_DensityConstBulkCut]
    type = NodalL2Error
    function = answer_DensityConstBulkCut
    variable = DensityConstBulkCut_Aux
  [../]
  [./cf_dDensityConstBulkCut]
    type = NodalL2Error
    function = answer_dDensityConstBulkCut
    variable = dDensityConstBulkCut_Aux
  [../]
  [./cf_d2DensityConstBulkCut]
    type = NodalL2Error
    function = answer_d2DensityConstBulkCut
    variable = d2DensityConstBulkCut_Aux
  [../]
[]



#############################################################################
#
# Following is largely unimportant as we are not running an actual similation
#
#############################################################################
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -5E6
  xmax = 5E6
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Kernels]
  active = 'richardst'
  [./richardst]
    type = RichardsMassChange
    richardsVarNames_UO = PPNames
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    richardsVarNames_UO = PPNames
    variable = pressure
  [../]
[]

[Materials]
  [./unimportant_material]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-20 0 0  0 1E-20 0  0 0 1E-20'
    richardsVarNames_UO = PPNames
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = SeffVG
    SUPG_UO = SUPGstandard
    viscosity = 1E-3
    gravity = '0 0 -10'
    linear_shape_fcns = true
  [../]
[]

[Preconditioning]
  [./does_nothing]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E50 1E50 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
  dt = 1E-100
[]

[Outputs]
  execute_on = 'timestep_end'
  active = 'csv'
  file_base = uo2
  [./csv]
    type = CSV
    [../]
  [./exodus]
    type = Exodus
    hide = pressure
  [../]
[]

(modules/level_set/examples/rotating_circle/circle_rotate_master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 32
  ny = 32
  uniform_refine = 2
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[Variables]
  [./phi]
  [../]
[]

[BCs]
  [./all]
    type = DirichletBC
    variable = phi
    boundary = 'top bottom left right'
    value = 0
  [../]
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '4*y'
    value_y = '-4*x'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1.570796
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[MultiApps]
  [./reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'circle_rotate_sub.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    to_multi_app = reinit
    execute_on = 'timestep_end'
  [../]
  [./to_sub_init]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi_0
    to_multi_app = reinit
    execute_on = 'timestep_end'
  [../]
  [./from_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    from_multi_app = reinit
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/phase_field/examples/interfacekernels/interface_gradient.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
  []
  [./box1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.51 1 0'
  [../]
  [./box2]
    input = box1
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.49 0 0'
    top_right = '1 1 0'
  [../]
  [./iface]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = 10
    input = box2
  [../]
  [./rotate]
    type = TransformGenerator
    transform = ROTATE
    vector_value = '5 0 0'
    input = iface
  [../]
[]

[GlobalParams]
  order = FIRST
  family = LAGRANGE
[]

[Variables]
  [./u]
    block = 1
    [./InitialCondition]
      type = FunctionIC
      function = 'r:=sqrt((x-0.4)^2+(y-0.5)^2);if(r<0.05,5,1)'
    [../]
  [../]
  [./v]
    block = 2
    initial_condition = 0.8
  [../]
[]

[Kernels]
  [./u_diff]
    type = Diffusion
    variable = u
    block = 1
  [../]
  [./u_dt]
    type = TimeDerivative
    variable = u
    block = 1
  [../]
  [./v_diff]
    type = Diffusion
    variable = v
    block = 2
  [../]
  [./v_dt]
    type = TimeDerivative
    variable = v
    block = 2
  [../]
[]

[InterfaceKernels]
  [./flux_continuity]
    type = InterfaceDiffusionFluxMatch
    variable = u
    boundary = 10
    neighbor_var = v
  [../]
  [./diffusion_surface_term]
    type = InterfaceDiffusionBoundaryTerm
    boundary = 10
    variable = u
    neighbor_var = v
  [../]
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 0.001
  num_steps = 20
[]

[Outputs]
  [./out]
    type = Exodus
    use_problem_dimension = false
  [../]
  print_linear_residuals = false
[]

(modules/richards/test/tests/excav/ex02.i)

###########################################
#                                         #
#   THIS EXAMPLE CONTAINS AN EXCAVATION   #
#                                         #
###########################################


# Easiest way of figuring out what's happening:
# Run this example, load into paraview, take
# a slice through (0,0,0) with normal (0,0,1),
# colour by pressure and play the animation.


# This mesh has an interior sideset called excav_bdy
[Mesh]
  type = FileMesh
  file = ex01_input.e
[]



# This is a boundary condition acting on excav_bdy
# All it does is to set the pressure to p_excav=0
# at places on excav_bdy wherever excav_fcn tells it to.
[BCs]
  [./excav_bdy]
    type = RichardsExcav
    boundary = excav_bdy
    p_excav = 0.0
    variable = pressure
    excav_geom_function = excav_fcn
  [../]
[]



[Functions]
# excav_fcn controls where to set pressure=p_excav
# You supply start and end positions and times and
# by a linear interpolation these define the position
# of the coal face at all times
  [./excav_fcn]
    type = RichardsExcavGeom
    start_posn = '0 -500 0'
    start_time = 0
    end_posn = '0 500 0'
    end_time = 3E7
    active_length = 1E4
  [../]

# mass_bal_fcn calculates the mass balance
  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((mi-fout-mf)/2/(mi+mf))
    vars = 'mi mf fout'
    vals = 'mass_init mass_final flux_out'
  [../]

# initial pressure - unimportant in this example
  [./initial_pressure]
    type = ParsedFunction
    value = -10000*(z-100)
  [../]
[]




# following is needed by postprocessors, kernels, etc
# unimportant in this example
[GlobalParams]
  richardsVarNames_UO = PPNames
[]




# following does the calculation of relevant
# masses and mass-flux to the excavation
[Postprocessors]

# note that this is calculated at beginning of timestep
  [./mass_init]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

# note this is calculated at end of timestep
  [./mass_final]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

# this is what calculates the mass flux to the excavation
# it is calculating it for boundary=excav_bdy, and the
# excavation time-dependence is set through the excav_fcn
  [./flux_out]
    type = RichardsExcavFlow
    boundary = excav_bdy
    variable = pressure
    excav_geom_function = excav_fcn
  [../]

# mass_bal just outputs the result to screen
  [./mass_bal]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
  [../]
[]




######################################
#                                    #
#  THE FOLLOWING STUFF IS STANDARD   #
#                                    #
######################################


[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E+2
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = '1 2 3 4'
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-15 0 0  0 1E-15 0  0 0 1E-15'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 -10'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 3E7
  dt = 1E6
  solve_type = NEWTON
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = ex02
  exodus = true
[]

(modules/porous_flow/examples/co2_intercomparison/1Dradial/properties.i)

# Liquid and gas properties for code intercomparison problem 3
#
# From Pruess et al, Code intercomparison builds confidence in
# numerical simulation models for geologic disposal of CO2, Energy 29 (2004)
#
# This test simply calculates density and viscosity of each phase for
# various pressures and salinities, as well as mass fractions of CO2 in the
# liquid phase and H2O in the gas phase.
#
# Four versions of this are run:
# 1) No CO2, 0 salt mass fraction (pure water)
# 2) Enough CO2 to form gas phase, 0 salt mass fraction (pure water)
# 3) No CO2, 0.15 salt mass fraction
# 4) Enough CO2 to form gas phase, 0.15 salt mass fraction
#
# These results compare well with detailed results presented in Pruess et al,
# Intercomparison of numerical simulation codes for geologic disposal of CO2,
# LBNL-51813 (2002)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 4
  xmax = 4
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[AuxVariables]
  [density_liquid]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_liquid]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1]
    order = CONSTANT
    family = MONOMIAL
  []
  [y0]
    order = CONSTANT
    family = MONOMIAL
  []
  [xnacl]
    initial_condition = 0.0
  []
[]

[AuxKernels]
  [density_liquid]
    type = PorousFlowPropertyAux
    variable = density_liquid
    property = density
    phase = 0
    execute_on = timestep_end
  []
  [density_gas]
    type = PorousFlowPropertyAux
    variable = density_gas
    property = density
    phase = 1
    execute_on = timestep_end
  []
  [viscosity_liquid]
    type = PorousFlowPropertyAux
    variable = viscosity_liquid
    property = viscosity
    phase = 0
    execute_on = timestep_end
  []
  [viscosity_gas]
    type = PorousFlowPropertyAux
    variable = viscosity_gas
    property = viscosity
    phase = 1
    execute_on = timestep_end
  []
  [x1]
    type = PorousFlowPropertyAux
    variable = x1
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = timestep_end
  []
  [y0]
    type = PorousFlowPropertyAux
    variable = y0
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = timestep_end
  []
[]

[Variables]
  [pgas]
    order = CONSTANT
    family = MONOMIAL
  []
  [zi]
    initial_condition = 0.0
  []
[]

[Functions]
  [pic]
    type = ParsedFunction
    value = 'if(x<1,12e6,if(x<2,16e6,if(x<3,20e6,24e6)))'
  []
[]

[ICs]
  [pic]
    type = FunctionIC
    function = pic
    variable = pgas
  []
[]

[Kernels]
  [diffusionp]
    type = NullKernel
    variable = pgas
  []
  [diffusionz]
    type = NullKernel
    variable = zi
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 45
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  perf_graph = true
  csv = true
  execute_on = timestep_end
  file_base = properties_water
[]

[VectorPostprocessors]
  [vpp]
    type = ElementValueSampler
    variable = 'pgas density_liquid density_gas viscosity_liquid viscosity_gas x1 y0'
    sort_by = x
  []
[]

(test/tests/misc/check_error/function_file_test5.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = dummy
    xy_data = '1 2'
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/misc/check_error/function_file_test2.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_rows.csv #Will generate error because data is expected in columns
    format = columns
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/richards/test/tests/user_objects/uo4.i)

# Seff 2-phase User objects give the correct value
#
# If you want to add another test for another UserObject
# then add the UserObject, add a Function defining the expected result,
# add an AuxVariable and AuxKernel that will record the UserObjects value
# and finally add a NodalL2Error that compares this with the Function
#
# Here pressure is x where x is between -5 and 5

[UserObjects]
  [./Seff2waterVG]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 0.3
  [../]
  [./Seff2gasVG]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 0.3
  [../]

  [./Seff2waterVGshifted]
    type = RichardsSeff2waterVGshifted
    m = 0.8
    al = 0.3
    shift = 2
  [../]
  [./Seff2gasVGshifted]
    type = RichardsSeff2gasVGshifted
    m = 0.8
    al = 0.3
    shift = 2
  [../]

  # following are unimportant in this test
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.10101
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.05
    sum_s_res = 0.1
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1
  [../]
[]

[Functions]
  [./initial_pwater]
    type = ParsedFunction
    value = x
  [../]
  [./initial_pgas]
    type = ParsedFunction
    value = 5.0
  [../]

  [./answer_Seff2waterVG]
    type = ParsedFunction
    value = (1+max((-(x-5))*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '0.3 0.8'
  [../]
  [./answer_dSeff2waterVG]
    type = GradParsedFunction
    direction = '1E-5 0 0'
    value = (1+max((-(x-5))*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '0.3 0.8'
  [../]
  [./answer_d2Seff2waterVG]
    type = Grad2ParsedFunction
    direction = '1E-4 0 0'
    value = (1+max((-(x-5))*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '0.3 0.8'
  [../]

  [./answer_Seff2gasVG]
    type = ParsedFunction
    value = 1-(1+max((-(x-5))*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '0.3 0.8'
  [../]
  [./answer_dSeff2gasVG]
    type = GradParsedFunction
    direction = '1E-5 0 0'
    value = 1-(1+max((-(x-5))*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '0.3 0.8'
  [../]
  [./answer_d2Seff2gasVG]
    type = Grad2ParsedFunction
    direction = '1E-4 0 0'
    value = 1-(1+max((-(x-5))*al,0)^(1/(1-m)))^(-m)
    vars = 'al m'
    vals = '0.3 0.8'
  [../]

  [./answer_Seff2waterVGshifted]
    type = ParsedFunction
    value = ((1+max((-(x-5-shift))*al,0)^(1/(1-m)))^(-m))/((1+max((-(-shift))*al,0)^(1/(1-m)))^(-m))
    vars = 'al m shift'
    vals = '0.3 0.8 2'
  [../]
  [./answer_dSeff2waterVGshifted]
    type = GradParsedFunction
    direction = '1E-5 0 0'
    value = ((1+max((-(x-5-shift))*al,0)^(1/(1-m)))^(-m))/((1+max((-(-shift))*al,0)^(1/(1-m)))^(-m))
    vars = 'al m shift'
    vals = '0.3 0.8 2'
  [../]
  [./answer_d2Seff2waterVGshifted]
    type = Grad2ParsedFunction
    direction = '1E-4 0 0'
    value = ((1+max((-(x-5-shift))*al,0)^(1/(1-m)))^(-m))/((1+max((-(-shift))*al,0)^(1/(1-m)))^(-m))
    vars = 'al m shift'
    vals = '0.3 0.8 2'
  [../]

  [./answer_Seff2gasVGshifted]
    type = ParsedFunction
    value = 1-((1+max((-(x-5-shift))*al,0)^(1/(1-m)))^(-m))/((1+max((-(-shift))*al,0)^(1/(1-m)))^(-m))
    vars = 'al m shift'
    vals = '0.3 0.8 2'
  [../]
  [./answer_dSeff2gasVGshifted]
    type = GradParsedFunction
    direction = '1E-5 0 0'
    value = 1-((1+max((-(x-5-shift))*al,0)^(1/(1-m)))^(-m))/((1+max((-(-shift))*al,0)^(1/(1-m)))^(-m))
    vars = 'al m shift'
    vals = '0.3 0.8 2'
  [../]
  [./answer_d2Seff2gasVGshifted]
    type = Grad2ParsedFunction
    direction = '1E-4 0 0'
    value = 1-((1+max((-(x-5-shift))*al,0)^(1/(1-m)))^(-m))/((1+max((-(-shift))*al,0)^(1/(1-m)))^(-m))
    vars = 'al m shift'
    vals = '0.3 0.8 2'
  [../]
[]

[AuxVariables]
  [./Seff2waterVG_Aux]
  [../]
  [./dSeff2waterVG_Aux]
  [../]
  [./d2Seff2waterVG_Aux]
  [../]
  [./Seff2gasVG_Aux]
  [../]
  [./dSeff2gasVG_Aux]
  [../]
  [./d2Seff2gasVG_Aux]
  [../]

  [./Seff2waterVGshifted_Aux]
  [../]
  [./dSeff2waterVGshifted_Aux]
  [../]
  [./d2Seff2waterVGshifted_Aux]
  [../]
  [./Seff2gasVGshifted_Aux]
  [../]
  [./dSeff2gasVGshifted_Aux]
  [../]
  [./d2Seff2gasVGshifted_Aux]
  [../]

  [./check_Aux]
  [../]
[]

[AuxKernels]
  [./Seff2waterVG_AuxK]
    type = RichardsSeffAux
    variable = Seff2waterVG_Aux
    seff_UO = Seff2waterVG
    pressure_vars = 'pwater pgas'
  [../]
  [./dSeff2waterVG_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff2waterVG_Aux
    seff_UO = Seff2waterVG
    pressure_vars = 'pwater pgas'
    wrtnum = 0
  [../]
  [./d2Seff2waterVG_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff2waterVG_Aux
    seff_UO = Seff2waterVG
    pressure_vars = 'pwater pgas'
    wrtnum1 = 0
    wrtnum2 = 0
  [../]
  [./Seff2gasVG_AuxK]
    type = RichardsSeffAux
    variable = Seff2gasVG_Aux
    seff_UO = Seff2gasVG
    pressure_vars = 'pwater pgas'
  [../]
  [./dSeff2gasVG_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff2gasVG_Aux
    seff_UO = Seff2gasVG
    pressure_vars = 'pwater pgas'
    wrtnum = 0
  [../]
  [./d2Seff2gasVG_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff2gasVG_Aux
    seff_UO = Seff2gasVG
    pressure_vars = 'pwater pgas'
    wrtnum1 = 0
    wrtnum2 = 0
  [../]

  [./Seff2waterVGshifted_AuxK]
    type = RichardsSeffAux
    variable = Seff2waterVGshifted_Aux
    seff_UO = Seff2waterVGshifted
    pressure_vars = 'pwater pgas'
  [../]
  [./dSeff2waterVGshifted_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff2waterVGshifted_Aux
    seff_UO = Seff2waterVGshifted
    pressure_vars = 'pwater pgas'
    wrtnum = 0
  [../]
  [./d2Seff2waterVGshifted_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff2waterVGshifted_Aux
    seff_UO = Seff2waterVGshifted
    pressure_vars = 'pwater pgas'
    wrtnum1 = 0
    wrtnum2 = 0
  [../]
  [./Seff2gasVGshifted_AuxK]
    type = RichardsSeffAux
    variable = Seff2gasVGshifted_Aux
    seff_UO = Seff2gasVGshifted
    pressure_vars = 'pwater pgas'
  [../]
  [./dSeff2gasVGshifted_AuxK]
    type = RichardsSeffPrimeAux
    variable = dSeff2gasVGshifted_Aux
    seff_UO = Seff2gasVGshifted
    pressure_vars = 'pwater pgas'
    wrtnum = 0
  [../]
  [./d2Seff2gasVGshifted_AuxK]
    type = RichardsSeffPrimePrimeAux
    variable = d2Seff2gasVGshifted_Aux
    seff_UO = Seff2gasVGshifted
    pressure_vars = 'pwater pgas'
    wrtnum1 = 0
    wrtnum2 = 0
  [../]

  [./check_AuxK]
    type = FunctionAux
    variable = check_Aux
    function = answer_d2Seff2waterVGshifted
  [../]
[]

[Postprocessors]
  [./cf_Seff2waterVG]
    type = NodalL2Error
    function = answer_Seff2waterVG
    variable = Seff2waterVG_Aux
  [../]
  [./cf_dSeff2waterVG]
    type = NodalL2Error
    function = answer_dSeff2waterVG
    variable = dSeff2waterVG_Aux
  [../]
  [./cf_d2Seff2waterVG]
    type = NodalL2Error
    function = answer_d2Seff2waterVG
    variable = d2Seff2waterVG_Aux
  [../]

  [./cf_Seff2gasVG]
    type = NodalL2Error
    function = answer_Seff2gasVG
    variable = Seff2gasVG_Aux
  [../]
  [./cf_dSeff2gasVG]
    type = NodalL2Error
    function = answer_dSeff2gasVG
    variable = dSeff2gasVG_Aux
  [../]
  [./cf_d2Seff2gasVG]
    type = NodalL2Error
    function = answer_d2Seff2gasVG
    variable = d2Seff2gasVG_Aux
  [../]

  [./cf_Seff2waterVGshifted]
    type = NodalL2Error
    function = answer_Seff2waterVGshifted
    variable = Seff2waterVGshifted_Aux
  [../]
  [./cf_dSeff2waterVGshifted]
    type = NodalL2Error
    function = answer_dSeff2waterVGshifted
    variable = dSeff2waterVGshifted_Aux
  [../]
  [./cf_d2Seff2waterVGshifted]
    type = NodalL2Error
    function = answer_d2Seff2waterVGshifted
    variable = d2Seff2waterVGshifted_Aux
  [../]

  [./cf_Seff2gasVGshifted]
    type = NodalL2Error
    function = answer_Seff2gasVGshifted
    variable = Seff2gasVGshifted_Aux
  [../]
  [./cf_dSeff2gasVGshifted]
    type = NodalL2Error
    function = answer_dSeff2gasVGshifted
    variable = dSeff2gasVGshifted_Aux
  [../]
  [./cf_d2Seff2gasVGshifted]
    type = NodalL2Error
    function = answer_d2Seff2gasVGshifted
    variable = d2Seff2gasVGshifted_Aux
  [../]

[]



#############################################################################
#
# Following is largely unimportant as we are not running an actual similation
#
#############################################################################
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = -5
  xmax = 5
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pwater
    [../]
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pgas
    [../]
  [../]
[]

[Kernels]
  active = 'watert gast'
  [./watert]
    type = RichardsMassChange
    richardsVarNames_UO = PPNames
    variable = pwater
  [../]
  [./gast]
    type = RichardsMassChange
    richardsVarNames_UO = PPNames
    variable = pgas
  [../]
[]

[Materials]
  [./unimportant_material]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-20 0 0  0 1E-20 0  0 0 1E-20'
    richardsVarNames_UO = PPNames
    density_UO = 'DensityConstBulk DensityConstBulk'
    relperm_UO = 'RelPermPower RelPermPower'
    sat_UO = 'Saturation Saturation'
    seff_UO = 'Seff2waterVG Seff2gasVG'
    SUPG_UO = 'SUPGstandard SUPGstandard'
    viscosity = '1E-3 1E-5'
    gravity = '0 0 -10'
    linear_shape_fcns = true
  [../]
[]

