ADHeatConductionTimeDerivative

Description

The ADHeatConductionTimeDerivative kernel implements a time derivative for the domain $var element = document.getElementById("moose-equation-0b81e456-9741-4448-9b77-f81055aff7f8");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ given by

$var element = document.getElementById("moose-equation-83c5c7df-81ad-4c9b-b605-97fc883afe01");katex.render("\\underbrace{\\rho c_p \\frac{\\partial u}{\\partial t}}_{\\textrm{ADHeatConductionTimeDerivative}} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-1e5b83c7-2e9b-4d31-9588-e94ff0464b10");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the material density, $var element = document.getElementById("moose-equation-953365de-e62e-49c0-ae26-691fd87874f5");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the specific heat, and the second term on the left hand side corresponds to the strong forms of other kernels. The corresponding ADHeatConductionTimeDerivative weak form using inner-product notation is

$var element = document.getElementById("moose-equation-7c800eb2-7e82-42ee-a99a-79372d464542");katex.render("R_i(u_h) = (\\psi_i, \\rho c_p\\frac{\\partial u_h}{\\partial t}) \\quad \\forall \\psi_i,", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-3e6599ce-cf3a-40da-ba2e-d1ea8e4cb01c");katex.render("u_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the approximate solution and $var element = document.getElementById("moose-equation-4380ea8a-d75e-40c6-a9be-9aeea8278716");katex.render("\\psi_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a finite element test function.

The Jacobian is given by automatic differentiation, and should be perfect as long as $var element = document.getElementById("moose-equation-70072078-c422-4560-ac3b-a762fed2423d");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-7d54db24-1500-47f7-bde5-537390be4062");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are provided using ADMaterial derived objects.

Input Parameters

variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this residual object operates on

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of blocks (ids or names) that this object will be applied
density_namedensityProperty name of the density material property
Default:density
C++ Type:MaterialPropertyName
Options:
Description:Property name of the density material property
displacementsThe displacements
C++ Type:std::vector<VariableName>
Options:
Description:The displacements
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Options:
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
specific_heatspecific_heatProperty name of the specific heat material property
Default:specific_heat
C++ Type:MaterialPropertyName
Options:
Description:Property name of the specific heat material property

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
use_displaced_meshTrueWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:True
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Options:nontime, system, time
Description:The tag for the matrices this Kernel should fill
vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Options:nontime, time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/problems/step6a_coupled.i)
(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/tests/kernels/darcy_advection/darcy_advection.i)
(modules/heat_conduction/test/tests/ad_heat_conduction/test.i)
(modules/combined/test/tests/ad_power_law_creep/power_law_creep_smallstrain.i)
(modules/heat_conduction/test/tests/verify_against_analytical/ad_1D_transient.i)
(modules/combined/test/tests/ad_power_law_creep/power_law_creep_restart2.i)
(tutorials/darcy_thermo_mech/step05_heat_conduction/problems/step5c_outflow.i)
(tutorials/darcy_thermo_mech/step05_heat_conduction/problems/step5b_transient.i)
(tutorials/darcy_thermo_mech/step09_mechanics/problems/step9.i)
(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7a_coarse.i)
(modules/heat_conduction/test/tests/function_ellipsoid_heat_source/function_heat_source.i)
(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/problems/step6c_decoupled.i)
(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7d_adapt_blocks.i)
(tutorials/darcy_thermo_mech/step10_multiapps/problems/step10.i)
(tutorials/darcy_thermo_mech/step05_heat_conduction/tests/bcs/outflow/outflow.i)
(tutorials/darcy_thermo_mech/step08_postprocessors/problems/step8.i)
(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7c_adapt.i)
(modules/heat_conduction/test/tests/joule_heating/transient_ad_jouleheating.i)
(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/problems/step6b_transient_inflow.i)
(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7b_fine.i)
(modules/combined/test/tests/ad_power_law_creep/power_law_creep.i)
(modules/combined/test/tests/ad_power_law_creep/power_law_creep_restart1.i)

(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/problems/step6a_coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 200
  ny = 10
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = right
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = left
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    temperature = temperature
    radius = 1
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true

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

  end_time = 100
  dt = 0.25
  start_time = -1

  steady_state_tolerance = 1e-5
  steady_state_detection = true

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]

[Outputs]
  exodus = true
[]

(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/tests/kernels/darcy_advection/darcy_advection.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 200
  ny = 10
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [pressure]
    initial_condition = 10000
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[BCs]
  [inlet_temperature]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 350
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    radius = 1
    temperature = temperature
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/heat_conduction/test/tests/ad_heat_conduction/test.i)