[Preconditioning]
  [./does_nothing]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E50 1E50 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
  dt = 1E-100
[]

[Outputs]
  execute_on = 'timestep_end'
  active = 'csv'
  file_base = uo4
  [./csv]
    type = CSV
    [../]
  [./exodus]
    type = Exodus
  [../]
[]

(test/tests/functions/image_function/subset.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  uniform_refine = 2
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    origin = '0.25 0.25 0'
    dimensions = '0.5 0.5 0'
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/implicit_bcs/hllc_sod_shocktube.i)

rho_left = 1
E_left = 2.501505578
u_left = 1e-15

rho_right = 0.125
E_right = 1.999770935
u_right = 1e-15

middle = 0.5

[GlobalParams]
  fp = fp
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${fparse 2 * middle}
    nx = 5
    ymin = 0
    ymax = 1
    ny = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
      allow_imperfect_jacobians = true
    []
  []
[]

[Variables]
  [rho]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [rho_u]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [rho_v]
    order = CONSTANT
    family = MONOMIAL
    fv = true
    initial_condition = 1e-10
  []
  [rho_E]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[FVKernels]
  [mass_time]
    type = FVTimeKernel
    variable = rho
  []

  [mass_advection]
    type = CNSFVMassHLLC
    variable = rho
  []

  [momentum_x_time]
    type = FVTimeKernel
    variable = rho_u
  []

  [momentum_x_advection]
    type = CNSFVMomentumHLLC
    variable = rho_u
    momentum_component = x
  []

  [momentum_y_time]
    type = FVTimeKernel
    variable = rho_v
  []

  [momentum_y_advection]
    type = CNSFVMomentumHLLC
    variable = rho_v
    momentum_component = y
  []

  [fluid_energy_time]
    type = FVTimeKernel
    variable = rho_E
  []

  [fluid_energy_advection]
    type = CNSFVFluidEnergyHLLC
    variable = rho_E
  []
[]

[FVBCs]
  [mass_implicit]
    type = CNSFVHLLCMassImplicitBC
    variable = rho
    fp = fp
    boundary = 'left right'
  []

  [mom_x_implicit]
    type = CNSFVHLLCMomentumImplicitBC
    variable = rho_u
    momentum_component = x
    fp = fp
    boundary = 'left right'
  []

  [wall]
    type = CNSFVMomImplicitPressureBC
    variable = rho_v
    momentum_component = y
    boundary = 'top bottom'
  []

  [fluid_energy_implicit]
    type = CNSFVHLLCFluidEnergyImplicitBC
    variable = rho_E
    fp = fp
    boundary = 'left right'
  []
[]

[ICs]
  [rho_ic]
    type = FunctionIC
    variable = rho
    function = 'if (x < ${middle}, ${rho_left}, ${rho_right})'
  []

  [rho_u_ic]
    type = FunctionIC
    variable = rho_u
    function = 'if (x < ${middle}, ${fparse rho_left * u_left}, ${fparse rho_right * u_right})'
  []

  [rho_E_ic]
    type = FunctionIC
    variable = rho_E
    function = 'if (x < ${middle}, ${fparse E_left * rho_left}, ${fparse E_right * rho_right})'
  []
[]

[Materials]
  [var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = rho_u
    rhov = rho_v
    rho_et = rho_E
    fp = fp
  []
[]

[Executioner]
  type = Transient
  [TimeIntegrator]
    type = ExplicitSSPRungeKutta
    order = 2
  []
  l_tol = 1e-8

  # run to t = 0.15
  start_time = 0.0
  dt = 1e-1
  end_time = 10
  abort_on_solve_fail = true
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/dirac/bh05.i)

# unsaturated
# injection
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '500 500 1E1'
    x = '4000 5000 6500'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh03.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = -1
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = -2E5
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]

[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 6500
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  file_base = bh05
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/fsi/test/tests/fsi_acoustics/wave_height_bc/wave_height_bc.i)

# Test for `FluidFreeSurfaceBC` BC with only the fluid domain. The domain is 3D with
# lengths 1 X 1 X 0.01 meters. It is subjected to a 2D Gaussian initial condition
# with the peak at the midpoint (0.5, 0.5, 0.01). Wave heights are recorded at the
# midpoint at different times. The recorded wave heights should match with the values
# that are provided.

# Input parameters:
# Dimensions = 3
# Lengths = 1 X 1 X 0.01 meters
# Fluid speed of sound = 1500 m/s
# Initial condition = 0.00001*exp(-((x-0.5)/0.1)^2-((y-0.5)/0.1)^2)
# Fluid domain = true
# Fluid BCs = pressures are zero on all the four edges of the domain and `FluidFreeSurfaceBC` is applied on the front
# Structural domain = false

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 15
    ny = 15
    nz = 1
    xmax = 1
    ymax = 1
    zmax = 0.01
  []
[]

[GlobalParams]
[]

[Variables]
  [./p]
  [../]
[]

[AuxVariables]
  [./Wave1]
  [../]
[]

[Kernels]
  [./diffusion]
    type = Diffusion
    variable = 'p'
  [../]
  [./inertia]
    type = AcousticInertia
    variable = p
  [../]
[]

[AuxKernels]
  [./waves]
    type = WaveHeightAuxKernel
    variable = 'Wave1'
    pressure = p
    density = 1e-6
    gravity = 9.81
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./leftright_pressure]
    type = DirichletBC
    variable = p
    boundary = 'left right top bottom'
    value = 0
  [../]
  [./free]
    type = FluidFreeSurfaceBC
    variable = p
    boundary = 'front'
    alpha = '0.1'
  []
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = 'p'
    function = initial_cond
    boundary = 'front'
  [../]
[]

[Functions]
  [./initial_cond]
    type = ParsedFunction
    value = '0.00001*exp(-((x-0.5)/0.1)^2-((y-0.5)/0.1)^2)'
  [../]
[]

[Materials]
  [./co_sq]
    type = GenericConstantMaterial
    prop_names = inv_co_sq
    prop_values = 4.44e-7
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  start_time = 0.0
  end_time = 0.2
  dt = 0.005
  dtmin = 0.00001
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  l_tol = 1e-12
  l_max_its = 25
  timestep_tolerance = 1e-8
  automatic_scaling = true
  [TimeIntegrator]
    type = NewmarkBeta
  []
[]

[Postprocessors]
  [./W1]
    type = PointValue
    point = '0.5 0.5 0.01'
    variable = Wave1
  [../]
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

(test/tests/misc/check_error/function_file_test12.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_columns_more_data.csv
    format = columns
    xy_in_file_only = false
    y_index_in_file = 3 #Will generate error because data does not contain 4 columns
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/porous_flow/test/tests/buckley_leverett/bl01.i)

# Buckley-Leverett 1-phase.
# The front starts at (around) x=5, and at t=50 it should
# have moved to x=9.6.  The version below has a nonzero
# suction function, and at t=50, the front sits between
# (about) x=9.6 and x=9.9.  Changing the van-Genuchten
# al parameter to 1E-4 softens the front so it sits between
# (about) x=9.7 and x=10.4, and the simulation runs much faster.
# With al=1E-2 and nx=600, the front sits between x=9.6 and x=9.8,
# but takes about 100 times longer to run.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]

[GlobalParams]
  PorousFlowDictator = dictator
  compute_enthalpy = false
  compute_internal_energy = false
[]

[Variables]
  [pp]
    [InitialCondition]
      type = FunctionIC
      function = 'max((1000000-x/5*1000000)-20000,-20000)'
    []
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '0 0 0'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 980000
  []
[]

[AuxVariables]
  [sat]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [sat]
    type = MaterialStdVectorAux
    variable = sat
    execute_on = timestep_end
    index = 0
    property = PorousFlow_saturation_qp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.8
    alpha = 1e-3
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e6
      viscosity = 1e-3
      density0 = 1000
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.15
  []
[]

[Preconditioning]
  active = andy
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres bjacobi 1E-10 1E-10 20'
  []
[]

[Functions]
  [timestepper]
    type = PiecewiseLinear
    x = '0    0.01 0.1 1   1.5 2   20  30  40  50'
    y = '0.01 0.1  0.2 0.3 0.1 0.3 0.3 0.4 0.4 0.5'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 50
  [TimeStepper]
    type = FunctionDT
    function = timestepper
  []
[]

[VectorPostprocessors]
  [pp]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '15 0 0'
    num_points = 150
    sort_by = x
    variable = pp
  []
  [sat]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0 0 0'
    end_point = '15 0 0'
    num_points = 150
    sort_by = x
    variable = sat
  []
[]


[Outputs]
  file_base = bl01
  [csv]
    type = CSV
    sync_only = true
    sync_times = '0.01 50'
  []
  [exodus]
    type = Exodus
    execute_on = 'initial final'
  []
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/jacobian_03.i)

# Checking the Jacobian of Flux-Limited TVD Advection, using flux_limiter_type = vanleer
#
# The initial conditions are u=x.  This means that the argument of the flux limiter is 1, so that
# the flux_limiter=1 everywhere, irrespective of flux_limiter_type (except for 'none').  However
# superbee and minmod are nondifferentiable at this point, so using those flux_limiter_type will
# result in a poor Jacobian
#
# Here we use snes_check_jacobian instead of snes_type=test.  The former just checks the Jacobian for the
# random initial conditions, while the latter checks for u=1 and u=-1
#
# The Jacobian is correct for u=1 and u=-1, but the finite-difference scheme used by snes_type=test gives the
# wrong answer.
# For u=1, the Kuzmin-Turek scheme adds as much antidiffusion as possible, resulting in a central-difference
# version of advection (flux_limiter = 1).  This is correct, and the Jacobian is calculated correctly.
# However, when computing the Jacobian using finite differences, u is increased or decreased at a node.
# This results in that node being at a maximum or minimum, which means no antidiffusion should be added
# (flux_limiter = 0).  This corresponds to a full-upwind scheme.  So the finite-difference computes the
# Jacobian in the full-upwind scenario, which is incorrect (the original residual = 0, after finite-differencing
# the residual comes from the full-upwind scenario).
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 6
[]

[Variables]
  [u]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [flux]
    type = FluxLimitedTVDAdvection
    variable = u
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = vanleer
    u = u
    velocity = '1 -2 1.5'
  []
[]


[Preconditioning]
  active = smp
  [smp]
    type = SMP
    full = true
    petsc_options = '-snes_check_jacobian'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear # this is to force convergence even though the nonlinear residual is high: we just care about the Jacobian in this test
  end_time = 1
  num_steps = 1
  dt = 1
[]

(modules/richards/test/tests/buckley_leverett/bl22.i)

# two-phase version
# super-sharp front version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1E-4 1E-3 1E-2 2E-2 5E-2 6E-2 0.1 0.2'
    x =  '0    1E-2 1E-1 1    5    20   40  41'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-4
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-4
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
  [./bounds_dummy]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
  [./richardsppenalty]
    type = RichardsPPenalty
    variable = pgas
    a = 1E-18
    lower_var = pwater
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_water
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_gas
  [../]
[]

[BCs]
  [./left_w]
    type = DirichletBC
    variable = pwater
    boundary = left
    value = 1E6
  [../]
  [./left_g]
    type = DirichletBC
    variable = pgas
    boundary = left
    value = 1E6
  [../]
  [./right_w]
    type = DirichletBC
    variable = pwater
    boundary = right
    value = -100000
  [../]
  [./right_g]
    type = DirichletBC
    variable = pgas
    boundary = right
    value = 0
  [../]
[]


[Functions]
  [./initial_water]
    type = ParsedFunction
    value = 1000000*(1-min(x/5,1))-100000*(max(x-5,0)/max(abs(x-5),1E-10))
  [../]
  [./initial_gas]
    type = ParsedFunction
    value = max(1000000*(1-x/5),0)+1000
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 1E-6'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]

  [./standard]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 20 1E-20 1E-20'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 50

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = bl22
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
  [./exodus]
    type = Exodus
    interval = 100000
    hide = pgas
    execute_on = 'initial final timestep_end'
  [../]
[]

(modules/richards/test/tests/gravity_head_2/gh04.i)

# unsaturated = true
# gravity = true
# supg = true
# transient = false

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmin = 0
  xmax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1.0E2
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 0.5
    bulk_mod = 0.5E2
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.15
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.05
    sum_s_res = 0.15
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-3
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-3
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  # get nonconvergence if initial condition is too crazy
  [./water_ic]
    type = FunctionIC
    function = '1-x/2'
    variable = pwater
  [../]
  [./gas_ic]
    type = FunctionIC
    function = '4-x/5'
    variable = pgas
  [../]
[]


[Kernels]
  active = 'richardsfwater richardsfgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]


[AuxVariables]
  [./seffgas]
  [../]
  [./seffwater]
  [../]
[]

[AuxKernels]
  [./seffgas_kernel]
    type = RichardsSeffAux
    pressure_vars = 'pwater pgas'
    seff_UO = SeffGas
    variable = seffgas
  [../]
  [./seffwater_kernel]
    type = RichardsSeffAux
    pressure_vars = 'pwater pgas'
    seff_UO = SeffWater
    variable = seffwater
  [../]
[]

[Postprocessors]
  [./pw_left]
    type = PointValue
    point = '0 0 0'
    variable = pwater
    outputs = none
  [../]
  [./pw_right]
    type = PointValue
    point = '1 0 0'
    variable = pwater
    outputs = none
  [../]
  [./error_water]
    type = FunctionValuePostprocessor
    function = fcn_error_water
  [../]

  [./pg_left]
    type = PointValue
    point = '0 0 0'
    variable = pgas
    outputs = none
  [../]
  [./pg_right]
    type = PointValue
    point = '1 0 0'
    variable = pgas
    outputs = none
  [../]
  [./error_gas]
    type = FunctionValuePostprocessor
    function = fcn_error_gas
  [../]
[]

[Functions]
  [./fcn_error_water]
    type = ParsedFunction
    value = 'abs((-b*log(-(gdens0*xval+(-b*exp(-p0/b)))/b)-p1)/p1)'
    vars = 'b gdens0 p0 xval p1'
    vals = '1E2 -1 pw_left 1 pw_right'
  [../]
  [./fcn_error_gas]
    type = ParsedFunction
    value = 'abs((-b*log(-(gdens0*xval+(-b*exp(-p0/b)))/b)-p1)/p1)'
    vars = 'b gdens0 p0 xval p1'
    vals = '0.5E2 -0.5 pg_left 1 pg_right'
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 0.5E-3'
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]



[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres asm lu NONZERO 1E-10 1E-10 10000'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = Newton
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = gh04
  csv = true
[]

(modules/combined/examples/phase_field-mechanics/kks_mechanics_KHS.i)

# KKS phase-field model coupled with elasticity using Khachaturyan's scheme as
# described in L.K. Aagesen et al., Computational Materials Science, 140, 10-21 (2017)
# Original run #170403a

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 640
  ny = 1
  nz = 1
  xmin = -10
  xmax = 10
  ymin = 0
  ymax = 0.03125
  zmin = 0
  zmax = 0.03125
  elem_type = HEX8
[]


[Variables]
  # order parameter
  [./eta]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute concentration
  [./c]
    order = FIRST
    family = LAGRANGE
  [../]

  # chemical potential
  [./w]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute phase concentration (matrix)
  [./cm]
    order = FIRST
    family = LAGRANGE
  [../]
  # solute phase concentration (precipitate)
  [./cp]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./eta_ic]
    variable = eta
    type = FunctionIC
    function = ic_func_eta
    block = 0
  [../]
  [./c_ic]
    variable = c
    type = FunctionIC
    function = ic_func_c
    block = 0
  [../]
  [./w_ic]
    variable = w
    type = ConstantIC
    value = 0.00991
    block = 0
  [../]
  [./cm_ic]
    variable = cm
    type = ConstantIC
    value = 0.131
    block = 0
  [../]
  [./cp_ic]
    variable = cp
    type = ConstantIC
    value = 0.236
    block = 0
  [../]
[]

[Functions]
  [./ic_func_eta]
    type = ParsedFunction
    value = '0.5*(1.0+tanh((x)/delta_eta/sqrt(2.0)))'
    vars = 'delta_eta'
    vals = '0.8034'
  [../]
  [./ic_func_c]
    type = ParsedFunction
    value = '0.2389*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10)+0.1339*(1-(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10))'
    vars = 'delta'
    vals = '0.8034'
  [../]
  [./psi_eq_int]
    type = ParsedFunction
    value = 'volume*psi_alpha'
    vars = 'volume psi_alpha'
    vals = 'volume psi_alpha'
  [../]
  [./gamma]
    type = ParsedFunction
    value = '(psi_int - psi_eq_int) / dy / dz'
    vars = 'psi_int psi_eq_int dy       dz'
    vals = 'psi_int psi_eq_int 0.03125  0.03125'
  [../]
[]

[AuxVariables]
  [./sigma11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./sigma22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./sigma33]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e12]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e33]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_el11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_el12]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_el22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./f_el]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./eigen_strain00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./Fglobal]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./psi]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_sigma11]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = sigma11
  [../]
  [./matl_sigma22]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = sigma22
  [../]
  [./matl_sigma33]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    variable = sigma33
  [../]
  [./matl_e11]
    type = RankTwoAux
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
    variable = e11
  [../]
  [./f_el]
    type = MaterialRealAux
    variable = f_el
    property = f_el_mat
    execute_on = timestep_end
  [../]
  [./GlobalFreeEnergy]
    variable = Fglobal
    type = KKSGlobalFreeEnergy
    fa_name = fm
    fb_name = fp
    w = 0.0264
    kappa_names = kappa
    interfacial_vars = eta
  [../]
  [./psi_potential]
    variable = psi
    type = ParsedAux
    args = 'Fglobal w c f_el sigma11 e11'
    function = 'Fglobal - w*c + f_el - sigma11*e11'
  [../]
[]


[BCs]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./right_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0
  [../]
  [./front_y]
    type = DirichletBC
    variable = disp_y
    boundary = front
    value = 0
  [../]
  [./back_y]
    type = DirichletBC
    variable = disp_y
    boundary = back
    value = 0
  [../]
  [./top_z]
    type = DirichletBC
    variable = disp_z
    boundary = top
    value = 0
  [../]
  [./bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  [../]
[]

[Materials]
  # Chemical free energy of the matrix
  [./fm]
    type = DerivativeParsedMaterial
    f_name = fm
    args = 'cm'
    function = '6.55*(cm-0.13)^2'
  [../]

  # Chemical Free energy of the precipitate phase
  [./fp]
    type = DerivativeParsedMaterial
    f_name = fp
    args = 'cp'
    function = '6.55*(cp-0.235)^2'
  [../]

# Elastic energy of the precipitate
  [./elastic_free_energy_p]
    type = ElasticEnergyMaterial
    f_name = f_el_mat
    args = 'eta'
    outputs = exodus
  [../]


  # h(eta)
  [./h_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta
  [../]

  # 1- h(eta), putting in function explicitly
  [./one_minus_h_eta_explicit]
    type = DerivativeParsedMaterial
    f_name = one_minus_h_explicit
    args = eta
    function = 1-eta^3*(6*eta^2-15*eta+10)
    outputs = exodus
  [../]

  # g(eta)
  [./g_eta]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'M   L   kappa      misfit'
    prop_values = '0.7 0.7 0.01704    0.00377'
  [../]

  #Mechanical properties
  [./Stiffness_matrix]
    type = ComputeElasticityTensor
    base_name = C_matrix
    C_ijkl = '103.3 74.25 74.25 103.3 74.25 103.3 46.75 46.75 46.75'
    fill_method = symmetric9
  [../]
  [./Stiffness_ppt]
    type = ComputeElasticityTensor
    C_ijkl = '100.7 71.45 71.45 100.7 71.45 100.7 50.10 50.10 50.10'
    base_name = C_ppt
    fill_method = symmetric9
  [../]
  [./C]
    type = CompositeElasticityTensor
    args = eta
    tensors = 'C_matrix               C_ppt'
    weights = 'one_minus_h_explicit   h'
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
  [./strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y disp_z'
    eigenstrain_names = 'eigenstrain_ppt'
  [../]
  [./eigen_strain]
    type = ComputeVariableEigenstrain
    eigen_base = '0.00377 0.00377 0.00377 0 0 0'
    prefactor = h
    args = eta
    eigenstrain_name = 'eigenstrain_ppt'
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y disp_z'
  [../]

  # enforce c = (1-h(eta))*cm + h(eta)*cp
  [./PhaseConc]
    type = KKSPhaseConcentration
    ca       = cm
    variable = cp
    c        = c
    eta      = eta
  [../]

  # enforce pointwise equality of chemical potentials
  [./ChemPotVacancies]
    type = KKSPhaseChemicalPotential
    variable = cm
    cb       = cp
    fa_name  = fm
    fb_name  = fp
  [../]

  #
  # Cahn-Hilliard Equation
  #
  [./CHBulk]
    type = KKSSplitCHCRes
    variable = c
    ca       = cm
    fa_name  = fm
    w        = w
  [../]

  [./dcdt]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
  [./ckernel]
    type = SplitCHWRes
    mob_name = M
    variable = w
  [../]

  #
  # Allen-Cahn Equation
  #
  [./ACBulkF]
    type = KKSACBulkF
    variable = eta
    fa_name  = fm
    fb_name  = fp
    w        = 0.0264
    args = 'cp cm'
  [../]
  [./ACBulkC]
    type = KKSACBulkC
    variable = eta
    ca       = cm
    cb       = cp
    fa_name  = fm
  [../]
  [./ACBulk_el] #This adds df_el/deta for strain interpolation
    type = AllenCahn
    variable = eta
    f_name = f_el_mat
  [../]
  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = kappa
  [../]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -sub_pc_type   -sub_pc_factor_shift_type'
  petsc_options_value = 'asm       ilu            nonzero'

  l_max_its = 30
  nl_max_its = 10
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-11
  num_steps = 200

  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.5
  [../]
[]

[Postprocessors]
  [./f_el_int]
    type = ElementIntegralMaterialProperty
    mat_prop = f_el_mat
  [../]
  [./c_alpha]
    type =  SideAverageValue
    boundary = left
    variable = c
  [../]
  [./c_beta]
    type =  SideAverageValue
    boundary = right
    variable = c
  [../]
  [./e11_alpha]
    type =  SideAverageValue
    boundary = left
    variable = e11
  [../]
  [./e11_beta]
    type =  SideAverageValue
    boundary = right
    variable = e11
  [../]
  [./s11_alpha]
    type =  SideAverageValue
    boundary = left
    variable = sigma11
  [../]
  [./s22_alpha]
    type =  SideAverageValue
    boundary = left
    variable = sigma22
  [../]
  [./s33_alpha]
    type =  SideAverageValue
    boundary = left
    variable = sigma33
  [../]
  [./s11_beta]
    type =  SideAverageValue
    boundary = right
    variable = sigma11
  [../]
  [./s22_beta]
    type =  SideAverageValue
    boundary = right
    variable = sigma22
  [../]
  [./s33_beta]
    type =  SideAverageValue
    boundary = right
    variable = sigma33
  [../]
  [./f_el_alpha]
    type =  SideAverageValue
    boundary = left
    variable = f_el
  [../]
  [./f_el_beta]
    type =  SideAverageValue
    boundary = right
    variable = f_el
  [../]
  [./f_c_alpha]
    type =  SideAverageValue
    boundary = left
    variable = Fglobal
  [../]
  [./f_c_beta]
    type =  SideAverageValue
    boundary = right
    variable = Fglobal
  [../]
  [./chem_pot_alpha]
    type =  SideAverageValue
    boundary = left
    variable = w
  [../]
  [./chem_pot_beta]
    type =  SideAverageValue
    boundary = right
    variable = w
  [../]
  [./psi_alpha]
    type =  SideAverageValue
    boundary = left
    variable = psi
  [../]
  [./psi_beta]
    type =  SideAverageValue
    boundary = right
    variable = psi
  [../]
  [./total_energy]
    type = ElementIntegralVariablePostprocessor
    variable = Fglobal
  [../]
  # Get simulation cell size from postprocessor
  [./volume]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
  [../]
  [./psi_eq_int]
    type = FunctionValuePostprocessor
    function = psi_eq_int
  [../]
  [./psi_int]
    type = ElementIntegralVariablePostprocessor
    variable = psi
  [../]
  [./gamma]
    type = FunctionValuePostprocessor
    function = gamma
  [../]
  [./int_position]
    type = FindValueOnLine
    start_point = '-10 0 0'
    end_point = '10 0 0'
    v = eta
    target = 0.5
  [../]
[]

#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
  [./full]
    type = SMP
    full = true
  [../]
[]


[Outputs]
  [./exodus]
    type = Exodus
    interval = 20
  [../]
  checkpoint = true
  [./csv]
    type = CSV
    execute_on = 'final'
  [../]
[]

(test/tests/materials/functor_properties/ad_conversion/1d_dirichlet.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmax = 2
[]

[Variables]
  [v]
    type = MooseVariableFVReal
  []
[]

[AuxVariables]
  [sink]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [sink]
    type = FunctionIC
    variable = sink
    function = 'x^3'
  []
[]


[FVKernels]
  [diff]
    type = FVDiffusion
    variable = v
    coeff = 1
  []
  [sink]
    type = FVFunctorElementalKernel
    variable = v
    functor_name = 'ad_sink'
  []
[]

[FVBCs]
  [bounds]
    type = FVDirichletBC
    variable = v
    boundary = 'left right'
    value = 0
  []
[]

[Materials]
  [converter_to_regular]
    type = FunctorADConverter
    ad_props_in = 'sink'
    reg_props_out = 'regular_sink_0'
  []
  # Just to change the name
  [functor]
    type = GenericFunctorMaterial
    prop_names = 'regular_sink_1'
    prop_values = 'regular_sink_0'
  []
  [converter_to_ad]
    type = FunctorADConverter
    reg_props_in = 'regular_sink_1'
    ad_props_out = 'ad_sink'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(test/tests/time_steppers/timesequence_stepper/timesequence_restart_failure.i)

[Mesh]
  file = timesequence_restart_failure1_cp/0002_mesh.cpr
[]

[Problem]
  restart_file_base = timesequence_restart_failure1_cp/0002
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  end_time = 4.0
  [./TimeStepper]
    type = TimeSequenceStepper
    time_sequence  = '0   0.85 1.2 1.3 2 4'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/energy_conservation/except02.i)

# checking that the heat-energy postprocessor throws the correct error if the kernel_variable_number is illegal
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 3
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [temp]
  []
[]

[ICs]
  [tinit]
    type = FunctionIC
    function = '100*x'
    variable = temp
  []
  [pinit]
    type = FunctionIC
    function = x
    variable = pp
  []
[]

[Kernels]
  [dummyt]
    type = TimeDerivative
    variable = temp
  []
  [dummyp]
    type = TimeDerivative
    variable = pp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      viscosity = 0.001
      thermal_expansion = 0
      cv = 1.3
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 2.2
    density = 0.5
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
[]

[Postprocessors]
  [total_heat]
    type = PorousFlowHeatEnergy
    kernel_variable_number = 2
  []
  [rock_heat]
    type = PorousFlowHeatEnergy
  []
  [fluid_heat]
    type = PorousFlowHeatEnergy
    include_porous_skeleton = false
    phase = 0
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = except01
  csv = true
[]

(test/tests/userobjects/solution_user_object/discontinuous_value_solution_uo_p1.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 2
  ny = 2
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./discontinuous_variable]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./continuous_variable]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Functions]
  [./discontinuous_function]
    type = ParsedFunction
    value = 'if(x<0.5,3,5)'
  [../]
  [./continuous_function]
    type = ParsedFunction
    value = 'if(x<0.5,x,2*x-0.5)'
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[ICs]
  [./discontinuous_variable]
    type = FunctionIC
    variable = discontinuous_variable
    function = discontinuous_function
  [../]
  [./continuous_variable]
    type = FunctionIC
    variable = continuous_variable
    function = continuous_function
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./one]
    type = DirichletBC
    variable = u
    boundary = 'right top bottom'
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  file_base = discontinuous_value_solution_uo_p1
  exodus = true
[]

(modules/chemical_reactions/test/tests/aqueous_equilibrium/1species_without_action.i)

# Simple equilibrium reaction example.
# This simulation is identical to 1species.i, but explicitly includes the AuxVariables,
# AuxKernels, and Kernels that the action in 1species.i adds

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
[]

[Variables]
  [./a]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1e-2
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
      variable = a
    [../]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pa2]
  [../]
[]

[AuxKernels]
  [./pa2eq]
    type = AqueousEquilibriumRxnAux
    variable = pa2
    v = a
    sto_v = 2
    log_k = 1
  [../]
[]

[ICs]
  [./pressure]
    type = FunctionIC
    variable = pressure
    function = 2-x
  [../]
[]

[Kernels]
  [./a_ie]
    type = PrimaryTimeDerivative
    variable = a
  [../]
  [./a_diff]
    type = PrimaryDiffusion
    variable = a
  [../]
  [./a_conv]
    type = PrimaryConvection
    variable = a
    p = pressure
  [../]
  [./aeq]
    type = CoupledBEEquilibriumSub
    variable = a
    log_k = 1
    weight = 2
    sto_u = 2
  [../]
  [./adiff]
    type = CoupledDiffusionReactionSub
    variable = a
    log_k = 1
    weight = 2
    sto_u = 2
  [../]
  [./aconv]
    type = CoupledConvectionReactionSub
    variable = a
    log_k = 1
    weight = 2
    sto_u = 2
    p = pressure
  [../]
[]

[BCs]
  [./a_right]
    type = ChemicalOutFlowBC
    variable = a
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-4 1e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-12
  start_time = 0.0
  end_time = 100
  dt = 10.0
[]

[Outputs]
  file_base = 1species_out
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

(modules/porous_flow/test/tests/heat_advection/heat_advection_1d_fully_saturated.i)

# 1phase, heat advecting with a moving fluid
# Using the FullySaturated Kernel
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 50
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [temp]
    initial_condition = 200
  []
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1-x'
  []
[]

[BCs]
  [pp0]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 1
  []
  [pp1]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 0
  []
  [spit_heat]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  []
  [suck_heat]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 200
  []
[]

[Kernels]
  [mass_dot]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [advection]
    type = PorousFlowFullySaturatedDarcyBase
    variable = pp
  []
  [energy_dot]
    type = PorousFlowEnergyTimeDerivative
    variable = temp
  []
  [convection]
    type = PorousFlowFullySaturatedHeatAdvection
    variable = temp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 100
      density0 = 1000
      viscosity = 4.4
      thermal_expansion = 0
      cv = 2
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 1.0
    density = 125
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 2 0 0 0 3'
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [PS]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres bjacobi 1E-15 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.01
  end_time = 0.6
[]

[VectorPostprocessors]
  [T]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 51
    sort_by = x
    variable = temp
  []
[]

[Outputs]
  file_base = heat_advection_1d_fully_saturated
  [csv]
    type = CSV
    sync_times = '0.1 0.6'
    sync_only = true
  []
[]

(modules/porous_flow/examples/multiapp_fracture_flow/diffusion_multiapp/two_vars.i)

# Heat transfer between matrix and fracture, with the matrix and fracture being identical spatial domains, but a multiapp approach is not used
[Mesh]
  [generate]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 100
    xmin = 0
    xmax = 50.0
  []
[]

[Variables]
  [frac_T]
  []
  [matrix_T]
  []
[]

[ICs]
  [frac_T]
    type = FunctionIC
    variable = frac_T
    function = 'if(x<0.5, 2, 0)'  # delta function
  []
[]

[Kernels]
  [dot_frac]
    type = TimeDerivative
    variable = frac_T
  []
  [frac_diffusion]
    type = Diffusion
    variable = frac_T
  []
  [toMatrix]
    type = PorousFlowHeatMassTransfer
    variable = frac_T
    v = matrix_T
    transfer_coefficient = 0.004
  []
  [dot_matrix]
    type = TimeDerivative
    variable = matrix_T
  []
  [matrix_diffusion]
    type = Diffusion
    variable = matrix_T
  []
  [toFrac]
    type = PorousFlowHeatMassTransfer
    variable = matrix_T
    v = frac_T
    transfer_coefficient = 0.004
  []
[]

[Preconditioning]
  [entire_jacobian]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 100
  end_time = 100
[]

[VectorPostprocessors]
  [final_results]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '50 0 0'
    num_points = 11
    sort_by = x
    variable = 'frac_T matrix_T'
    outputs = final_csv
  []
[]

[Outputs]
  print_linear_residuals = false
  [final_csv]
    type = CSV
    sync_times = 100
    sync_only = true
  []
[]

(modules/geochemistry/test/tests/kernels/time_deriv_2.i)

# A point-source is added to fluid in a material with spatially-varying porosity
# porosity * d(concentration)/dt = 3.0 * delta(x - 1.0)
# where delta is the Dirac delta function (a ConstantPointSource DiracKernel)
# The solution, at x = 1.0 is
# concentration = concentration_old + 3 * dt / porosity
# while concentration is unchanged elsewhere.
# Note that since GeochemistryTimeDerivative is mass-lumped, it produces this solution.
# If mass lumping had not been used, concentration would have decreased at x != 1.0
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  xmax = 2
[]

[Variables]
  [conc]
  []
[]

[Kernels]
  [dot]
    type = GeochemistryTimeDerivative
    porosity = porosity
    variable = conc
  []
[]

[DiracKernels]
  [source]
    type = ConstantPointSource
    point = '1.0 0 0'
    variable = conc
    value = 12.0
  []
[]

[ICs]
  [conc]
    type = FunctionIC
    function = 'x * x'
    variable = conc
  []
[]

[AuxVariables]
  [porosity]
  []
  [expected]
  []
  [should_be_zero]
  []
[]

[AuxKernels]
  [porosity]
    type = FunctionAux
    function = '6.0 + x'
    variable = porosity
  []
  [expected]
    type = FunctionAux
   function = 'if(x > 0.5 & x < 1.5, x * x + 2.0 * 12.0 / (6.0 + x), x * x)'
    variable = expected
  []
  [should_be_zero]
    type = ParsedAux
    args = 'expected conc'
    function = 'expected - conc'
    variable = should_be_zero
  []
[]

[Postprocessors]
  [error]
    type = NodalL2Norm
    variable = should_be_zero
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2
  end_time = 2
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/numerical_diffusion/pffltvd.i)

# Using flux-limited TVD advection ala Kuzmin and Turek, employing PorousFlow Kernels and UserObjects, with superbee flux-limiter
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [porepressure]
  []
  [tracer]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '1 - x'
  []
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = tracer
  []
  [flux0]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = advective_flux_calculator_0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = porepressure
  []
  [flux1]
    type = PorousFlowFluxLimitedTVDAdvection
    variable = porepressure
    advective_flux_calculator = advective_flux_calculator_1
  []
[]

[BCs]
  [constant_injection_porepressure]
    type = DirichletBC
    variable = porepressure
    value = 1
    boundary = left
  []
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_component_1]
    type = PorousFlowPiecewiseLinearSink
    variable = porepressure
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 1
    use_mobility = true
    flux_function = 1E3
  []
  [remove_component_0]
    type = PorousFlowPiecewiseLinearSink
    variable = tracer
    boundary = right
    fluid_phase = 0
    pt_vals = '0 1E3'
    multipliers = '0 1E3'
    mass_fraction_component = 0
    use_mobility = true
    flux_function = 1E3
  []
[]

[Modules]
  [FluidProperties]
    [the_simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2E9
      thermal_expansion = 0
      viscosity = 1.0
      density0 = 1000.0
    []
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'porepressure tracer'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
  [advective_flux_calculator_0]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 0
  []
  [advective_flux_calculator_1]
    type = PorousFlowAdvectiveFluxCalculatorSaturatedMultiComponent
    flux_limiter_type = superbee
    fluid_component = 1
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = porepressure
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = tracer
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = the_simple_fluid
    phase = 0
  []
  [relperm]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosity
    porosity_zero = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-2 0 0   0 1E-2 0   0 0 1E-2'
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  timestep_tolerance = 1E-3
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(test/tests/time_steppers/timesequence_stepper/timesequence_restart3.i)

[Mesh]
  file = timesequence_restart1_cp/0002_mesh.cpr
[]

[Problem]
  restart_file_base = timesequence_restart1_cp/0002
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  end_time = 4.5
  [./TimeStepper]
    type = TimeSequenceStepper
    time_sequence  = '0   0.85 1.3 1.9 2 4 4.5'
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/dirac/bh27.i)

#2-phase version of bh07 (go to steadystate with borehole)
[Mesh]
  type = FileMesh
  file = bh07_input.e
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
  viscosity = '1E-3 1E-5'
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1000 10000'
    x = '100 1000'
  [../]
[]


[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.6
    al = 1E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.6
    al = 1E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGnone
  [../]
  [./SUPGgas]
    type = RichardsSUPGnone
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = 1E7
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = 1E7
  [../]
[]

[BCs]
  [./fix_outer_w]
    type = DirichletBC
    boundary = perimeter
    variable = pwater
    value = 1E7
  [../]
  [./fix_outer_g]
    type = DirichletBC
    boundary = perimeter
    variable = pgas
    value = 1E7
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFullyUpwindFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFullyUpwindFlux
    variable = pgas
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh07.bh
    SumQuantityUO = borehole_total_outflow_mass
    fully_upwind = true
    variable = pwater
    unit_weight = '0 0 0'
    re_constant = 0.1594
    character = 2 # this is to make the length 1m borehole fill the entire 2m height
  [../]
  [./bh_gas_dummy]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh07.bh
    SumQuantityUO = borehole_total_outflow_mass
    fully_upwind = true
    variable = pgas
    unit_weight = '0 0 0'
    re_constant = 0.1594
    character = 2 # this is to make the length 1m borehole fill the entire 2m height
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
    execute_on = 'initial timestep_end'
  [../]

  [./water_mass]
    type = RichardsMass
    variable = pwater
    execute_on = 'initial timestep_end'
  [../]
  [./gas_mass]
    type = RichardsMass
    variable = pgas
    execute_on = 'initial timestep_end'
  [../]
[]



[Materials]
  [./all]
    type = RichardsMaterial
    block = 1
    mat_porosity = 0.1
    mat_permeability = '1E-11 0 0  0 1E-11 0  0 0 1E-11'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-10 1E-10 20 1E-10 1E-100'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1000
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]

[]

[Outputs]
  file_base = bh27
  execute_on = 'initial timestep_end final'
  interval = 1000000
  exodus = true
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/fltvd_2D_trimesh.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, with antidiffusion from superbee flux limiting
# 2D version
[Mesh]
  type = FileMesh
  file = trimesh.msh
[]

[GlobalParams]
  block = '50'
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.305,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0.04 0'
    num_points = 101
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/rdg/test/tests/advection_1d/1d_aefv_square_wave.i)

############################################################
[GlobalParams]
  order = CONSTANT
  family = MONOMIAL
  u = u
  slope_limiting = lslope
  implicit = false
[]
############################################################
[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 1
  nx = 100
[]
############################################################
[Functions]
  [./ic_u]
    type = PiecewiseConstant
    axis = x
    direction = right
    xy_data = '0.1 0.5
               0.6 1.0
               1.0 0.5'
  [../]
[]
############################################################
[UserObjects]
  [./lslope]
    type = AEFVSlopeLimitingOneD
    execute_on = 'linear'
    scheme = 'none' #none | minmod | mc | superbee
  [../]

  [./internal_side_flux]
    type = AEFVUpwindInternalSideFlux
    execute_on = 'linear'
  [../]

  [./free_outflow_bc]
    type = AEFVFreeOutflowBoundaryFlux
    execute_on = 'linear'
  [../]
[]
############################################################
[Variables]
  [./u]
  [../]
[]
############################################################
[ICs]
  [./u_ic]
    type = FunctionIC
    variable = 'u'
    function = ic_u
  [../]
[]
############################################################
[Kernels]
  [./time_u]
    implicit = true
    type = TimeDerivative
    variable = u
  [../]
[]
############################################################
[DGKernels]
  [./concentration]
    type = AEFVKernel
    variable = u
    component = 'concentration'
    flux = internal_side_flux
  [../]
[]
############################################################
[BCs]
  [./concentration]
    type = AEFVBC
    boundary = 'left right'
    variable = u
    component = 'concentration'
    flux = free_outflow_bc
  [../]
[]
############################################################
[Materials]
  [./aefv]
    type = AEFVMaterial
    block = 0
  [../]
[]
############################################################
[Executioner]
  type = Transient
  [./TimeIntegrator]
    type = ExplicitMidpoint
  [../]
  solve_type = 'LINEAR'

  l_tol = 1e-4
  nl_rel_tol = 1e-20
  nl_abs_tol = 1e-8
  nl_max_its = 60

  start_time = 0.0
  num_steps = 4 # 4 | 400 for complete run
  dt = 5e-4
  dtmin = 1e-6
[]

[Outputs]
  [./Exodus]
    type = Exodus
    file_base = 1d_aefv_square_wave_none_out
    interval = 2
  [../]
  perf_graph = true
[]

(test/tests/functions/image_function/image_mesh_3d.i)

[Mesh]
  type = ImageMesh
  dim = 3
  file_base = stack/test
  file_suffix = png
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    # ImageFunction gets its file range parameters from ImageMesh,
    # when it is present.  This prevents duplicating information in
    # input files.
    type = ImageFunction
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/sinks/s04.i)