# This test solves a 1D transient heat equation with a complicated thermal
# conductivity in order to verify jacobian calculation via AD

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  xmax = 0.001
  ymax = 0.001
[]

[Variables]
  [./T]
    initial_condition = 1.5
  [../]
  [./c]
    initial_condition = 1.5
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = ADHeatConduction
    variable = T
    thermal_conductivity = thermal_conductivity
  [../]
  [./heat_dt]
    type = ADHeatConductionTimeDerivative
    variable = T
    specific_heat = thermal_conductivity
    density_name = thermal_conductivity
  [../]
  [./c]
    type = ADDiffusion
    variable = c
  [../]
[]

[Kernels]
  [./c_dt]
    type = TimeDerivative
    variable = c
  [../]
[]

[BCs]
  [./left_c]
    type = DirichletBC
    variable = c
    boundary = left
    value = 2
  [../]
  [./right_c]
    type = DirichletBC
    variable = c
    boundary = right
    value = 1
  [../]
  [./left_T]
    type = DirichletBC
    variable = T
    boundary = top
    value = 1
  [../]
  [./right_T]
    type = DirichletBC
    variable = T
    boundary = bottom
    value = 2
  [../]
[]

[Materials]
  [./k]
    type = ADThermalConductivityTest
    c = c
    temperature = T
  [../]
[]

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

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/ad_power_law_creep/power_law_creep_smallstrain.i)

# 1x1x1 unit cube with uniform pressure on top face for the case of small strain.
#  This test does not have a solid mechanics analog because there is not an equvialent
#  small strain with rotations strain calculator material in solid mechanics

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000.0
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = SMALL
    incremental = true
    add_variables = true
    generate_output = 'stress_yy creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_yy'
    use_automatic_differentiation = true
  [../]
[]

[Functions]
  [./top_pull]
    type = PiecewiseLinear
    x = '0 1'
    y = '1 1'
  [../]
[]

[Kernels]
  [./heat]
    type = ADHeatConduction
    variable = temp
  [../]
  [./heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  [../]
[]

[BCs]
  [./u_top_pull]
    type = ADPressure
    variable = disp_y
    component = 1
    boundary = top
    constant = -10.0e6
    function = top_pull
  [../]
  [./u_bottom_fix]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./u_yz_fix]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./u_xy_fix]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./temp_fix]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top'
    value = 1000.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 2e11
    poissons_ratio = 0.3
    constant_on = SUBDOMAIN
  [../]
  [./radial_return_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'power_law_creep'
  [../]
  [./power_law_creep]
    type = ADPowerLawCreepStressUpdate
    coefficient = 1.0e-15
    n_exponent = 4
    activation_energy = 3.0e5
    temperature = temp
  [../]

  [./thermal]
    type = ADHeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 100.
  [../]
  [./density]
    type = ADDensity
    density = 1.0
  [../]
[]

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

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 20
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.0
  end_time = 1.0
  num_steps = 10
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(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/combined/test/tests/ad_power_law_creep/power_law_creep_restart2.i)

# 1x1x1 unit cube with uniform pressure on top face

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000.0
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = FINITE
    incremental = true
    add_variables = true
    generate_output = 'stress_yy creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_yy'
    use_automatic_differentiation = true
  [../]
[]

[Functions]
  [./top_pull]
    type = PiecewiseLinear
    x = '0 1'
    y = '1 1'
  [../]
[]

[Kernels]
  [./heat]
    type = ADHeatConduction
    variable = temp
  [../]
  [./heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  [../]
[]

[BCs]
  [./u_top_pull]
    type = ADPressure
    variable = disp_y
    component = 1
    boundary = top
    constant = -10.0e6
    function = top_pull
  [../]
  [./u_bottom_fix]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./u_yz_fix]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./u_xy_fix]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./temp_fix]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top'
    value = 1000.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 2e11
    poissons_ratio = 0.3
    constant_on = SUBDOMAIN
  [../]
  [./radial_return_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'power_law_creep'
  [../]
  [./power_law_creep]
    type = ADPowerLawCreepStressUpdate
    coefficient = 1.0e-15
    n_exponent = 4
    activation_energy = 3.0e5
    temperature = temp
  [../]

  [./thermal]
    type = ADHeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 100.
  [../]
  [./density]
    type = ADDensity
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 20
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.6
  end_time = 1.0
  num_steps = 12
  dt = 0.1
[]

[Outputs]
  file_base = power_law_creep_out
  exodus = true
[]

[Problem]
  restart_file_base = power_law_creep_restart1_out_cp/0006
[]

(tutorials/darcy_thermo_mech/step05_heat_conduction/problems/step5c_outflow.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 10
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
[]