# apply a piecewise-linear sink flux and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = y+1
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-5 0 0 0 1E-5 0 0 0 1E-5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[AuxVariables]
  [flux_out]
  []
  [xval]
  []
  [yval]
  []
  [pt_shift]
    initial_condition = 0.3
  []
[]

[ICs]
  [xval]
    type = FunctionIC
    variable = xval
    function = x
  []
  [yval]
    type = FunctionIC
    variable = yval
    function = y
  []
[]

[Functions]
  [mass10]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)'
    vars = 'vol por dens0 pp bulk'
    vals = '0.25 0.1 1.1 p10 1.3'
  []
  [rate10]
    type = ParsedFunction
    value = 'fcn*if(pp>0.8,1,if(pp<0.3,0.5,0.2+pp))'
    vars = 'fcn pp'
    vals = '8   p10'
  []
  [mass10_expect]
    type = ParsedFunction
    value = 'mass_prev-rate*area*dt'
    vars = 'mass_prev rate     area dt'
    vals = 'm10_prev  m10_rate 0.5 1E-3'
  []
  [mass11]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)'
    vars = 'vol por dens0 pp bulk'
    vals = '0.25 0.1 1.1 p11 1.3'
  []
  [rate11]
    type = ParsedFunction
    value = 'fcn*if(pp>0.8,1,if(pp<0.3,0.5,0.2+pp))'
    vars = 'fcn pp'
    vals = '8   p11'
  []
  [mass11_expect]
    type = ParsedFunction
    value = 'mass_prev-rate*area*dt'
    vars = 'mass_prev rate     area dt'
    vals = 'm11_prev  m11_rate 0.5 1E-3'
  []
[]

[Postprocessors]
  [p00]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p10]
    type = PointValue
    point = '1 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m10]
    type = FunctionValuePostprocessor
    function = mass10
    execute_on = 'initial timestep_end'
  []
  [m10_prev]
    type = FunctionValuePostprocessor
    function = mass10
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [m10_rate]
    type = FunctionValuePostprocessor
    function = rate10
    execute_on = 'timestep_end'
  []
  [m10_expect]
    type = FunctionValuePostprocessor
    function = mass10_expect
    execute_on = 'timestep_end'
  []
  [p01]
    type = PointValue
    point = '0 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p11]
    type = PointValue
    point = '1 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m11]
    type = FunctionValuePostprocessor
    function = mass11
    execute_on = 'initial timestep_end'
  []
  [m11_prev]
    type = FunctionValuePostprocessor
    function = mass11
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [m11_rate]
    type = FunctionValuePostprocessor
    function = rate11
    execute_on = 'timestep_end'
  []
  [m11_expect]
    type = FunctionValuePostprocessor
    function = mass11_expect
    execute_on = 'timestep_end'
  []
[]

[BCs]
  [flux]
    type = PorousFlowPiecewiseLinearSink
    boundary = 'right'
    PT_shift = pt_shift
    pt_vals = '0.0 0.5'
    multipliers = '0.5 1'
    variable = pp
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 8
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10000 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-3
  end_time = 1E-2
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s04
  [console]
    type = Console
    execute_on = 'nonlinear linear'
  []
  [csv]
    type = CSV
    execute_on = 'timestep_end'
  []
[]

(modules/porous_flow/test/tests/mass_conservation/mass08.i)

# Checking that the mass postprocessor throws the correct error when a given phase index
# is too large

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [sat]
  []
[]

[AuxVariables]
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
[]

[ICs]
  [pinit]
    type = ConstantIC
    value = 1
    variable = pp
  []
  [satinit]
    type = FunctionIC
    function = 1-x
    variable = sat
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sat
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp sat'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 1
      thermal_expansion = 0
    []
    [simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 1
      density0 = 0.1
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp
    phase1_saturation = sat
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Postprocessors]
  [comp1_total_mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = 2
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 1
[]

(python/peacock/tests/common/spherical_average.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 10
  nz = 10
  xmin = -5
  xmax = 5
  ymin = -5
  ymax = 5
  zmin = -5
  zmax = 5
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = sin(x*7.4+z*4.1)+cos(y*3.8+x*8.7)+sin(z*9.1+y*2.6)
    [../]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
[]

[VectorPostprocessors]
  [./average]
    type = SphericalAverage
    variable = c
    radius = 5
    bin_number = 10
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 1
  solve_type = PJFNK
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  csv = true
[]

(test/tests/transfers/multiapp_conservative_transfer/primary_skipped_adjuster.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
[]

[Variables]
  [u]
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[AuxVariables]
  [var]
    family = MONOMIAL
    order = THIRD
  []
[]

[ICs]
  [var_ic]
    type = FunctionIC
    variable = var
    function = '-exp(x * y)'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    input_files = secondary_negative_adjuster.i
    execute_on = timestep_begin
  []
[]

[Postprocessors]
  [from_postprocessor]
    type = ElementIntegralVariablePostprocessor
    variable = var
  []
[]

[Transfers]
  [to_sub]
    type = MultiAppMeshFunctionTransfer
    source_variable = var
    variable = var
    to_multi_app = sub
    from_postprocessors_to_be_preserved  = 'from_postprocessor'
    to_postprocessors_to_be_preserved  = 'to_postprocessor'
    allow_skipped_adjustment = true
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/solution_function/solution_function_rot2.i)

# checking rotation of points by 45 deg about y axis in a SolutionUserObject
[Mesh]
  # this is chosen so when i rotate through 45deg i get a length of "1" along the x or y or z direction
  type = GeneratedMesh
  dim = 3
  xmin = -0.70710678
  xmax = 0.70710678
  nx = 3
  ymin = -0.70710678
  ymax = 0.70710678
  ny = 3
  zmin = -0.70710678
  zmax = 0.70710678
  nz = 3
[]

[UserObjects]
  [./solution_uo]
    type = SolutionUserObject
    mesh = cube_with_u_equals_x.e
    timestep = 1
    system_variables = u
    rotation0_vector = '0 1 0'
    rotation0_angle = 45
    transformation_order = rotation0
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./u_init]
    type = FunctionIC
    variable = u
    function = solution_fcn
  [../]
[]

[Functions]
  [./solution_fcn]
    type = SolutionFunction
    from_variable = u
    solution = solution_uo
  [../]
[]

[Kernels]
  [./diff]
    type = TimeDerivative
    variable = u
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'

  l_max_its = 800
  nl_rel_tol = 1e-10
  num_steps = 1
  end_time = 1
  dt = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = solution_function_rot2
  exodus = true
[]

(test/tests/functions/image_function/image_3d_subset.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 20
  ny = 20
  nz = 6
  zmax = 0.3
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0 5'
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/function_file_test9.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/transfers/multiapp_projection_transfer/high_order_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 4
  ny = 4
[]

[Functions]
  [./test_function]
    type = ParsedFunction
    value = '2.5*x^2 + 0.75*y^2 + 0.15*x*y'
  [../]
[]

[AuxVariables]
  [./from_master]
    family = monomial
    order = first
  [../]
  [./test_var]
    family = monomial
    order = first
    [./InitialCondition]
      type = FunctionIC
      function = test_function
    [../]
  [../]
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(test/tests/multiapps/centroid_multiapp/centroid_multiapp.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 3
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./x]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./y]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[ICs]
  [./x]
    type = FunctionIC
    function = x
    variable = x
  [../]
  [./y]
    type = FunctionIC
    function = y
    variable = y
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 'left'
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 'right'
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  solve_type = PJFNK
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = CentroidMultiApp
    input_files = 'sub_app.i'
    output_in_position = true
  []
[]

[Transfers]
  [./incoming_x]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    source_variable = x
    to_multi_app = sub
    postprocessor = incoming_x
  [../]
  [./incoming_y]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    source_variable = y
    to_multi_app = sub
    postprocessor = incoming_y
  [../]
[]

(modules/porous_flow/test/tests/jacobian/fflux02_fully_saturated.i)

# Using PorousFlowFullySaturatedAdvectiveFlux
# 1phase, 3components, constant insitu permeability
# density with constant bulk, constant viscosity, nonzero gravity
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pp]
  []
  [massfrac0]
  []
  [massfrac1]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = -0.7+x+y
  []
  [massfrac0]
    type = RandomIC
    variable = massfrac0
    min = 0
    max = 0.3
  []
  [massfrac1]
    type = RandomIC
    variable = massfrac1
    min = 0
    max = 0.4
  []
[]

[Kernels]
  [flux0]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
  []
  [flux1]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
    gravity = '-1 -0.1 0'
  []
  [flux2]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 2
    variable = massfrac1
    gravity = '-1 -0.1 0'
  []
  [flux0_nodensity]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 0
    variable = pp
    gravity = '-1 -0.1 0'
    multiply_by_density = false
  []
  [flux1_nodensity]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
    gravity = '-1 -0.1 0'
    multiply_by_density = false
  []
  [flux2_nodensity]
    type = PorousFlowFullySaturatedAdvectiveFlux
    fluid_component = 2
    variable = massfrac1
    gravity = '-1 -0.1 0'
    multiply_by_density = false
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0 massfrac1'
    number_fluid_phases = 1
    number_fluid_components = 3
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      density0 = 1
      thermal_expansion = 0
      viscosity = 1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac0 massfrac1'
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '2 0 0 0 2 0 0 0 3'
  []
[]

[Preconditioning]
  active = check
  [check]
    type = SMP
    full = true
    petsc_options_iname = '-snes_type'
    petsc_options_value = 'test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  num_steps = 1
[]

(test/tests/auxkernels/forcing_function_aux/forcing_function_aux.i)

# This is a test of the ForcingFunctionAux AuxKernel.
# The diffusion equation for u is solved with boundary conditions to force a gradient
# du/dx = 2, which is constant in time.
# du/dx is integrated over the unit square domain using a postprocessor, resulting in 2.
# The value of this postprocessor is supplied to the forcing function f used by
# the ForcingFunctionAux AuxKernel, which increments the AuxVariable T.
# Since the time step is 1, the value of T increases by 2 for each time step.

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./grad_u_x]
    order = CONSTANT
    family = MONOMIAL
    initial_condition = 2
  [../]
  [./T]
    order = CONSTANT
    family = MONOMIAL
    initial_condition = 100
  [../]
[]

[Functions]
  [./u_ic_func]
    type = ParsedFunction
    value = '2*x'
  [../]
  [./f]
    type = ParsedFunction
    vars = f
    vals = grad_int
    value = f
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = u_ic_func
  [../]
[]

[Kernels]
  [./dudt]
    type = TimeDerivative
    variable = u
  [../]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[AuxKernels]
  [./grad_u_x_aux]
    type = VariableGradientComponent
    variable = grad_u_x
    component = x
    gradient_variable = u
  [../]
  [./T_increment]
    type = ForcingFunctionAux
    variable = T
    function = f
  [../]
[]

[Postprocessors]
  [./grad_int]
    type = ElementIntegralVariablePostprocessor
    variable = grad_u_x
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 2
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
  num_steps = 2
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/sinks/s09_fully_saturated.i)

# Apply a piecewise-linear sink flux to the right-hand side and watch fluid flow to it
#
# This test has a single phase with two components.  The test initialises with
# the porous material fully filled with component=1.  The left-hand side is fixed
# at porepressure=1 and mass-fraction of the zeroth component being unity.
# The right-hand side has a very strong piecewise-linear flux that keeps the
# porepressure~0 at that side.  Fluid mass is extracted by this flux in proportion
# to the fluid component mass fraction.
#
# Therefore, the zeroth fluid component will flow from left to right (down the
# pressure gradient).
#
# The important DE is
# porosity * dc/dt = (perm / visc) * grad(P) * grad(c)
# which is true for c = mass-fraction, and very large bulk modulus of the fluid.
# For grad(P) constant in time and space (as in this example) this is just the
# advection equation for c, with velocity = perm / visc / porosity.  The parameters
# are chosen to velocity = 1 m/s.
# In the numerical world, and especially with full upwinding, the advection equation
# suffers from diffusion.  In this example, the diffusion is obvious when plotting
# the mass-fraction along the line, but the average velocity of the front is still
# correct at 1 m/s.
# This test uses the FullySaturated version of the flow Kernel.  This does not
# suffer from as much numerical diffusion as the standard PorousFlow Kernel since
# it does not employ any upwinding.
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp frac'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
  []
[]

[Variables]
  [pp]
  []
  [frac]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = 1-x
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = frac
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = pp
  []
  [flux0]
    type = PorousFlowFullySaturatedDarcyFlow
    fluid_component = 0
    gravity = '0 0 0'
    variable = frac
  []
  [flux1]
    type = PorousFlowFullySaturatedDarcyFlow
    fluid_component = 1
    gravity = '0 0 0'
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1e10 # need large in order for constant-velocity advection
      density0 = 1 # almost irrelevant, except that the ability of the right BC to keep P fixed at zero is related to density_P0
      thermal_expansion = 0
      viscosity = 11
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = frac
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 1.1 0 0 0 1.1'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2 # irrelevant in this fully-saturated situation
    phase = 0
  []
[]

[BCs]
  [lhs_fixed_a]
    type = DirichletBC
    boundary = 'left'
    variable = frac
    value = 1
  []
  [lhs_fixed_b]
    type = DirichletBC
    boundary = 'left'
    variable = pp
    value = 1
  []
  [flux0]
    type = PorousFlowPiecewiseLinearSink
    boundary = 'right'
    pt_vals = '-100 100'
    multipliers = '-1 1'
    variable = frac # the zeroth comonent
    mass_fraction_component = 0
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 1E4
  []
  [flux1]
    type = PorousFlowPiecewiseLinearSink
    boundary = 'right'
    pt_vals = '-100 100'
    multipliers = '-1 1'
    variable = pp # comonent 1
    mass_fraction_component = 1
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 1E4
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10000 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-2
  end_time = 1
  nl_rel_tol = 1E-11
  nl_abs_tol = 1E-11
[]

[VectorPostprocessors]
  [mf]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 100
    sort_by = x
    variable = frac
  []
[]

[Outputs]
  file_base = s09_fully_saturated
  [console]
    type = Console
    execute_on = 'nonlinear linear'
  []
  [csv]
    type = CSV
    sync_times = '0.1 0.5 1'
    sync_only = true
  []
  interval = 10
[]

(modules/richards/test/tests/buckley_leverett/bl20.i)

# two-phase version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 30
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '0.1 0.5 0.5 1 2  4'
    x = '0   0.1 1   5 40 42'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E6
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 2E6
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1E-5
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
  [./bounds_dummy]
  [../]
[]


[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
  [./richardsppenalty]
    type = RichardsPPenalty
    variable = pgas
    a = 1E-18
    lower_var = pwater
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffWater
    pressure_vars = 'pwater pgas'
  [../]
[]

[Bounds]
  [./pwater_upper_bounds]
    type = ConstantBoundsAux
    variable = bounds_dummy
    bounded_variable = pwater
    bound_type = upper
    bound_value = 1E7
  [../]
  [./pwater_lower_bounds]
    type = ConstantBoundsAux
    variable = bounds_dummy
    bounded_variable = pwater
    bound_type = lower
    bound_value = -310000
  [../]
[]


[ICs]
  [./water_ic]
    type = FunctionIC
    variable = pwater
    function = initial_water
  [../]
  [./gas_ic]
    type = FunctionIC
    variable = pgas
    function = initial_gas
  [../]
[]

[BCs]
  [./left_w]
    type = DirichletBC
    variable = pwater
    boundary = left
    value = 1E6
  [../]
  [./left_g]
    type = DirichletBC
    variable = pgas
    boundary = left
    value = 1E6
  [../]
  [./right_w]
    type = DirichletBC
    variable = pwater
    boundary = right
    value = -300000
  [../]
  [./right_g]
    type = DirichletBC
    variable = pgas
    boundary = right
    value = 0
  [../]
[]


[Functions]
  [./initial_water]
    type = ParsedFunction
    value = 1000000*(1-min(x/5,1))-300000*(max(x-5,0)/max(abs(x-5),1E-10))
  [../]
  [./initial_gas]
    type = ParsedFunction
    value = max(1000000*(1-x/5),0)+1000
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 1E-6'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'standard'

  [./bounded]
  # must use --use-petsc-dm command line argument
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type -ksp_rtol -ksp_atol'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 50 vinewtonssls 1E-20 1E-20'
  [../]

  [./standard]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -snes_atol -snes_rtol -snes_max_it -ksp_rtol -ksp_atol'
    petsc_options_value = 'gmres asm lu NONZERO 1E-10 1E-10 20 1E-20 1E-20'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 50

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  file_base = bl20
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
  hide = pgas
[]

(test/tests/functions/image_function/moose_logo_test_2D.i)

[Problem]
  solve = false
[]

[Mesh]
  type = ImageMesh
  cells_per_pixel = 1
  dim = 2
  file = moose_logo_small.png
[]

[Variables]
  [original]
    family = MONOMIAL
    order = CONSTANT
  []
  [scaled]
    family = MONOMIAL
    order = CONSTANT
  []
  [shifted]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Functions]
  [image]
    type = ImageFunction
    file = moose_logo_small.png
  []
  [image_scale]
    type = ImageFunction
    file = moose_logo_small.png
    scale = 0.00392156862
  []
  [image_shift]
    type = ImageFunction
    file = moose_logo_small.png
    shift = -127.5
  []
[]

[ICs]
  [original_IC]
    type = FunctionIC
    function = image
    variable = original
  []
  [scaled_IC]
    type = FunctionIC
    function = image_scale
    variable = scaled
  []
  [shifted_IC]
    type = FunctionIC
    function = image_shift
    variable = shifted
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/hysteresis/hys_sat_03.i)

# 1-phase hysteresis.  Saturation calculation.  Primary drying curve with low_extension_type = exponential
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 10
    nx = 100
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = pp
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1 - 2 * x'
  []
[]

[BCs]
  [pp]
    type = FunctionDirichletBC
    variable = pp
    function = '1 - 2 * x'
    boundary = 'left right'
  []
[]

[Kernels]
  [dummy]
    type = Diffusion
    variable = pp
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
  []
  [saturation_calculator]
    type = PorousFlow1PhaseHysP
    alpha_d = 10.0
    alpha_w = 10.0
    n_d = 1.1
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 7.0
    low_extension_type = exponential
    porepressure = pp
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [saturation]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [saturation]
    type = PorousFlowPropertyAux
    variable = saturation
    property = saturation
    phase = 0
  []
[]

[VectorPostprocessors]
  [sat]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0.5 0 0'
    end_point = '9.5 0 0'
    num_points = 10
    sort_by = x
    variable = 'saturation pp'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(test/tests/bcs/misc_bcs/weak_gradient_bc_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  nz = 0
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Functions]
  [./initial_value]
    type = ParsedFunction
    value = 'x'
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = initial_value
    [../]
  [../]
[]

[Kernels]
  active = 'diff ie'

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ie]
    type = TimeDerivative
    variable = u
  [../]
[]

[BCs]
  active = 'left right top bottom'

  [./left]
    type = SinDirichletBC
    variable = u
    boundary = 3
    initial = 0.0
    final = 1.0
    duration = 10.0
  [../]

  [./right]
    type = SinDirichletBC
    variable = u
    boundary = 1
    initial = 1.0
    final = 0.0
    duration = 10.0
  [../]

  # Explicit Natural Boundary Conditions
  [./top]
    type = WeakGradientBC
    variable = u
    boundary = 2
  [../]

  [./bottom]
    type = WeakGradientBC
    variable = u
    boundary = 0
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  num_steps = 10
  dt = 1.0
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/missing_function_test.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = missing_function #should generate error
    [../]
  [../]

[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/phase_field/test/tests/MultiPhase/switchingfunction3phasematerial.i)

# This is a test of the SwitchingFunction3PhaseMaterial, a switching function
# used in a 3-phase phase-field model to prevent formation of the third phase
# at the interface between the two other phases
# See Folch and Plapp, Phys. Rev. E, v 72, 011602 (2005) for details

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 0.1
  nx = 20
  ny = 2
  elem_type = QUAD4
[]

[GlobalParams]
  derivative_order = 0
  outputs = exodus
[]

[AuxVariables]
  [./eta1]
    [./InitialCondition]
      type = FunctionIC
      function = x
    [../]
  [../]
  [./eta2]
    [./InitialCondition]
      type = FunctionIC
      function = 1.0-x
    [../]
  [../]
  [./eta3]
    [./InitialCondition]
      type = ConstantIC
      value = 0.0
    [../]
  [../]
[]

[Materials]
  [./h_material_1]
    type = SwitchingFunction3PhaseMaterial
    f_name = h_i1
    eta_i = eta1
    eta_j = eta2
    eta_k = eta3
    outputs = exodus
  [../]
# Next we reverse eta2 and eta3 to make sure the switching function is symmetric
# with respect to interchanging these two, as it is designed to be
  [./h_material_2]
    type = SwitchingFunction3PhaseMaterial
    f_name = h_i2
    eta_i = eta1
    eta_j = eta3
    eta_k = eta2
    outputs = exodus
  [../]
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  execute_on = 'TIMESTEP_END'
  exodus = true
[]

(test/tests/dgkernels/1d_advection_dg/1d_advection_dg.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmin = 0
  xmax = 1
[]

[Functions]
  [./ic_u]
    type = PiecewiseConstant
    axis = x
    direction = right
    xy_data = '0.1 0.0
               0.6 1.0
               1.0 0.0'
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./time_u]
    type = TimeDerivative
    variable = u
  [../]

  [./adv_u]
    implicit = false
    type = ConservativeAdvection
    variable = u
    velocity = '1 0 0'
  [../]
[]

[DGKernels]
  [./dg_advection_u]
    implicit = false
    type = DGConvection
    variable = u
    velocity = '1 0 0'
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    variable = u
    function = ic_u
  [../]
[]

[Executioner]
  type = Transient
  [./TimeIntegrator]
    type = ExplicitMidpoint
  [../]
  solve_type = 'LINEAR'
  num_steps = 4
  dt = 2e-4
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/image_function/threshold_adapt_parallel.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  parallel_type = distributed
[]

[Variables]
  [u]
  []
[]

[Functions]
  [image_func]
    type = ImageFunction
    file_base = stack/test
    file_suffix = png
    file_range = '0' # file_range is a vector input, a single entry means "read only 1 file"
    threshold = 2.7e4
    upper_value = 1
    lower_value = -1
  []
[]

[ICs]
  [u_ic]
    type = FunctionIC
    function = image_func
    variable = u
  []
[]

[Problem]
  type = FEProblem
  solve = false
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.1
[]

[Adaptivity]
  max_h_level = 5
  initial_steps = 5
  initial_marker = marker
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = u
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      refine = 0.9
    []
  []
[]

[Outputs]
[]

(test/tests/misc/check_error/function_file_test11.i)

# Test for usage of missing function
[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = ic_function
    [../]
  [../]

[]

[Functions]
  [./ic_function]
    type = PiecewiseLinear
    data_file = piecewise_linear_columns_more_data.csv #Will generate error because data has more than two columns
    format = columns
    scale_factor = 1.0
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/ray_tracing/test/tests/userobjects/ray_tracing_study/kernel_change_ray/kernel_change_ray.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmax = 5
    ymax = 5
  []
[]

[Variables/phase]
  [InitialCondition]
    type = FunctionIC
    variable = field
    function = '(x > 2.99) * 1.0'
  []
[]

[RayBCs/kill]
  type = KillRayBC
  boundary = 'top right bottom left'
[]

[RayKernels/test]
  type = RefractionRayKernelTest
  field = phase
[]

[UserObjects/lots]
  type = LotsOfRaysRayStudy
  vertex_to_vertex = true
  centroid_to_vertex = true
  centroid_to_centroid = false
  execute_on = initial
[]

[Postprocessors/total_distance]
  type = RayTracingStudyResult
  study = lots
  result = total_distance
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/richards/test/tests/mass/m01.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  xmin = -1
  xmax = 1
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.5
    al = 1
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.2
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = x
  [../]
[]

[Postprocessors]
  [./total_mass]
    type = RichardsMass
    variable = pressure
  [../]
[]

[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    SUPG_UO = SUPGstandard
    sat_UO = Saturation
    seff_UO = SeffVG
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1 1 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-10
  end_time = 1E-10
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = m01
  csv = true
[]

(modules/porous_flow/examples/tutorial/13.i)

# Example of reactive transport model with dissolution of dolomite
#
# The equilibrium system has 5 primary species (Variables) and
# 5 secondary species (PorousFlowMassFractionAqueousEquilibrium).
# Some of the equilibrium constants have been chosen rather arbitrarily.
#
# Equilibrium reactions
# H+  + HCO3-                      = CO2(aq)
# -H+ + HCO3-                      = CO32-
#       HCO3- + Ca2+               = CaHCO3+
#       HCO3-        + Mg2+        = MgHCO3+
#       HCO3-               + Fe2+ = FeHCO3+
#
# The kinetic reaction that dissolves dolomite involves all 5 primary species.
#
# -2H+ + 2HCO3- + Ca2+ + 0.8Mg2+ + 0.2Fe2+ = CaMg0.8Fe0.2(CO3)2
#
# The initial concentration of precipitated dolomite is high, so it starts
# to dissolve immediately, increasing the concentrations of the primary species.
#
# Only single-phase, fully saturated physics is used.
# The pressure gradient is fixed, so that the Darcy velocity is 0.1m/s.
#
# Primary species are injected from the left side, and they flow to the right.
# Less dolomite dissolution therefore occurs on the left side (where
# the primary species have higher concentration).
#
# This test is more fully documented in tutorial_13
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmax = 1
[]

[Variables]
  [h+]
  []
  [hco3-]
  []
  [ca2+]
  []
  [mg2+]
  []
  [fe2+]
  []
[]

[AuxVariables]
  [eqm_k0]
    initial_condition = 2.19E6
  []
  [eqm_k1]
    initial_condition = 4.73E-11
  []
  [eqm_k2]
    initial_condition = 0.222
  []
  [eqm_k3]
    initial_condition = 1E-2
  []
  [eqm_k4]
    initial_condition = 1E-3
  []
  [kinetic_k]
    initial_condition = 326.2
  []
  [pressure]
  []
  [dolomite]
    family = MONOMIAL
    order = CONSTANT
  []
  [dolomite_initial]
    initial_condition = 1E-7
  []
[]

[AuxKernels]
  [dolomite]
    type = PorousFlowPropertyAux
    property = mineral_concentration
    mineral_species = 0
    variable = dolomite
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[ICs]
  [pressure_ic]
    type = FunctionIC
    variable = pressure
    function = '(1 - x) * 1E6'
  []
  [h+_ic]
    type = BoundingBoxIC
    variable = h+
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 5.0e-2
    outside = 1.0e-6
  []
  [hco3_ic]
    type = BoundingBoxIC
    variable = hco3-
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 5.0e-2
    outside = 1.0e-6
  []
  [ca2_ic]
    type = BoundingBoxIC
    variable = ca2+
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 5.0e-2
    outside = 1.0e-6
  []
  [mg2_ic]
    type = BoundingBoxIC
    variable = mg2+
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 5.0e-2
    outside = 1.0e-6
  []
  [fe2_ic]
    type = BoundingBoxIC
    variable = fe2+
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 5.0e-2
    outside = 1.0e-6
  []
[]

[Kernels]
  [h+_ie]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = h+
  []
  [h+_conv]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = h+
  []
  [predis_h+]
    type = PorousFlowPreDis
    variable = h+
    mineral_density = 2875.0
    stoichiometry = -2
  []
  [hco3-_ie]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = hco3-
  []
  [hco3-_conv]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = hco3-
  []
  [predis_hco3-]
    type = PorousFlowPreDis
    variable = hco3-
    mineral_density = 2875.0
    stoichiometry = 2
  []
  [ca2+_ie]
    type = PorousFlowMassTimeDerivative
    fluid_component = 2
    variable = ca2+
  []
  [ca2+_conv]
    type = PorousFlowAdvectiveFlux
    fluid_component = 2
    variable = ca2+
  []
  [predis_ca2+]
    type = PorousFlowPreDis
    variable = ca2+
    mineral_density = 2875.0
    stoichiometry = 1
  []
  [mg2+_ie]
    type = PorousFlowMassTimeDerivative
    fluid_component = 3
    variable = mg2+
  []
  [mg2+_conv]
    type = PorousFlowAdvectiveFlux
    fluid_component = 3
    variable = mg2+
  []
  [predis_mg2+]
    type = PorousFlowPreDis
    variable = mg2+
    mineral_density = 2875.0
    stoichiometry = 0.8
  []
  [fe2+_ie]
    type = PorousFlowMassTimeDerivative
    fluid_component = 4
    variable = fe2+
  []
  [fe2+_conv]
    type = PorousFlowAdvectiveFlux
    fluid_component = 4
    variable = fe2+
  []
  [predis_fe2+]
    type = PorousFlowPreDis
    variable = fe2+
    mineral_density = 2875.0
    stoichiometry = 0.2
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'h+ hco3- ca2+ mg2+ fe2+'
    number_fluid_phases = 1
    number_fluid_components = 6
    number_aqueous_equilibrium = 5
    number_aqueous_kinetic = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      viscosity = 1E-3
    []
  []
[]

[BCs]
  [hco3-_left]
    type = DirichletBC
    variable = hco3-
    boundary = left
    value = 5E-2
  []
  [h+_left]
    type = DirichletBC
    variable = h+
    boundary = left
    value = 5E-2
  []
  [ca2+_left]
    type = DirichletBC
    variable = ca2+
    boundary = left
    value = 5E-2
  []
  [mg2+_left]
    type = DirichletBC
    variable = mg2+
    boundary = left
    value = 5E-2
  []
  [fe2+_left]
    type = DirichletBC
    variable = fe2+
    boundary = left
    value = 5E-2
  []
  [hco3-_right]
    type = DirichletBC
    variable = hco3-
    boundary = right
    value = 1E-6
  []
  [h+_right]
    type = DirichletBC
    variable = h+
    boundary = right
    value = 1e-6
  []
  [ca2+_right]
    type = DirichletBC
    variable = ca2+
    boundary = right
    value = 1E-6
  []
  [mg2+_right]
    type = DirichletBC
    variable = mg2+
    boundary = right
    value = 1E-6
  []
  [fe2+_right]
    type = DirichletBC
    variable = fe2+
    boundary = right
    value = 1E-6
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 298.15
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pressure
  []
  [equilibrium_massfrac]
    type = PorousFlowMassFractionAqueousEquilibriumChemistry
    mass_fraction_vars = 'h+ hco3- ca2+ mg2+ fe2+'
    num_reactions = 5
    equilibrium_constants = 'eqm_k0 eqm_k1 eqm_k2 eqm_k3 eqm_k4'
    primary_activity_coefficients = '1 1 1 1 1'
    secondary_activity_coefficients = '1 1 1 1 1'
    reactions = '1 1 0 0 0
                -1 1 0 0 0
                 0 1 1 0 0
                 0 1 0 1 0
                 0 1 0 0 1'
  []
  [kinetic]
    type = PorousFlowAqueousPreDisChemistry
    primary_concentrations = 'h+ hco3- ca2+ mg2+ fe2+'
    num_reactions = 1
    equilibrium_constants = kinetic_k
    primary_activity_coefficients = '1 1 1 1 1'
    reactions = '-2 2 1 0.8 0.2'
    specific_reactive_surface_area = '1.2E-8'
    kinetic_rate_constant = '3E-4'
    activation_energy = '1.5e4'
    molar_volume = 64365.0
    gas_constant = 8.314
    reference_temperature = 298.15
  []
  [dolomite_conc]
    type = PorousFlowAqueousPreDisMineral
    initial_concentrations = dolomite_initial
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-10 0 0 0 1E-10 0 0 0 1E-10'
  []
  [relp]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.1
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  exodus = true
[]

(modules/porous_flow/test/tests/chemistry/2species_equilibrium_2phase.i)

# Using a two-phase system (see 2species_equilibrium for the single-phase)
# The saturations, porosity, mass fractions, tortuosity and diffusion coefficients are chosen so that the results are identical to 2species_equilibrium
#
# PorousFlow analogy of chemical_reactions/test/tests/aqueous_equilibrium/2species.i
#
# Simple equilibrium reaction example to illustrate the use of PorousFlowMassFractionAqueousEquilibriumChemistry
#
# In this example, two primary species a and b are transported by diffusion and convection
# from the left of the porous medium, reacting to form two equilibrium species pa2 and pab
# according to the equilibrium reaction:
#
#      reactions = '2a = pa2     rate = 10^2
#                   a + b = pab  rate = 10^-2'
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
[]

[Variables]
  [a]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    []
  []
  [b]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = BoundingBoxIC
      x1 = 0.0
      y1 = 0.0
      x2 = 1.0e-10
      y2 = 1
      inside = 1.0e-2
      outside = 1.0e-10
    []
  []
[]

[AuxVariables]
  [eqm_k0]
    initial_condition = 1E2
  []
  [eqm_k1]
    initial_condition = 1E-2
  []
  [pressure0]
  []
  [saturation1]
    initial_condition = 0.25
  []
  [a_in_phase0]
    initial_condition = 0.0
  []
  [b_in_phase0]
    initial_condition = 0.0
  []
  [pa2]
    family = MONOMIAL
    order = CONSTANT
  []
  [pab]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [pa2]
    type = PorousFlowPropertyAux
    property = secondary_concentration
    secondary_species = 0
    variable = pa2
  []
  [pab]
    type = PorousFlowPropertyAux
    property = secondary_concentration
    secondary_species = 1
    variable = pab
  []
[]

[ICs]
  [pressure0]
    type = FunctionIC
    variable = pressure0
    function = 2-x
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Kernels]
  [mass_a]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = a
  []
  [flux_a]
    type = PorousFlowAdvectiveFlux
    variable = a
    fluid_component = 0
  []
  [diff_a]
    type = PorousFlowDispersiveFlux
    variable = a
    fluid_component = 0
    disp_trans = '0 0'
    disp_long = '0 0'
  []
  [mass_b]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = b
  []
  [flux_b]
    type = PorousFlowAdvectiveFlux
    variable = b
    fluid_component = 1
  []
  [diff_b]
    type = PorousFlowDispersiveFlux
    variable = b
    fluid_component = 1
    disp_trans = '0 0'
    disp_long = '0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'a b'
    number_fluid_phases = 2
    number_fluid_components = 3
    number_aqueous_equilibrium = 2
    aqueous_phase_number = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9 # huge, so mimic chemical_reactions
      density0 = 1000
      thermal_expansion = 0
      viscosity = 1e-3
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow2PhasePS
    capillary_pressure = pc
    phase0_porepressure = pressure0
    phase1_saturation = saturation1
  []
  [massfrac]
    type = PorousFlowMassFractionAqueousEquilibriumChemistry
    mass_fraction_vars = 'a_in_phase0 b_in_phase0 a b'
    num_reactions = 2
    equilibrium_constants = 'eqm_k0 eqm_k1'
    primary_activity_coefficients = '1 1'
    secondary_activity_coefficients = '1 1'
    reactions = '2 0
                 1 1'
  []
  [simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.8
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    # porous_flow permeability / porous_flow viscosity = chemical_reactions conductivity = 1E-4
    permeability = '1E-7 0 0 0 1E-7 0 0 0 1E-7'
  []
  [relp0]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [relp1]
    type = PorousFlowRelativePermeabilityConst
    phase = 1
  []
  [diff]
    type = PorousFlowDiffusivityConst
    # porous_flow diffusion_coeff * tortuousity * porosity = chemical_reactions diffusivity = 1E-4
    diffusion_coeff = '5E-4 5E-4 5E-4
                       5E-4 5E-4 5E-4'
    tortuosity = '0.25 0.25'
  []
[]

[BCs]
  [a_left]
    type = DirichletBC
    variable = a
    boundary = left
    value = 1.0e-2
  []
  [b_left]
    type = DirichletBC
    variable = b
    boundary = left
    value = 1.0e-2
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 10
  end_time = 100
[]

[Outputs]
  print_linear_residuals = true
  exodus = true
  perf_graph = true
[]

(modules/level_set/examples/vortex/vortex.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 1
  ymax = 1
  nx = 16
  ny = 16
  uniform_refine = 2
  elem_type = QUAD9
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[AuxKernels]
  [./vec]
    type = VectorFunctionAux
    variable = velocity
    function = velocity_func
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Variables]
  [./phi]
    family = LAGRANGE
    order = FIRST
  [../]
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.01184
    center = '0.5 0.75 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = LevelSetOlssonVortex
    reverse_time = 2
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 2
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/porous_flow/examples/lava_lamp/1phase_convection.i)

# Two phase density-driven convection of dissolved CO2 in brine
#
# The model starts with CO2 in the liquid phase only.  The CO2 diffuses into the brine.
# As the density of the CO2-saturated brine is greater
# than the unsaturated brine, a gravitational instability arises and density-driven
# convection of CO2-rich fingers descend into the unsaturated brine.
#
# The instability is seeded by a random perturbation to the porosity field.
# Mesh adaptivity is used to refine the mesh as the fingers form.
#
# Note: this model is computationally expensive, so should be run with multiple cores.

[GlobalParams]
  PorousFlowDictator = 'dictator'
  gravity = '0 -9.81 0'
[]

[Adaptivity]
  max_h_level = 2
  marker = marker
  initial_marker = initial
  initial_steps = 2
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = zi
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      refine = 0.8
    []
    [initial]
      type = BoxMarker
      bottom_left = '0 1.95 0'
      top_right = '2 2 0'
      inside = REFINE
      outside = DO_NOTHING
    []
  []
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  ymin = 1.5
  ymax = 2
  xmax = 2
  ny = 20
  nx = 40
  bias_y = 0.95
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.01
  []
  [saturation_gas]
    order = FIRST
    family = MONOMIAL
  []
  [xco2l]
    order = FIRST
    family = MONOMIAL
  []
  [density_liquid]
    order = FIRST
    family = MONOMIAL
  []
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = 'timestep_end'
  []
  [xco2l]
    type = PorousFlowPropertyAux
    variable = xco2l
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = 'timestep_end'
  []
  [density_liquid]
    type = PorousFlowPropertyAux
    variable = density_liquid
    property = density
    phase = 0
    execute_on = 'timestep_end'
  []
[]

[Variables]
  [pgas]
  []
  [zi]
    scaling = 1e4
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    function = 10e6-9.81*1000*y
    variable = pgas
  []
  [zi]
    type = ConstantIC
    value = 0
    variable = zi
  []
  [porosity]
    type = RandomIC
    variable = porosity
    min = 0.25
    max = 0.275
    seed = 0
  []
[]

[BCs]
  [top]
    type = DirichletBC
    value = 0.04
    variable = zi
    boundary = top
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pgas
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pgas
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    fluid_component = 0
    variable = pgas
    disp_long = '0 0'
    disp_trans = '0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = zi
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = zi
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = zi
    disp_long = '0 0'
    disp_trans = '0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2sw]
      type = CO2FluidProperties
    []
    [co2]
      type = TabulatedFluidProperties
      fp = co2sw
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = '45'
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = 'pgas'
    z = 'zi'
    temperature_unit = Celsius
    xnacl = 'xnacl'
    capillary_pressure = pc
    fluid_state = fs
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = porosity
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0 0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    phase = 0
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [diffusivity]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '2e-9 2e-9 2e-9 2e-9'
    tortuosity = '1 1'
  []
[]

[Preconditioning]
  active = basic
  [mumps_is_best_for_parallel_jobs]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e6
  nl_max_its = 25
  l_max_its = 100
  dtmax = 1e4
  nl_abs_tol = 1e-6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 100
    growth_factor = 2
    cutback_factor = 0.5
  []
[]

[Functions]
  [flux]
    type = ParsedFunction
    vals = 'delta_xco2 dt'
    vars = 'dx dt'
    value = 'dx/dt'
  []
[]

[Postprocessors]
  [total_co2_in_gas]
    type = PorousFlowFluidMass
    phase = 1
    fluid_component = 1
  []
  [total_co2_in_liquid]
    type = PorousFlowFluidMass
    phase = 0
    fluid_component = 1
  []
  [numdofs]
    type = NumDOFs
  []
  [delta_xco2]
    type = ChangeOverTimePostprocessor
    postprocessor = total_co2_in_liquid
  []
  [dt]
    type = TimestepSize
  []
  [flux]
    type = FunctionValuePostprocessor
    function = flux
  []
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  exodus = true
  csv = true
[]

(modules/xfem/test/tests/switching_material/two_cuts_stationary.i)

[Problem]
  solve = false
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [cut1]
    type = LevelSetCutUserObject
    level_set_var = phi1
    negative_id = 1
    positive_id = 33
    execute_on = NONE
  []
  [cut2]
    type = LevelSetCutUserObject
    level_set_var = phi2
    negative_id = 5
    positive_id = 16
    execute_on = NONE
  []
  [combo]
    type = ComboCutUserObject
    geometric_cut_userobjects = 'cut1 cut2'
    cut_subdomain_combinations = '1 5;
                                  1 16;
                                  33 5;
                                  33 16'
    cut_subdomains = '1 3 5 7'
  []
[]

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
  []
[]