[BCs]
  [inlet_temperature]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 350 # (K)
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [steel]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '18 466 8000' # W/m*K, J/kg-K, kg/m^3 @ 296K
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  num_steps = 10
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(tutorials/darcy_thermo_mech/step05_heat_conduction/problems/step5b_transient.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 10
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
[]

[BCs]
  [inlet_temperature]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 350 # (K)
  []
  [outlet_temperature]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300 # (K)
  []
[]

[Materials]
  [steel]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '18 0.466 8000' # W/m*K, J/kg-K, kg/m^3 @ 296K
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  num_steps = 10
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(tutorials/darcy_thermo_mech/step09_mechanics/problems/step9.i)

[GlobalParams]
  displacements = 'disp_r disp_z'
[]

[Mesh]
  [generate]
    type = GeneratedMeshGenerator
    dim = 2
    ny = 200
    nx = 10
    ymax = 0.304 # Length of test chamber
    xmax = 0.0257 # Test chamber radius
  []
  [bottom]
    type = SubdomainBoundingBoxGenerator
    input = generate
    location = inside
    bottom_left = '0 0 0'
    top_right = '0.01285 0.304 0'
    block_id = 1
  []
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Modules/TensorMechanics/Master]
  [all]
    # This block adds all of the proper Kernels, strain calculators, and Variables
    # for TensorMechanics in the correct coordinate system (autodetected)
    add_variables = true
    strain = FINITE
    eigenstrain_names = eigenstrain
    use_automatic_differentiation = true
    generate_output = 'vonmises_stress elastic_strain_xx elastic_strain_yy strain_xx strain_yy'
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = bottom
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = top
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = bottom
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = top
  []
  [hold_inlet]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []
  [hold_center]
    type = DirichletBC
    variable = disp_r
    boundary = left
    value = 0
  []
  [hold_outside]
    type = DirichletBC
    variable = disp_r
    boundary = right
    value = 0
  []
[]

[Materials]
  viscosity_file = data/water_viscosity.csv
  density_file = data/water_density.csv
  thermal_conductivity_file = data/water_thermal_conductivity.csv
  specific_heat_file = data/water_specific_heat.csv
  thermal_expansion_file = data/water_thermal_expansion.csv

  [column_top]
    type = PackedColumn
    block = 0
    temperature = temperature
    radius = 1.15
    fluid_viscosity_file = ${viscosity_file}
    fluid_density_file = ${density_file}
    fluid_thermal_conductivity_file = ${thermal_conductivity_file}
    fluid_specific_heat_file = ${specific_heat_file}
    fluid_thermal_expansion_file = ${thermal_expansion_file}
  []
  [column_bottom]
    type = PackedColumn
    block = 1
    temperature = temperature
    radius = 1
    fluid_viscosity_file = ${viscosity_file}
    fluid_density_file = ${density_file}
    fluid_thermal_conductivity_file = ${thermal_conductivity_file}
    fluid_specific_heat_file = ${specific_heat_file}
    fluid_thermal_expansion_file = ${thermal_expansion_file}
  []

  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 200e9 # (Pa) from wikipedia
    poissons_ratio = .3 # from wikipedia

  []
  [elastic_stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    stress_free_temperature = 300
    eigenstrain_name = eigenstrain
    temperature = temperature
    thermal_expansion_coeff = 1e-5 # TM modules doesn't support material property, but it will
  []
[]

[Postprocessors]
  [average_temperature]
    type = ElementAverageValue
    variable = temperature
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
[]

[Executioner]
  type = Transient
  start_time = -1
  end_time = 200
  steady_state_tolerance = 1e-7
  steady_state_detection = true
  dt = 0.25
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  #petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  #petsc_options_value = 'hypre boomeramg 500'
  line_search = none
  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]

[Outputs]
  [out]
    type = Exodus
    elemental_as_nodal = true
  []
[]

(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7a_coarse.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 30
  ny = 3
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = right
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = left
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    radius = 1
    temperature = temperature
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true

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

  end_time = 100
  dt = 0.25
  start_time = -1

  steady_state_tolerance = 1e-5
  steady_state_detection = true

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]

[Outputs]
  exodus = true
[]

(modules/heat_conduction/test/tests/function_ellipsoid_heat_source/function_heat_source.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = -5.0
  xmax = 5.0
  nx = 10

  ymin = -5.0
  ymax = 5.0
  ny = 10

  zmin = 0.0
  zmax = 1.0
  nz = 1
[]

[Variables]
  [./temp]
    initial_condition = 300
  [../]
[]

[Kernels]
  [./time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  [../]
  [./heat_conduct]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  [../]
  [./heat_source]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
  [../]
[]