[AuxVariables]
  [phi1]
    [InitialCondition]
      type = FunctionIC
      function = 'x-0.213'
    []
  []
  [phi2]
    [InitialCondition]
      type = FunctionIC
      function = 'x-0.728'
    []
  []
  [cut1_id]
    order = CONSTANT
    family = MONOMIAL
  []
  [cut2_id]
    order = CONSTANT
    family = MONOMIAL
  []
  [combo_id]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [cut1_id]
    type = CutSubdomainIDAux
    variable = cut1_id
    cut = cut1
  []
  [cut2_id]
    type = CutSubdomainIDAux
    variable = cut2_id
    cut = cut2
  []
  [combo_id]
    type = CutSubdomainIDAux
    variable = combo_id
    cut = combo
  []
[]

[Materials]
  [diffusivity_A]
    type = GenericConstantMaterial
    prop_names = 'A_D'
    prop_values = '5'
  []
  [diffusivity_B]
    type = GenericConstantMaterial
    prop_names = 'B_D'
    prop_values = '0.5'
  []
  [diffusivity_C]
    type = GenericConstantMaterial
    prop_names = 'C_D'
    prop_values = '12'
  []
  [diffusivity_D]
    type = GenericConstantMaterial
    prop_names = 'D_D'
    prop_values = '9'
  []
  [diff_combined]
    type = XFEMCutSwitchingMaterialReal
    cut_subdomain_ids = '1 3 5 7'
    base_names = 'A B C D'
    prop_name = D
    geometric_cut_userobject = combo
    outputs = 'exodus'
    output_properties = 'D'
  []
[]

[Executioner]
  type = Transient

  num_steps = 1

  max_xfem_update = 1
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/heterogeneous_materials/constant_poroperm.i)

# Assign porosity and permeability variables from constant AuxVariables to create
# a heterogeneous model

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 3
  ny = 3
  nz = 3
  xmax = 3
  ymax = 3
  zmax = 3
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 -10'
[]

[Variables]
  [ppwater]
    initial_condition = 1.5e6
  []
[]

[AuxVariables]
  [poro]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxx]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxy]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxz]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyx]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyy]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyz]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzx]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzy]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzz]
    family = MONOMIAL
    order = CONSTANT
  []
  [poromat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxxmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxymat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permxzmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyxmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyymat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permyzmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzxmat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzymat]
    family = MONOMIAL
    order = CONSTANT
  []
  [permzzmat]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [poromat]
    type = PorousFlowPropertyAux
    property = porosity
    variable = poromat
  []
  [permxxmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permxxmat
    column = 0
    row = 0
  []
  [permxymat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permxymat
    column = 1
    row = 0
  []
  [permxzmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permxzmat
    column = 2
    row = 0
  []
  [permyxmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permyxmat
    column = 0
    row = 1
  []
  [permyymat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permyymat
    column = 1
    row = 1
  []
  [permyzmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permyzmat
    column = 2
    row = 1
  []
  [permzxmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permzxmat
    column = 0
    row = 2
  []
  [permzymat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permzymat
    column = 1
    row = 2
  []
  [permzzmat]
    type = PorousFlowPropertyAux
    property = permeability
    variable = permzzmat
    column = 2
    row = 2
  []
[]

[ICs]
  [poro]
    type = RandomIC
    seed = 0
    variable = poro
    max = 0.5
    min = 0.1
  []
  [permx]
    type = FunctionIC
    function = permx
    variable = permxx
  []
  [permy]
    type = FunctionIC
    function = permy
    variable = permyy
  []
  [permz]
    type = FunctionIC
    function = permz
    variable = permzz
  []
[]

[Functions]
  [permx]
    type = ParsedFunction
    value = '(1+x)*1e-11'
  []
  [permy]
    type = ParsedFunction
    value = '(1+y)*1e-11'
  []
  [permz]
    type = ParsedFunction
    value = '(1+z)*1e-11'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = ppwater
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    variable = ppwater
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      viscosity = 1e-3
      thermal_expansion = 0
      cv = 2
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = ppwater
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = poro
  []
  [permeability]
    type = PorousFlowPermeabilityConstFromVar
    perm_xx = permxx
    perm_yy = permyy
    perm_zz = permzz
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 100
  dt = 100
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  perf_graph = true
[]

(test/tests/time_integrators/rk-2/2d-quadratic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 20
  ny = 20
  elem_type = QUAD9
[]

[Functions]
  [./ic]
    type = ParsedFunction
    value = 0
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*((x*x)+(y*y))-(4*t*t)
  [../]

  [./exact_fn]
    type = ParsedFunction
    value = t*t*((x*x)+(y*y))
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = ic
    [../]
  [../]
[]

[Kernels]
  [./ie]
    type = TimeDerivative
    variable = u
    implicit = true
  [../]

  [./diff]
    type = Diffusion
    variable = u
    implicit = false
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
    implicit = false
  [../]
[]

[BCs]
  active = 'all'

  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = ExplicitMidpoint
  [../]
  solve_type = 'LINEAR'

  start_time = 0.0
  num_steps = 10
  dt = 0.0001
  l_tol = 1e-8
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/richards/test/tests/dirac/st01.i)

# fully-saturated
# production
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./stream_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./stream]
    type = RichardsPolyLineSink
    pressures = '0.2E7 0.8E7'
    fluxes = '1 2'
    point_file = st01.stream
    SumQuantityUO = stream_total_outflow_mass
    variable = pressure
  [../]
[]


[Postprocessors]
  [./stream_report]
    type = RichardsPlotQuantity
    uo = stream_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '0 0 0'
    execute_on = timestep_end
  [../]
[]


[Functions]
 active = 'mass_bal_fcn initial_pressure'

  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 stream_report'
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 2.5
  dt = 0.1
  solve_type = NEWTON

[]

[Outputs]
  file_base = st01
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/sinks/s06.i)

# apply a half-cubic sink flux and observe the correct behavior
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1.1
  []
[]

[Variables]
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = x*(y+1)
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1.3
      density0 = 1.1
      thermal_expansion = 0
      viscosity = 1.1
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-5 0 0 0 1E-5 0 0 0 1E-5'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
[]

[AuxVariables]
  [flux_out]
  []
[]

[Functions]
  [mass10]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)*if(pp>=0,1,pow(1+pow(-al*pp,1.0/(1-m)),-m))'
    vars = 'vol por dens0 pp bulk al m'
    vals = '0.25 0.1 1.1 p10 1.3 1.1 0.5'
  []
  [rate10]
    type = ParsedFunction
    value = 'fcn*if(pp>center,m,if(pp<themin,0,m/c/c/c*(2*(pp-center)+c)*((pp-center)-c)*((pp-center)-c)))'
    vars = 'm fcn pp  center sd  themin c'
    vals = '2 3   p10 0.9    0.5 0.1   -0.8'
  []
  [mass10_expect]
    type = ParsedFunction
    value = 'mass_prev-rate*area*dt'
    vars = 'mass_prev rate     area dt'
    vals = 'm10_prev  m10_rate 0.5 2E-3'
  []
  [mass11]
    type = ParsedFunction
    value = 'vol*por*dens0*exp(pp/bulk)*if(pp>=0,1,pow(1+pow(-al*pp,1.0/(1-m)),-m))'
    vars = 'vol por dens0 pp bulk al m'
    vals = '0.25 0.1 1.1 p11 1.3 1.1 0.5'
  []
  [rate11]
    type = ParsedFunction
    value = 'fcn*if(pp>center,m,if(pp<themin,0,m/c/c/c*(2*(pp-center)+c)*((pp-center)-c)*((pp-center)-c)))'
    vars = 'm fcn pp  center sd  themin c'
    vals = '2 3   p11 0.9    0.5 0.1   -0.8'
  []
  [mass11_expect]
    type = ParsedFunction
    value = 'mass_prev-rate*area*dt'
    vars = 'mass_prev rate     area dt'
    vals = 'm11_prev  m11_rate 0.5 2E-3'
  []
[]

[Postprocessors]
  [flux00]
    type = PointValue
    variable = flux_out
    point = '0 0 0'
  []
  [flux01]
    type = PointValue
    variable = flux_out
    point = '0 1 0'
  []
  [flux10]
    type = PointValue
    variable = flux_out
    point = '1 0 0'
  []
  [flux11]
    type = PointValue
    variable = flux_out
    point = '1 1 0'
  []
  [p00]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p10]
    type = PointValue
    point = '1 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m10]
    type = FunctionValuePostprocessor
    function = mass10
    execute_on = 'initial timestep_end'
  []
  [m10_prev]
    type = FunctionValuePostprocessor
    function = mass10
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [m10_rate]
    type = FunctionValuePostprocessor
    function = rate10
    execute_on = 'timestep_end'
  []
  [m10_expect]
    type = FunctionValuePostprocessor
    function = mass10_expect
    execute_on = 'timestep_end'
  []
  [p01]
    type = PointValue
    point = '0 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [p11]
    type = PointValue
    point = '1 1 0'
    variable = pp
    execute_on = 'initial timestep_end'
  []
  [m11]
    type = FunctionValuePostprocessor
    function = mass11
    execute_on = 'initial timestep_end'
  []
  [m11_prev]
    type = FunctionValuePostprocessor
    function = mass11
    execute_on = 'timestep_begin'
    outputs = 'console'
  []
  [m11_rate]
    type = FunctionValuePostprocessor
    function = rate11
    execute_on = 'timestep_end'
  []
  [m11_expect]
    type = FunctionValuePostprocessor
    function = mass11_expect
    execute_on = 'timestep_end'
  []
[]

[BCs]
  [flux]
    type = PorousFlowHalfCubicSink
    boundary = 'left right'
    max = 2
    cutoff = -0.8
    center = 0.9
    variable = pp
    use_mobility = false
    use_relperm = false
    fluid_phase = 0
    flux_function = 3
    save_in = flux_out
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres asm lu 10000 NONZERO 2'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 2E-3
  end_time = 6E-2
  nl_rel_tol = 1E-12
  nl_abs_tol = 1E-12
[]

[Outputs]
  file_base = s06
  [console]
    type = Console
    execute_on = 'nonlinear linear'
    interval = 5
  []
  [csv]
    type = CSV
    execute_on = 'timestep_end'
    interval = 3
  []
[]

(modules/richards/test/tests/jacobian_2/jn17.i)

# two phase
# water saturated

# gravity = true
# supg = true
# transient = true


[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1.0 # notice small quantity, so the PETSc constant state works
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 0.5
    bulk_mod = 0.5 # notice small quantity, so the PETSc constant state works
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1 # notice small quantity, so the PETSc constant state works
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1 # notice small quantity, so the PETSc constant state works
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.2
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.1
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.15
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.05
    sum_s_res = 0.15
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 0.01
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      block = 0
      function = init_p
    [../]
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      block = 0
      function = init_p
    [../]
  [../]
[]

[Functions]
  [./init_p]
    type = ParsedFunction
    value = x+0.6*y+0.3*z
  [../]
[]

[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFlux
    variable = pgas
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    density_UO = 'DensityWater DensityGas'
    relperm_UO = 'RelPermWater RelPermGas'
    SUPG_UO = 'SUPGwater SUPGgas'
    sat_UO = 'SatWater SatGas'
    seff_UO = 'SeffWater SeffGas'
    viscosity = '1E-3 0.5E-3'
    gravity = '1 2 3'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-5
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = jn17
  exodus = false
[]

(test/tests/bcs/coupled_var_neumann/coupled_var_neumann.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[AuxVariables]
  [./coupled_bc_var]
  [../]
[]

[ICs]
  [./coupled_bc_var]
    type = FunctionIC
    variable = coupled_bc_var
    function = set_coupled_bc_var
  [../]
[]

[Functions]
  [./set_coupled_bc_var]
    type = ParsedFunction
    value = 'y - 0.5'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = CoupledVarNeumannBC
    variable = u
    boundary = 1
    v = coupled_bc_var
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/richards/test/tests/dirac/bh_fu_03.i)

# fully-saturated
# injection
# fullyupwind
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  sat_UO = Saturation
  seff_UO = Seff1VG
  SUPG_UO = SUPGstandard
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 1E7
    point_file = bh03.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = -1
    fully_upwind = true
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 0
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]

[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 0.5
  dt = 1E-2
  solve_type = NEWTON

[]

[Outputs]
  file_base = bh_fu_03
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/richards/test/tests/dirac/bh04.i)

# unsaturated
# production
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '1E-2 1E-1 1 1E1 1E2 1E3'
    x = '0 1E-1 1 1E1 1E2 1E3'
  [../]
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = -1E6
    point_file = bh02.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = 1
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 0
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]

[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 1E3
  solve_type = NEWTON

  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]


[]

[Outputs]
  file_base = bh04
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/test/tests/dispersion/disp01.i)

# Test dispersive part of PorousFlowDispersiveFlux kernel by setting diffusion
# coefficients to zero. A pressure gradient is applied over the mesh to give a
# uniform velocity. Gravity is set to zero.
# Mass fraction is set to 1 on the left hand side and 0 on the right hand side.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 100
  xmax = 10
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [pp]
  []
  [massfrac0]
  []
[]

[AuxVariables]
  [velocity]
    family = MONOMIAL
    order = FIRST
  []
[]

[AuxKernels]
  [velocity]
    type = PorousFlowDarcyVelocityComponent
    variable = velocity
    component = x
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = pic
  []
  [massfrac0]
    type = ConstantIC
    variable = massfrac0
    value = 0
  []
[]

[Functions]
  [pic]
    type = ParsedFunction
    value = 1.1e5-x*1e3
  []
[]

[BCs]
  [xleft]
    type = DirichletBC
    value = 1
    variable = massfrac0
    boundary = left
  []
  [xright]
    type = DirichletBC
    value = 0
    variable = massfrac0
    boundary = right
  []
  [pright]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 1e5
  []
  [pleft]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 1.1e5
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    variable = pp
    disp_trans = 0
    disp_long = 0.2
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = massfrac0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = massfrac0
    disp_trans = 0
    disp_long = 0.2
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1e9
      density0 = 1000
      viscosity = 0.001
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = massfrac0
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [poro]
    type = PorousFlowPorosityConst
    porosity = 0.3
  []
  [diff]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '0 0'
    tortuosity = 0.1
  []
  [relp]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-9 0 0 0 1e-9 0 0 0 1e-9'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e3
  dtmax = 50
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.5
    cutback_factor = 0.5
    dt = 1
  []
[]

[VectorPostprocessors]
  [xmass]
    type = NodalValueSampler
    sort_by = id
    variable = massfrac0
  []
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/fluid_properties/test/tests/co2/co2.i)

# Test thermophysical property calculations in CO2FluidProperties
#
# Comparison with values from Span and Wagner, "A New Equation of State for
# Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature
# to 1100K at Pressures up to 800 MPa", J. Phys. Chem. Ref. Data, 25 (1996)
#
# Viscosity values from Fenghour et al., "The viscosity of carbon dioxide",
# J. Phys. Chem. Ref. Data, 27, 31-44 (1998)
#
#
#  --------------------------------------------------------------
#  Pressure (Mpa)             |   1       |    1      |   1
#  Temperature (K)            |  280      |  360      |  500
#  --------------------------------------------------------------
#  Expected values
#  --------------------------------------------------------------
#  Density (kg/m^3)           |  20.199   |  15.105   |  10.664
#  Internal energy (kJ/kg/K)  |  -75.892  |  -18.406  |  91.829
#  Enthalpy (kJ/kg)           |  -26.385  |  47.797   |  185.60
#  Entropy (kJ/kg/K)          |  -0.51326 |  -0.28033 |  0.04225
#  cv (kJ/kg/K)               |  0.67092  |  0.72664  |  0.82823
#  cp (kJ/kg/K)               |  0.92518  |  0.94206  |  1.0273
#  Speed of sound (m/s)       |  252.33   |  289.00   |  339.81
#  Viscosity (1e-6Pa.s)       |  14.15    |  17.94    |  24.06
#  --------------------------------------------------------------
#  Calculated values
#  --------------------------------------------------------------
#  Density (kg/m^3)           |  20.199   |  15.105   |  10.664
#  Internal energy (kJ/kg/K)  |  -75.892  |  -18.406  |  91.829
#  Enthalpy (kJ/kg)           |  -26.385  |  47.797   |  185.60
#  Entropy (kJ/kg/K)          |  -0.51326 |  -0.28033 |  0.04225
#  cv (kJ/kg/K)               |  0.67092  |  0.72664  |  0.82823
#  cp (kJ/kg/K)               |  0.92518  |  0.94206  |  1.0273
#  Speed of sound (m/s)       |  252.33   |  289.00   |  339.81
#  Viscosity (1e-6 Pa.s)      |  14.15    |  17.94    |  24.06
#  --------------------------------------------------------------

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  xmax = 3
  # This test uses ElementalVariableValue postprocessors on specific
  # elements, so element numbering needs to stay unchanged
  allow_renumbering = false
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./pressure]
    initial_condition = 1e6
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./temperature]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./rho]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./mu]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./e]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./h]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./s]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./cv]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./cp]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./c]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Functions]
  [./tic]
    type = ParsedFunction
    value = if(x<1,280,if(x<2,360,500))
  [../]
[]

[ICs]
  [./t_ic]
    type = FunctionIC
    function = tic
    variable = temperature
  [../]
[]

[AuxKernels]
  [./rho]
    type = MaterialRealAux
    variable = rho
    property = density
  [../]
  [./my]
    type = MaterialRealAux
    variable = mu
    property = viscosity
  [../]
  [./internal_energy]
    type = MaterialRealAux
    variable = e
    property = e
  [../]
  [./enthalpy]
    type = MaterialRealAux
    variable = h
    property = h
  [../]
  [./entropy]
    type = MaterialRealAux
    variable = s
    property = s
  [../]
  [./cv]
    type = MaterialRealAux
    variable = cv
    property = cv
  [../]
  [./cp]
    type = MaterialRealAux
    variable = cp
    property = cp
  [../]
  [./c]
    type = MaterialRealAux
    variable = c
    property = c
  [../]
[]

[Modules]
  [./FluidProperties]
    [./co2]
      type = CO2FluidProperties
    [../]
  []
[]

[Materials]
  [./fp_mat]
    type = FluidPropertiesMaterialPT
    pressure = pressure
    temperature = temperature
    fp = co2
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Postprocessors]
  [./rho0]
    type = ElementalVariableValue
    elementid = 0
    variable = rho
  [../]
  [./rho1]
    type = ElementalVariableValue
    elementid = 1
    variable = rho
  [../]
  [./rho2]
    type = ElementalVariableValue
    elementid = 2
    variable = rho
  [../]
  [./mu0]
    type = ElementalVariableValue
    elementid = 0
    variable = mu
  [../]
  [./mu1]
    type = ElementalVariableValue
    elementid = 1
    variable = mu
  [../]
  [./mu2]
    type = ElementalVariableValue
    elementid = 2
    variable = mu
  [../]
  [./e0]
    type = ElementalVariableValue
    elementid = 0
    variable = e
  [../]
  [./e1]
    type = ElementalVariableValue
    elementid = 1
    variable = e
  [../]
  [./e2]
    type = ElementalVariableValue
    elementid = 2
    variable = e
  [../]
  [./h0]
    type = ElementalVariableValue
    elementid = 0
    variable = h
  [../]
  [./h1]
    type = ElementalVariableValue
    elementid = 1
    variable = h
  [../]
  [./h2]
    type = ElementalVariableValue
    elementid = 2
    variable = h
  [../]
  [./s0]
    type = ElementalVariableValue
    elementid = 0
    variable = s
  [../]
  [./s1]
    type = ElementalVariableValue
    elementid = 1
    variable = s
  [../]
  [./s2]
    type = ElementalVariableValue
    elementid = 2
    variable = s
  [../]
  [./cv0]
    type = ElementalVariableValue
    elementid = 0
    variable = cv
  [../]
  [./cv1]
    type = ElementalVariableValue
    elementid = 1
    variable = cv
  [../]
  [./cv2]
    type = ElementalVariableValue
    elementid = 2
    variable = cv
  [../]
  [./cp0]
    type = ElementalVariableValue
    elementid = 0
    variable = cp
  [../]
  [./cp1]
    type = ElementalVariableValue
    elementid = 1
    variable = cp
  [../]
  [./cp2]
    type = ElementalVariableValue
    elementid = 2
    variable = cp
  [../]
  [./c0]
    type = ElementalVariableValue
    elementid = 0
    variable = c
  [../]
  [./c1]
    type = ElementalVariableValue
    elementid = 1
    variable = c
  [../]
  [./c2]
    type = ElementalVariableValue
    elementid = 2
    variable = c
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'TIMESTEP_END'
[]

(modules/navier_stokes/test/tests/finite_volume/cns/benchmark_shock_tube_1D/hllc_sod_shocktube.i)

rho_left = 1
E_left = 2.501505578
u_left = 1e-15

rho_right = 0.125
E_right = 1.999770935
u_right = 1e-15

middle = 50

[GlobalParams]
  fp = fp
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${fparse 2 * middle}
    nx = 1000
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Variables]
  [rho]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [rho_u]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [rho_E]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[AuxVariables]
  [rho_a]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[FVKernels]
  [mass_time]
    type = FVTimeKernel
    variable = rho
  []

  [mass_advection]
    type = CNSFVMassHLLC
    variable = rho
  []

  [momentum_time]
    type = FVTimeKernel
    variable = rho_u
  []

  [momentum_advection]
    type = CNSFVMomentumHLLC
    variable = rho_u
    momentum_component = x
  []

  [fluid_energy_time]
    type = FVTimeKernel
    variable = rho_E
  [../]

  [fluid_energy_advection]
    type = CNSFVFluidEnergyHLLC
    variable = rho_E
  []
[]

[FVBCs]
  [mass_implicit]
    type = CNSFVHLLCMassImplicitBC
    variable = rho
    fp = fp
    boundary = 'left right'
  []

  [mom_implicit]
    type = CNSFVHLLCMomentumImplicitBC
    variable = rho_u
    momentum_component = x
    fp = fp
    boundary = 'left right'
  []

  [fluid_energy_implicit]
    type = CNSFVHLLCFluidEnergyImplicitBC
    variable = rho_E
    fp = fp
    boundary = 'left right'
  []
[]

[ICs]
  [rho_ic]
    type = FunctionIC
    variable = rho
    function = 'if (x < ${middle}, ${rho_left}, ${rho_right})'
  []

  [rho_u_ic]
    type = FunctionIC
    variable = rho_u
    function = 'if (x < ${middle}, ${fparse rho_left * u_left}, ${fparse rho_right * u_right})'
  []

  [rho_E_ic]
    type = FunctionIC
    variable = rho_E
    function = 'if (x < ${middle}, ${fparse E_left * rho_left}, ${fparse E_right * rho_right})'
  []
[]

[Materials]
  [var_mat]
    type = ConservedVarValuesMaterial
    rho = rho
    rhou = rho_u
    rho_et = rho_E
    fp = fp
  []
[]

[Preconditioning]
  active = ''
  [./smp]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  [../]
[]

[Executioner]
  type = Transient
  [TimeIntegrator]
    type = ExplicitSSPRungeKutta
    order = 2
  []
  l_tol = 1e-8

  start_time = 0.0
  dt = 1e-2
  end_time = 20
  abort_on_solve_fail = true
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/level_set/examples/circle/circle_16.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 16
  ny = 16
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.05
    center = '0.5 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '3'
    value_y = '3'
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = phi
      auto_direction = 'x y'
    [../]
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(test/tests/functions/solution_function/solution_function_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
  # This test uses SolutionUserObject which doesn't work with DistributedMesh.
  parallel_type = replicated
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_cond_func
    [../]
  [../]
[]

[AuxVariables]
  [./u_aux]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_cond_func
    [../]
  [../]
[]

[Functions]
  [./initial_cond_func]
    type = SolutionFunction
    solution = ex_soln
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[UserObjects]
  [./ex_soln]
    type = SolutionUserObject
    system_variables = u
    mesh = build_out_0001_mesh.xda
    es = build_out_0001.xda
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'

  nl_rel_tol = 1e-10
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/combined/test/tests/DiffuseCreep/variable_base_eigen_strain.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 50
  ny = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);0.1+0.01*v'
    [../]
  [../]
  [./mu]
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./gb]
    family = LAGRANGE
    order  = FIRST
  [../]
  [./eigen_strain_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./eigen_strain_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_xx]
    family = MONOMIAL
    order  = CONSTANT
  [../]
  [./stress_yy]
    family = MONOMIAL
    order  = CONSTANT
  [../]
[]

[Kernels]
  [./conc]
    type = CHSplitConcentration
    variable = c
    mobility = mobility_prop
    chemical_potential_var = mu
  [../]
  [./chempot]
    type = CHSplitChemicalPotential
    variable = mu
    chemical_potential_prop = mu_prop
    c = c
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./gb]
    type = FunctionAux
    variable = gb
    function = 'x0:=5.0;thk:=0.5;m:=2;r:=abs(x-x0);v:=exp(-(r/thk)^m);v'
  [../]
  [./eigenstrain_xx]
    type = RankTwoAux
    variable = eigen_strain_xx
    rank_two_tensor = eigenstrain
    index_i = 0
    index_j = 0
  [../]
  [./eigenstrain_yy]
    type = RankTwoAux
    variable = eigen_strain_yy
    rank_two_tensor = eigenstrain
    index_i = 1
    index_j = 1
  [../]
  [./stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    variable = stress_yy
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
[]

[Materials]
  [./chemical_potential]
    type = DerivativeParsedMaterial
    block = 0
    f_name = mu_prop
    args = c
    function = 'c'
    derivative_order = 1
  [../]
  [./var_dependence]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c*(1.0-c)'
    args = c
    f_name = var_dep
    derivative_order = 1
  [../]
  [./mobility]
    type = CompositeMobilityTensor
    block = 0
    M_name = mobility_prop
    tensors = diffusivity
    weights = var_dep
    args = c
  [../]
  [./phase_normal]
    type = PhaseNormalTensor
    phase = gb
    normal_tensor_name = gb_normal
  [../]
  [./aniso_tensor]
    type = GBDependentAnisotropicTensor
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = aniso_tensor
  [../]
  [./diffusivity]
    type = GBDependentDiffusivity
    gb = gb
    bulk_parameter = 0.1
    gb_parameter = 1
    gb_normal_tensor_name = gb_normal
    gb_tensor_prop_name = diffusivity
  [../]
  [./eigenstrain_prefactor]
    type = DerivativeParsedMaterial
    block = 0
    function = 'c-0.1'
    args = c
    f_name = eigenstrain_prefactor
    derivative_order = 1
  [../]
  [./eigenstrain]
    type = ComputeVariableBaseEigenStrain
    base_tensor_property_name = aniso_tensor
    prefactor = eigenstrain_prefactor
    eigenstrain_name = eigenstrain
  [../]
  [./strain]
    type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y'
    eigenstrain_names = eigenstrain
  [../]
  [./stress]
    type = ComputeStrainIncrementBasedStress
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '120.0 80.0'
    fill_method = symmetric_isotropic
  [../]
[]

[BCs]
  [./Periodic]
    [./cbc]
      auto_direction = 'x y'
      variable = c
    [../]
  [../]
  [./fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  preonly       lu           1'

  nl_rel_tol = 1e-10
  nl_max_its = 5

  l_tol = 1e-4
  l_max_its = 20

  dt = 1
  num_steps = 5
[]

[Preconditioning]
  [./smp]
     type = SMP
     full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/dispersion/disp01_heavy.i)

# Test dispersive part of PorousFlowDispersiveFlux kernel by setting diffusion
# coefficients to zero. A pressure gradient is applied over the mesh to give a
# uniform velocity. Gravity is set to zero.
# Mass fraction is set to 1 on the left hand side and 0 on the right hand side.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 200
  xmax = 10
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
  compute_enthalpy = false
  compute_internal_energy = false
[]

[Variables]
  [pp]
  []
  [massfrac0]
  []
[]

[AuxVariables]
  [velocity]
    family = MONOMIAL
    order = FIRST
  []
[]

[AuxKernels]
  [velocity]
    type = PorousFlowDarcyVelocityComponent
    variable = velocity
    component = x
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = pic
  []
  [massfrac0]
    type = ConstantIC
    variable = massfrac0
    value = 0
  []
[]

[Functions]
  [pic]
    type = ParsedFunction
    value = 1.1e5-x*1e3
  []
[]

[BCs]
  [xleft]
    type = DirichletBC
    value = 1
    variable = massfrac0
    boundary = left
  []
  [xright]
    type = DirichletBC
    value = 0
    variable = massfrac0
    boundary = right
  []
  [pright]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 1e5
  []
  [pleft]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 1.1e5
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    variable = pp
    disp_trans = 0
    disp_long = 0.2
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = massfrac0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = massfrac0
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = massfrac0
    disp_trans = 0
    disp_long = 0.2
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp massfrac0'
    number_fluid_phases = 1
    number_fluid_components = 2
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 1e9
      density0 = 1000
      viscosity = 0.001
      thermal_expansion = 0
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [ppss]
    type = PorousFlow1PhaseFullySaturated
    porepressure = pp
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = massfrac0
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [poro]
    type = PorousFlowPorosityConst
    porosity = 0.3
  []
  [diff]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '0 0'
    tortuosity = 0.1
  []
  [relp]
    type = PorousFlowRelativePermeabilityConst
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-9 0 0 0 1e-9 0 0 0 1e-9'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e3
  dtmax = 10
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.5
    cutback_factor = 0.5
    dt = 1
  []
[]

[VectorPostprocessors]
  [xmass]
    type = NodalValueSampler
    sort_by = id
    variable = massfrac0
  []
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(test/tests/time_steppers/timesequence_stepper/csvtimesequence.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  end_time = 10
  [./TimeStepper]
    type = CSVTimeSequenceStepper
    file_name = timesequence.csv
    column_name = time1
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/basic-conserved-pcnsfv-kt.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

[Modules]
  [FluidProperties]
    [fp]
      type = IdealGasFluidProperties
    []
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [rho]
    type = MooseVariableFVReal
  []
  [rho_ud]
    type = MooseVariableFVReal
  []
  [rho_et]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = rho
    function = 'exact_rho'
  []
  [sup_vel_x]
    type = FunctionIC
    variable = rho_ud
    function = 'exact_rho_ud'
  []
  [T_fluid]
    type = FunctionIC
    variable = rho_et
    function = 'exact_rho_et'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = rho
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = rho
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = rho_ud
    momentum_component = x
    eqn = "momentum"
  []
  [momentum_fn]
    type = FVBodyForce
    variable = rho_ud
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = rho_et
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = rho_et
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = rho
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = rho_ud
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = rho_et
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = rho
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = rho_ud
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = rho_et
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [rho_right]
    type = FVFunctionDirichletBC
    variable = rho
    function = exact_rho
    boundary = 'right'
  []
  [rho_ud_left]
    type = FVFunctionDirichletBC
    variable = rho_ud
    function = exact_rho_ud
    boundary = 'left'
  []
  [rho_et_left]
    type = FVFunctionDirichletBC
    variable = rho_et
    function = exact_rho_et
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousConservedVarMaterial
    rho = rho
    superficial_rhou = rho_ud
    rho_et = rho_et
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  value = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  value = '-3.45300378856215*sin(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  value = '3.13909435323832*cos(1.1*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  value = '-0.9*(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + 0.9*(10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) + 3.13909435323832*sin(x)*cos(1.1*x)^2/cos(x)^2 - 6.9060075771243*sin(1.1*x)*cos(1.1*x)/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  value = '26.7439413073546*cos(1.2*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  value = '0.9*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(x)*cos(1.1*x)/cos(x)^2 - 0.99*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(1.1*x)/cos(x) + 0.9*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) - 32.0927295688256*sin(1.2*x))*cos(1.1*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  value = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  value = '3.13909435323832*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_p]
  type = ParsedFunction
  value = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  value = '0.9*cos(1.1*x)/cos(x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  value_x = '0.9*cos(1.1*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  value = '0.9'
[]
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options = '-snes_linesearch_monitor'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho]
    type = ElementL2Error
    variable = rho
    function = exact_rho
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_ud]
    variable = rho_ud
    function = exact_rho_ud
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_et]
    variable = rho_et
    function = exact_rho_et
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/porosity_jump/1d-rc-epsjump.i)

mu=1.1
rho=1.1
advected_interp_method='upwind'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 1
    dx = '1 1'
    ix = '30 30'
    subdomain_id = '1 2'
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = u
    pressure = pressure
    porosity = porosity
  []
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []
[]

[ICs]
  inactive = 'porosity_continuous'
  [porosity_1]
    type = ConstantIC
    variable = porosity
    block = 1
    value = 1
  []
  [porosity_2]
    type = ConstantIC
    variable = porosity
    block = 2
    value = 0.5
  []
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    block = '1 2'
    function = smooth_jump
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1)))'
  []
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/porous_flow/examples/restart/gas_injection_new_mesh.i)

# Using the results from the equilibrium run to provide the initial condition for
# porepressure, we now inject a gas phase into the brine-saturated reservoir. In this
# example, the mesh is not identical to the mesh used in gravityeq.i. Rather, it is
# generated so that it is more refined near the injection boundary and at the top of
# the model, as that is where the gas plume will be present.
#
# To use the hydrostatic pressure calculated using the gravity equilibrium run as the initial
# condition for the pressure, a SolutionUserObject is used, along with a SolutionFunction to
# interpolate the pressure from the gravity equilibrium run to the initial condition for liqiud
# porepressure in this example.
#
# Even though the gravity equilibrium is established using a 2D mesh, in this example,
# we use a mesh shifted 0.1 m to the right and rotate it about the Y axis to make a 2D radial
# model.
#
# Methane injection takes place over the surface of the hole created by rotating the mesh,
# and hence the injection area is 2 pi r h. We can calculate this using an AreaPostprocessor,
# and then use this in a ParsedFunction to calculate the injection rate so that 10 kg/s of
# methane is injected.
#
# Note: as this example uses the results from a previous simulation, gravityeq.i MUST be
# run before running this input file.

[Mesh]
  type = GeneratedMesh
  dim = 2
  ny = 25
  nx = 50
  ymax = 100
  xmin = 0.1
  xmax = 5000
  bias_x = 1.05
  bias_y = 0.95
[]

[Problem]
  coord_type = RZ
  rz_coord_axis = Y
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -9.81 0'
  temperature_unit = Celsius
[]

[Variables]
  [pp_liq]
  []
  [sat_gas]
    initial_condition = 0
  []
[]

[ICs]
  [ppliq_ic]
    type = FunctionIC
    variable = pp_liq
    function = ppliq_ic
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 50
  []
  [xnacl]
    initial_condition = 0.1
  []
  [brine_density]
    family = MONOMIAL
    order = CONSTANT
  []
  [methane_density]
    family = MONOMIAL
    order = CONSTANT
  []
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
  [pp_gas]
    family = MONOMIAL
    order = CONSTANT
  []
  [sat_liq]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pp_liq
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    variable = pp_liq
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = sat_gas
    fluid_component = 1
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    variable = sat_gas
    fluid_component = 1
  []
[]

[AuxKernels]
  [brine_density]
    type = PorousFlowPropertyAux
    property = density
    variable = brine_density
    execute_on = 'initial timestep_end'
  []
  [methane_density]
    type = PorousFlowPropertyAux
    property = density
    variable = methane_density
    phase = 1
    execute_on = 'initial timestep_end'
  []
  [pp_gas]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = pp_gas
    execute_on = 'initial timestep_end'
  []
  [sat_liq]
    type = PorousFlowPropertyAux
    property = saturation
    variable = sat_liq
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [gas_injection]
    type = PorousFlowSink
    boundary = left
    variable = sat_gas
    flux_function = injection_rate
    fluid_phase = 1
  []
  [brine_out]
    type = PorousFlowPiecewiseLinearSink
    boundary = right
    variable = pp_liq
    multipliers = '0 1e9'
    pt_vals = '0 1e9'
    fluid_phase = 0
    flux_function = 1e-6
    use_mobility = true
    use_relperm = true
    mass_fraction_component = 0
  []
[]

[Functions]
  [injection_rate]
    type = ParsedFunction
    vals = injection_area
    vars = area
    value = '-1/area'
  []
  [ppliq_ic]
    type = SolutionFunction
    solution = soln
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp_liq sat_gas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1e-5
    m = 0.5
    sat_lr = 0.2
    pc_max = 1e7
  []
  [soln]
    type = SolutionUserObject
    mesh = gravityeq_out.e
    system_variables = porepressure
  []
[]

[Modules]
  [FluidProperties]
    [brine]
      type = BrineFluidProperties
    []
    [methane]
      type = MethaneFluidProperties
    []
    [methane_tab]
      type = TabulatedFluidProperties
      fp = methane
      save_file = false
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [ps]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp_liq
    phase1_saturation = sat_gas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [brine]
    type = PorousFlowBrine
    compute_enthalpy = false
    compute_internal_energy = false
    xnacl = xnacl
    phase = 0
  []
  [methane]
    type = PorousFlowSingleComponentFluid
    compute_enthalpy = false
    compute_internal_energy = false
    fp = methane_tab
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-13 0 0 0 5e-14 0  0 0 1e-13'
  []
  [relperm_liq]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.2
    sum_s_res = 0.3
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
    s_res = 0.1
    sum_s_res = 0.3
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
    petsc_options_value = ' asm      lu           NONZERO'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1e8
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-06
  nl_max_its = 20
  dtmax = 1e6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e1
    growth_factor = 1.5
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
  [injection_area]
    type = AreaPostprocessor
    boundary = left
    execute_on = initial
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  perf_graph = true
[]

(modules/richards/test/tests/buckley_leverett/bl01_lumped.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 150
  xmin = 0
  xmax = 15
[]


[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = DensityConstBulk
  relperm_UO = RelPermPower
  SUPG_UO = SUPGstandard
  sat_UO = Saturation
  seff_UO = SeffVG
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2.0E6
  [../]
  [./SeffVG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-4
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0.0
    sum_s_res = 0.0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E-5
  [../]
[]


[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]

[AuxKernels]
  active = 'calculate_seff'
  [./calculate_seff]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = SeffVG
    pressure_vars = pressure
  [../]
[]

[Variables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = initial_pressure
    [../]
  [../]
[]

[BCs]
  active = 'left'
  [./left]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 980000
  [../]
[]

[Kernels]
  active = 'richardsf richardst'

  [./richardst]
    type = RichardsLumpedMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]


[Functions]
 active = 'initial_pressure'
  [./initial_pressure]
    type = ParsedFunction
    value = max((1000000-x/5*1000000)-20000,-20000)
  [../]
[]


[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.15
    mat_permeability = '1E-10 0 0  0 1E-10 0  0 0 1E-10'
    viscosity = 1E-3
    gravity = '-1 0 0'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  active = 'andy'

  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 20'
  [../]

[]

[Executioner]
  type = Transient
  end_time = 50
  dt = 2
  snesmf_reuse_base = false
[]

[Outputs]
  file_base = bl01_lumped
  execute_on = 'initial timestep_end final'
  interval = 10000
  exodus = true
[]

(modules/richards/test/tests/sinks/q2p01.i)

# Q2PPiecewiseLinearSink (and the Flux Postprocessor)
# There are three sinks: water with no relperm and density;
# water with relperm and density; gas with relperm and density.
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
[]



[UserObjects]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 0.5
    bulk_mod = 0.5
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./RelPermGas]
    type = Q2PRelPermPowerGas
    simm = 0.0
    n = 3
  [../]
[]

[Variables]
  [./pp]
    [./InitialCondition]
      type = FunctionIC
      function = 1
    [../]
  [../]
  [./sat]
    [./InitialCondition]
      type = FunctionIC
      function = 0.5
    [../]
  [../]
[]

[Q2P]
  porepressure = pp
  saturation = sat
  water_density = DensityWater
  water_relperm = RelPermWater
  water_viscosity = 0.8
  gas_density = DensityGas
  gas_relperm = RelPermGas
  gas_viscosity = 0.5
  diffusivity = 0.0
  output_total_masses_to = 'CSV'
  save_gas_flux_in_Q2PGasFluxResidual = true
  save_water_flux_in_Q2PWaterFluxResidual = true
  save_gas_Jacobian_in_Q2PGasJacobian = true
  save_water_Jacobian_in_Q2PWaterJacobian = true
[]

[Postprocessors]
  [./left_water_out]
    type = Q2PPiecewiseLinearSinkFlux
    boundary = left
    porepressure = pp
    pressures = '0 1'
    bare_fluxes = '0 1.5'
    multiplying_fcn = 0.1
    execute_on = 'initial timestep_end'
  [../]
  [./right_water_out]
    type = Q2PPiecewiseLinearSinkFlux
    boundary = right
    porepressure = pp
    pressures = '0 1'
    bare_fluxes = '1 2'
    fluid_density = DensityWater
    fluid_viscosity = 0.8
    fluid_relperm = RelPermWater
    saturation = sat
    execute_on = 'initial timestep_end'
  [../]
  [./right_gas_out]
    type = Q2PPiecewiseLinearSinkFlux
    boundary = right
    porepressure = pp
    pressures = '0 1'
    bare_fluxes = '1 1'
    fluid_density = DensityGas
    fluid_viscosity = 0.5
    fluid_relperm = RelPermGas
    saturation = sat
    execute_on = 'initial timestep_end'
  [../]
  [./p_left]
    type = PointValue
    point = '0 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  [../]
  [./sat_left]
    type = PointValue
    point = '0 0 0'
    variable = sat
    execute_on = 'initial timestep_end'
  [../]
  [./p_right]
    type = PointValue
    point = '1 0 0'
    variable = pp
    execute_on = 'initial timestep_end'
  [../]
  [./sat_right]
    type = PointValue
    point = '1 0 0'
    variable = sat
    execute_on = 'initial timestep_end'
  [../]
[]