[BCs]
  [./temp_bottom_fix]
    type = ADDirichletBC
    variable = temp
    boundary = 1
    value = 300
  [../]
[]

[Materials]
  [./heat]
    type = ADHeatConductionMaterial
    specific_heat = 603
    thermal_conductivity = 10e-2
  [../]
  [./density]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = '4.43e-6'
  [../]
  [./volumetric_heat]
    type = FunctionPathEllipsoidHeatSource
    rx = 1
    ry = 1
    rz = 1
    power = 1000
    efficiency = 0.5
    factor = 2
    function_x= path_x
    function_y= path_y
    function_z= path_z
  [../]
[]

[Functions]
  [./path_x]
    type = ParsedFunction
    value = 2*cos(2.0*pi*t)
  [../]
  [./path_y]
    type = ParsedFunction
    value = 2*sin(2.0*pi*t)
  [../]
  [./path_z]
    type = ParsedFunction
    value = 1.0
  [../]
[]

[Postprocessors]
  [temp_max]
    type = ElementExtremeValue
    variable = temp
  []
  [temp_min]
    type = ElementExtremeValue
    variable = temp
    value_type = min
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
[]

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

[Executioner]
  type = Transient
  solve_type = PJFNK

  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'

  l_max_its = 100

  end_time = 1
  dt = 0.1
  dtmin = 1e-4
[]

[Outputs]
  csv = true
[]

(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/problems/step6c_decoupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 200
  ny = 10
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [pressure]
  []
[]

[AuxKernels]
  [pressure]
    type = FunctionAux
    variable = pressure
    function = 't*x*x*y'
    execute_on = timestep_end
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[BCs]
  [inlet_temperature]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 350
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    radius = 1
    temperature = 293.15 # 20C
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  num_steps = 300
  dt = 0.1
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7d_adapt_blocks.i)

[Mesh]
  uniform_refine = 3
  [generate]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 4
    xmax = 0.304 # Length of test chamber
    ymax = 0.0257 # Test chamber radius
  []
  [bottom]
    type = SubdomainBoundingBoxGenerator
    input = generate
    location = inside
    bottom_left = '0 0 0'
    top_right = '0.304 0.01285 0'
    block_id = 1
  []
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = right
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = left
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  viscosity_file = data/water_viscosity.csv
  density_file = data/water_density.csv
  thermal_conductivity_file = data/water_thermal_conductivity.csv
  specific_heat_file = data/water_specific_heat.csv

  [column_bottom]
    type = PackedColumn
    block = 1
    radius = 1.15
    temperature = temperature
    fluid_viscosity_file = ${viscosity_file}
    fluid_density_file = ${density_file}
    fluid_thermal_conductivity_file = ${thermal_conductivity_file}
    fluid_specific_heat_file = ${specific_heat_file}
  []
  [column_top]
    type = PackedColumn
    block = 0
    radius = 1
    temperature = temperature
    porosity = '0.25952 + 0.7*x/0.304'
    fluid_viscosity_file = ${viscosity_file}
    fluid_density_file = ${density_file}
    fluid_thermal_conductivity_file = ${thermal_conductivity_file}
    fluid_specific_heat_file = ${specific_heat_file}
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true

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

  end_time = 100
  dt = 0.25
  start_time = -1

  steady_state_tolerance = 1e-5
  steady_state_detection = true

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]

[Adaptivity]
  marker = error_frac
  max_h_level = 3
  [Indicators]
    [temperature_jump]
      type = GradientJumpIndicator
      variable = temperature
      scale_by_flux_faces = true
    []
  []
  [Markers]
    [error_frac]
      type = ErrorFractionMarker
      coarsen = 0.025
      indicator = temperature_jump
      refine = 0.9
    []
  []
[]

[Outputs]
  [out]
    type = Exodus
    output_material_properties = true
  []
[]

(tutorials/darcy_thermo_mech/step10_multiapps/problems/step10.i)

[GlobalParams]
  displacements = 'disp_r disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 100
  ymax = 0.304 # Length of test chamber
  xmax = 0.0257 # Test chamber radius
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [k_eff]
    initial_condition = 15.0 # water at 20C
  []
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Modules/TensorMechanics/Master]
  [all]
    # This block adds all of the proper Kernels, strain calculators, and Variables
    # for TensorMechanics in the correct coordinate system (autodetected)
    add_variables = true
    strain = FINITE
    eigenstrain_names = eigenstrain
    use_automatic_differentiation = true
    generate_output = 'vonmises_stress elastic_strain_xx elastic_strain_yy strain_xx strain_yy'
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = bottom
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = top
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = bottom
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = top
  []
  [hold_inlet]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []
  [hold_center]
    type = DirichletBC
    variable = disp_r
    boundary = left
    value = 0
  []
  [hold_outside]
    type = DirichletBC
    variable = disp_r
    boundary = right
    value = 0
  []
[]