[BCs]
  [./left_water]
    type = Q2PPiecewiseLinearSink
    boundary = left
    pressures = '0 1'
    bare_fluxes = '0 1.5'
    multiplying_fcn = 0.1
    variable = sat
    other_var = pp
    var_is_porepressure = false
    use_mobility = false
    use_relperm = false
    fluid_density = DensityWater
    fluid_viscosity = 0.8
    fluid_relperm = RelPermWater
  [../]
  [./right_water]
    type = Q2PPiecewiseLinearSink
    boundary = right
    pressures = '0 1'
    bare_fluxes = '1 2'
    variable = sat
    other_var = pp
    var_is_porepressure = false
    use_mobility = true
    use_relperm = true
    fluid_density = DensityWater
    fluid_viscosity = 0.8
    fluid_relperm = RelPermWater
  [../]
  [./right_gas]
    type = Q2PPiecewiseLinearSink
    boundary = right
    pressures = '0 1'
    bare_fluxes = '1 1'
    variable = pp
    other_var = sat
    var_is_porepressure = true
    use_mobility = true
    use_relperm = true
    fluid_density = DensityGas
    fluid_viscosity = 0.5
    fluid_relperm = RelPermGas
  [../]
[]

[AuxVariables]
  [./one]
    initial_condition = 1
  [../]
[]

[Materials]
  [./rock]
    type = Q2PMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-2 0 0  0 1E-2 0  0 0 1E-2'
    gravity = '0 0 0'
  [../]
[]


[Preconditioning]
  active = 'andy'
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-12 1E-10 10000'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.1
  end_time = 0.5
[]

[Outputs]
  file_base = q2p01
  exodus = true
  [./CSV]
    type = CSV
  [../]
[]

(modules/porous_flow/test/tests/hysteresis/hys_pc_02.i)

# Capillary-pressure calculation.  Primary drying curve with low_extension_type = quadratic
# When comparing the results with a by-hand computation, remember the MOOSE results are averaged over an element
[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 100
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    number_fluid_phases = 1
    number_fluid_components = 1
    porous_flow_vars = ''
  []
[]

[Variables]
  [sat]
  []
[]

[ICs]
  [sat]
    type = FunctionIC
    variable = sat
    function = 'x'
  []
[]

[BCs]
  [sat]
    type = FunctionDirichletBC
    variable = sat
    function = 'x'
    boundary = 'left right'
  []
[]


[Kernels]
  [dummy]
    type = Diffusion
    variable = sat
  []
[]

[Materials]
  [hys_order]
    type = PorousFlowHysteresisOrder
  []
  [pc_calculator]
    type = PorousFlowHystereticInfo
    alpha_d = 10.0
    alpha_w = 10.0
    n_d = 1.5
    n_w = 1.9
    S_l_min = 0.1
    S_lr = 0.2
    S_gr_max = 0.3
    Pc_max = 12.0
    low_extension_type = quadratic
    sat_var = sat
  []
[]

[AuxVariables]
  [hys_order]
    family = MONOMIAL
    order = CONSTANT
  []
  [pc]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [hys_order]
    type = PorousFlowPropertyAux
    variable = hys_order
    property = hysteresis_order
  []
  [pc]
    type = PorousFlowPropertyAux
    variable = pc
    property = hysteretic_info
  []
[]

[VectorPostprocessors]
  [pc]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 10
    sort_by = x
    variable = 'sat pc'
  []
[]

[Executioner]
  type = Transient
  solve_type = Linear
  dt = 1
  end_time = 1
[]

[Outputs]
  csv = true
[]

(modules/phase_field/examples/kim-kim-suzuki/kks_example_ternary.i)

#
# KKS ternary (3 chemical component) system example in the split form
# We track c1 and c2 only, since c1 + c2 + c3 = 1
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 150
  ny = 15
  nz = 0
  xmin = -25
  xmax = 25
  ymin = -2.5
  ymax = 2.5
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[AuxVariables]
  [./Fglobal]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Variables]
  # order parameter
  [./eta]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute 1 concentration
  [./c1]
    order = FIRST
    family = LAGRANGE
  [../]

  # solute 2 concentration
  [./c2]
    order = FIRST
    family = LAGRANGE
  [../]


  # chemical potential solute 1
  [./w1]
    order = FIRST
    family = LAGRANGE
  [../]

  # chemical potential solute 2
  [./w2]
    order = FIRST
    family = LAGRANGE
  [../]


  # Liquid phase solute 1 concentration
  [./c1l]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  [../]

  # Liquid phase solute 2 concentration
  [./c2l]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.05
  [../]

  # Solid phase solute 1 concentration
  [./c1s]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.8
  [../]

  # Solid phase solute 2 concentration
  [./c2s]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  [../]

[]

[Functions]
  [./ic_func_eta]
    type = ParsedFunction
    value = '0.5*(1.0-tanh((x)/sqrt(2.0)))'
  [../]
  [./ic_func_c1]
    type = ParsedFunction
    value = '0.8*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.1*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
  [../]
  [./ic_func_c2]
    type = ParsedFunction
    value = '0.1*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.05*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
  [../]

[]


[ICs]
  [./eta]
    variable = eta
    type = FunctionIC
    function = ic_func_eta
  [../]
  [./c1]
    variable = c1
    type = FunctionIC
    function = ic_func_c1
  [../]
  [./c2]
    variable = c2
    type = FunctionIC
    function = ic_func_c2
  [../]

[]

[Materials]
  # Free energy of the liquid
  [./fl]
    type = DerivativeParsedMaterial
    f_name = fl
    args = 'c1l c2l'
    function = '(0.1-c1l)^2+(0.05-c2l)^2'
  [../]

  # Free energy of the solid
  [./fs]
    type = DerivativeParsedMaterial
    f_name = fs
    args = 'c1s c2s'
    function = '(0.8-c1s)^2+(0.1-c2s)^2'
  [../]

  # h(eta)
  [./h_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta
  [../]

  # g(eta)
  [./g_eta]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta
  [../]

  # constant properties
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'M   L   eps_sq'
    prop_values = '0.7 0.7 1.0  '
  [../]
[]

[Kernels]
  # enforce c1 = (1-h(eta))*c1l + h(eta)*c1s
  [./PhaseConc1]
    type = KKSPhaseConcentration
    ca       = c1l
    variable = c1s
    c        = c1
    eta      = eta
  [../]

  # enforce c2 = (1-h(eta))*c2l + h(eta)*c2s
  [./PhaseConc2]
    type = KKSPhaseConcentration
    ca       = c2l
    variable = c2s
    c        = c2
    eta      = eta
  [../]

  # enforce pointwise equality of chemical potentials
  [./ChemPotSolute1]
    type = KKSPhaseChemicalPotential
    variable = c1l
    cb       = c1s
    fa_name  = fl
    fb_name  = fs
    args_a   = 'c2l'
    args_b   = 'c2s'
  [../]
  [./ChemPotSolute2]
    type = KKSPhaseChemicalPotential
    variable = c2l
    cb       = c2s
    fa_name  = fl
    fb_name  = fs
    args_a   = 'c1l'
    args_b   = 'c1s'

  [../]

  #
  # Cahn-Hilliard Equations
  #
  [./CHBulk1]
    type = KKSSplitCHCRes
    variable = c1
    ca       = c1l
    fa_name  = fl
    w        = w1
    args_a   = 'c2l'
  [../]
  [./CHBulk2]
    type = KKSSplitCHCRes
    variable = c2
    ca       = c2l
    fa_name  = fl
    w        = w2
    args_a   = 'c1l'
  [../]

  [./dc1dt]
    type = CoupledTimeDerivative
    variable = w1
    v = c1
  [../]
  [./dc2dt]
    type = CoupledTimeDerivative
    variable = w2
    v = c2
  [../]

  [./w1kernel]
    type = SplitCHWRes
    mob_name = M
    variable = w1
  [../]
  [./w2kernel]
    type = SplitCHWRes
    mob_name = M
    variable = w2
  [../]


  #
  # Allen-Cahn Equation
  #
  [./ACBulkF]
    type = KKSACBulkF
    variable = eta
    fa_name  = fl
    fb_name  = fs
    w        = 1.0
    args = 'c1l c1s c2l c2s'
  [../]
  [./ACBulkC1]
    type = KKSACBulkC
    variable = eta
    ca       = c1l
    cb       = c1s
    fa_name  = fl
    args     = 'c2l'
  [../]
  [./ACBulkC2]
    type = KKSACBulkC
    variable = eta
    ca       = c2l
    cb       = c2s
    fa_name  = fl
    args     = 'c1l'
  [../]
  [./ACInterface]
    type = ACInterface
    variable = eta
    kappa_name = eps_sq
  [../]
  [./detadt]
    type = TimeDerivative
    variable = eta
  [../]
[]

[AuxKernels]
  [./GlobalFreeEnergy]
    variable = Fglobal
    type = KKSGlobalFreeEnergy
    fa_name = fl
    fb_name = fs
    w = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      ilu          nonzero'

  l_max_its = 100
  nl_max_its = 100

  num_steps = 50
  dt = 0.1
[]

#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
  [./full]
    type = SMP
    full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/test/tests/heat_advection/heat_advection_1d.i)

# 1phase, heat advecting with a moving fluid
# Full upwinding is used
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 50
  xmin = 0
  xmax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [temp]
    initial_condition = 200
  []
  [pp]
  []
[]

[ICs]
  [pp]
    type = FunctionIC
    variable = pp
    function = '1-x'
  []
[]

[BCs]
  [pp0]
    type = DirichletBC
    variable = pp
    boundary = left
    value = 1
  []
  [pp1]
    type = DirichletBC
    variable = pp
    boundary = right
    value = 0
  []
  [spit_heat]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  []
  [suck_heat]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 200
  []
[]

[Kernels]
  [mass_dot]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pp
  []
  [advection]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pp
  []
  [energy_dot]
    type = PorousFlowEnergyTimeDerivative
    variable = temp
  []
  [heat_advection]
    type = PorousFlowHeatAdvection
    variable = temp
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp pp'
    number_fluid_phases = 1
    number_fluid_components = 1
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.6
    alpha = 1.3
  []
[]

[Modules]
  [FluidProperties]
    [simple_fluid]
      type = SimpleFluidProperties
      bulk_modulus = 100
      density0 = 1000
      viscosity = 4.4
      thermal_expansion = 0
      cv = 2
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 1.0
    density = 125
  []
  [simple_fluid]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid
    phase = 0
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1.1 0 0 0 2 0 0 0 3'
  []
  [relperm]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [PS]
    type = PorousFlow1PhaseP
    porepressure = pp
    capillary_pressure = pc
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres bjacobi 1E-15 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 0.01
  end_time = 0.6
[]

[VectorPostprocessors]
  [T]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 51
    sort_by = x
    variable = temp
  []
[]

[Outputs]
  [csv]
    type = CSV
    sync_times = '0.1 0.6'
    sync_only = true
  []
[]

(modules/richards/test/tests/jacobian_2/jn_fu_17.i)

# two phase
# water saturated

# gravity = true
# supg = true
# transient = true


[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
  density_UO = 'DensityWater DensityGas'
  relperm_UO = 'RelPermWater RelPermGas'
  SUPG_UO = 'SUPGwater SUPGgas'
  sat_UO = 'SatWater SatGas'
  seff_UO = 'SeffWater SeffGas'
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = 'pwater pgas'
  [../]
  [./DensityWater]
    type = RichardsDensityConstBulk
    dens0 = 1
    bulk_mod = 1.0 # notice small quantity, so the PETSc constant state works
  [../]
  [./DensityGas]
    type = RichardsDensityConstBulk
    dens0 = 0.5
    bulk_mod = 0.5 # notice small quantity, so the PETSc constant state works
  [../]
  [./SeffWater]
    type = RichardsSeff2waterVG
    m = 0.8
    al = 1 # notice small quantity, so the PETSc constant state works
  [../]
  [./SeffGas]
    type = RichardsSeff2gasVG
    m = 0.8
    al = 1 # notice small quantity, so the PETSc constant state works
  [../]
  [./RelPermWater]
    type = RichardsRelPermPower
    simm = 0.2
    n = 2
  [../]
  [./RelPermGas]
    type = RichardsRelPermPower
    simm = 0.1
    n = 3
  [../]
  [./SatWater]
    type = RichardsSat
    s_res = 0.1
    sum_s_res = 0.15
  [../]
  [./SatGas]
    type = RichardsSat
    s_res = 0.05
    sum_s_res = 0.15
  [../]
  [./SUPGwater]
    type = RichardsSUPGstandard
    p_SUPG = 0.1
  [../]
  [./SUPGgas]
    type = RichardsSUPGstandard
    p_SUPG = 0.01
  [../]
[]

[Variables]
  [./pwater]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      block = 0
      function = init_p
    [../]
  [../]
  [./pgas]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      block = 0
      function = init_p
    [../]
  [../]
[]

[Functions]
  [./init_p]
    type = ParsedFunction
    value = x+0.6*y+0.3*z
  [../]
[]

[Kernels]
  active = 'richardsfwater richardstwater richardsfgas richardstgas'
  [./richardstwater]
    type = RichardsMassChange
    variable = pwater
  [../]
  [./richardsfwater]
    type = RichardsFullyUpwindFlux
    variable = pwater
  [../]
  [./richardstgas]
    type = RichardsMassChange
    variable = pgas
  [../]
  [./richardsfgas]
    type = RichardsFullyUpwindFlux
    variable = pgas
  [../]
[]

[Materials]
  [./rock]
    type = RichardsMaterial
    block = 0
    mat_porosity = 0.1
    mat_permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
    viscosity = '1E-3 0.5E-3'
    gravity = '1 2 3'
    linear_shape_fcns = true
  [../]
[]


[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1E-5
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = jn17
  exodus = false
[]

(modules/porous_flow/test/tests/flux_limited_TVD_advection/fltvd_1D.i)

# Using Flux-Limited TVD Advection ala Kuzmin and Turek, with antidiffusion from superbee flux limiting
# 1D version
[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmin = 0
  xmax = 1
[]

[Variables]
  [tracer]
  []
[]

[ICs]
  [tracer]
    type = FunctionIC
    variable = tracer
    function = 'if(x<0.1,0,if(x>0.3,0,1))'
  []
[]

[Kernels]
  [mass_dot]
    type = MassLumpedTimeDerivative
    variable = tracer
  []
  [flux]
    type = FluxLimitedTVDAdvection
    variable = tracer
    advective_flux_calculator = fluo
  []
[]

[UserObjects]
  [fluo]
    type = AdvectiveFluxCalculatorConstantVelocity
    flux_limiter_type = superbee
    u = tracer
    velocity = '0.1 0 0'
  []
[]

[BCs]
  [no_tracer_on_left]
    type = DirichletBC
    variable = tracer
    value = 0
    boundary = left
  []
  [remove_tracer]
# Ideally, an OutflowBC would be used, but that does not exist in the framework
# In 1D VacuumBC is the same as OutflowBC, with the alpha parameter being twice the velocity
    type = VacuumBC
    boundary = right
    alpha = 0.2 # 2 * velocity
    variable = tracer
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[VectorPostprocessors]
  [tracer]
    type = LineValueSampler
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 11
    sort_by = x
    variable = tracer
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 6
  dt = 6E-2
  nl_abs_tol = 1E-8
  nl_max_its = 500
  timestep_tolerance = 1E-3
[]

[Outputs]
  print_linear_residuals = false
  [out]
    type = CSV
    execute_on = final
  []
[]

(modules/richards/test/tests/dirac/bh02.i)

# fully-saturated
# production
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  zmin = -1
  zmax = 1
[]

[GlobalParams]
  richardsVarNames_UO = PPNames
[]

[UserObjects]
  [./PPNames]
    type = RichardsVarNames
    richards_vars = pressure
  [../]
  [./DensityConstBulk]
    type = RichardsDensityConstBulk
    dens0 = 1000
    bulk_mod = 2E9
  [../]
  [./Seff1VG]
    type = RichardsSeff1VG
    m = 0.8
    al = 1E-5
  [../]
  [./RelPermPower]
    type = RichardsRelPermPower
    simm = 0.0
    n = 2
  [../]
  [./Saturation]
    type = RichardsSat
    s_res = 0
    sum_s_res = 0
  [../]
  [./SUPGstandard]
    type = RichardsSUPGstandard
    p_SUPG = 1E8
  [../]

  [./borehole_total_outflow_mass]
    type = RichardsSumQuantity
  [../]
[]


[Variables]
  active = 'pressure'
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    variable = pressure
    function = initial_pressure
  [../]
[]

[AuxVariables]
  [./Seff1VG_Aux]
  [../]
[]


[Kernels]
  active = 'richardsf richardst'
  [./richardst]
    type = RichardsMassChange
    variable = pressure
  [../]
  [./richardsf]
    type = RichardsFlux
    variable = pressure
  [../]
[]

[DiracKernels]
  [./bh]
    type = RichardsBorehole
    bottom_pressure = 0
    point_file = bh02.bh
    SumQuantityUO = borehole_total_outflow_mass
    variable = pressure
    unit_weight = '0 0 0'
    character = 1
  [../]
[]


[Postprocessors]
  [./bh_report]
    type = RichardsPlotQuantity
    uo = borehole_total_outflow_mass
  [../]

  [./fluid_mass0]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_begin
  [../]

  [./fluid_mass1]
    type = RichardsMass
    variable = pressure
    execute_on = timestep_end
  [../]

  [./zmass_error]
    type = FunctionValuePostprocessor
    function = mass_bal_fcn
    execute_on = timestep_end
  [../]

  [./p0]
    type = PointValue
    variable = pressure
    point = '1 1 1'
    execute_on = timestep_end
  [../]
[]


[Functions]
  [./initial_pressure]
    type = ParsedFunction
    value = 1E7
  [../]

  [./mass_bal_fcn]
    type = ParsedFunction
    value = abs((a-c+d)/2/(a+c))
    vars = 'a c d'
    vals = 'fluid_mass1 fluid_mass0 bh_report'
  [../]
[]


[Materials]
  [./all]
    type = RichardsMaterial
    block = 0
    viscosity = 1E-3
    mat_porosity = 0.1
    mat_permeability = '1E-12 0 0  0 1E-12 0  0 0 1E-12'
    density_UO = DensityConstBulk
    relperm_UO = RelPermPower
    sat_UO = Saturation
    seff_UO = Seff1VG
    SUPG_UO = SUPGstandard
    gravity = '0 0 0'
    linear_shape_fcns = true
  [../]
[]

[AuxKernels]
  [./Seff1VG_AuxK]
    type = RichardsSeffAux
    variable = Seff1VG_Aux
    seff_UO = Seff1VG
    pressure_vars = pressure
  [../]
[]


[Preconditioning]
  [./usual]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-10 1E-10 10000 30'
  [../]
[]


[Executioner]
  type = Transient
  end_time = 0.5
  dt = 1E-2
  solve_type = NEWTON

[]

[Outputs]
  file_base = bh02
  exodus = false
  csv = true
  execute_on = timestep_end
[]

(test/tests/time_steppers/timesequence_stepper/timesequence_restart1.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  end_time = 4.0
  [./TimeStepper]
    type = TimeSequenceStepper
    time_sequence  = '0   0.85 1.3 2 4'
  [../]
[]

[Outputs]
  exodus = true
  [./checkpoint]
    type = Checkpoint
    num_files = 4
  [../]
[]

(test/tests/time_steppers/timesequence_stepper/exodustimesequence.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = t*t*(x*x+y*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 2*t*(x*x+y*y)-4*t*t
  [../]
[]

[Variables]
  [./u]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[ICs]
  [./u_var]
    type = FunctionIC
    variable = u
    function = exact_fn
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = exact_fn
  [../]
[]

[Executioner]
  type = Transient
  end_time = 4.0
  [./TimeStepper]
    type = ExodusTimeSequenceStepper
    mesh = timesequence_no_start_time.e
  [../]
[]

[Outputs]
  exodus = true
[]

(framework/include/ics/IntegralPreservingFunctionIC.h)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "FunctionIC.h"

/**
 * Initial conditions specifying an initial condition as a general function
 * while preserving a total integral magnitude.
 */
class IntegralPreservingFunctionIC : public FunctionIC
{
public:
  static InputParameters validParams();

  IntegralPreservingFunctionIC(const InputParameters & parameters);

  virtual void initialSetup() override;

  /**
   * @returns The magnitude of the function
   */
  Real magnitude() const { return _magnitude; }

protected:
  virtual Real value(const Point & p) override;

  /// Name of postprocessor providing the integral of the function
  const PostprocessorName & _pp_name;

  /// Integral of the function
  const PostprocessorValue & _integral;

  /// Magnitude of the initial condition upon integration
  const Real & _magnitude;
};