[Materials]
  viscosity_file = data/water_viscosity.csv
  density_file = data/water_density.csv
  specific_heat_file = data/water_specific_heat.csv
  thermal_expansion_file = data/water_thermal_expansion.csv
  [column]
    type = PackedColumn
    temperature = temperature
    radius = 1
    thermal_conductivity = k_eff # Use the AuxVariable instead of calculating
    fluid_viscosity_file = ${viscosity_file}
    fluid_density_file = ${density_file}
    fluid_specific_heat_file = ${specific_heat_file}
    fluid_thermal_expansion_file = ${thermal_expansion_file}
  []

  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 200e9 # (Pa) from wikipedia
    poissons_ratio = .3 # from wikipedia
  []
  [elastic_stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    stress_free_temperature = 300
    thermal_expansion_coeff = 1e-6
    eigenstrain_name = eigenstrain
    temperature = temperature
  []
[]

[Postprocessors]
  [average_temperature]
    type = ElementAverageValue
    variable = temperature
  []
[]

[Executioner]
  type = Transient
  start_time = -1
  end_time = 200
  steady_state_tolerance = 1e-7
  steady_state_detection = true
  dt = 0.25
  solve_type = PJFNK
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 500'
  line_search = none
  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]


[MultiApps]
  [micro]
    type = TransientMultiApp
    app_type = DarcyThermoMechApp
    positions = '0.01285 0.0    0
                 0.01285 0.0608 0
                 0.01285 0.1216 0
                 0.01285 0.1824 0
                 0.01285 0.2432 0
                 0.01285 0.304  0'
    input_files = step10_micro.i
    execute_on = 'timestep_end'
  []
[]

[Transfers]
  [keff_from_sub]
    type = MultiAppPostprocessorInterpolationTransfer
    direction = from_multiapp
    multi_app = micro
    variable = k_eff
    power = 1
    postprocessor = k_eff
    execute_on = 'timestep_end'
  []
  [temperature_to_sub]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    direction = to_multiapp
    multi_app = micro
    source_variable = temperature
    postprocessor = temperature_in
    execute_on = 'timestep_end'
  []
[]

[Controls]
  [multiapp]
    type = TimePeriod
    disable_objects = 'MultiApps::micro Transfers::keff_from_sub Transfers::temperature_to_sub'
    start_time = '0'
    execute_on = 'initial'
  []
[]

[Outputs]
  [out]
    type = Exodus
    elemental_as_nodal = true
  []
[]

(tutorials/darcy_thermo_mech/step05_heat_conduction/tests/bcs/outflow/outflow.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 30
  ny = 5
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[Kernels]
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
[]

[BCs]
  [inlet_temperature]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 350 # (K)
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [steel]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '18 466 8000' # W/m*K, J/kg-K, kg/m^3 @ 296K
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  num_steps = 2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(tutorials/darcy_thermo_mech/step08_postprocessors/problems/step8.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 30
  ny = 3
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
  uniform_refine = 2
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = right
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = left
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    radius = 1
    temperature = temperature
    porosity = '0.25952 + 0.7*y/0.0257'
  []
[]

[Postprocessors]
  [average_temperature]
    type = ElementAverageValue
    variable = temperature
  []
  [outlet_heat_flux]
    type = ADSideDiffusiveFluxIntegral
    variable = temperature
    boundary = right
    diffusivity = thermal_conductivity
  []
[]

[VectorPostprocessors]
  [temperature_sample]
    type = LineValueSampler
    num_points = 500
    start_point = '0.1 0      0'
    end_point =   '0.1 0.0257 0'
    variable = temperature
    sort_by = y
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true

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

  end_time = 100
  dt = 0.25
  start_time = -1

  steady_state_tolerance = 1e-5
  steady_state_detection = true

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7c_adapt.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 30
  ny = 3
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
  uniform_refine = 3
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = right
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = left
    function = 'if(t<0,350+50*t,350)'
  []

  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    radius = 1
    temperature = temperature
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true

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

  end_time = 100
  dt = 0.25
  start_time = -1

  steady_state_tolerance = 1e-5
  steady_state_detection = true

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]

[Outputs]
  exodus = true
[]

[Adaptivity]
  marker = error_frac
  max_h_level = 3
  [Indicators]
    [temperature_jump]
      type = GradientJumpIndicator
      variable = temperature
      scale_by_flux_faces = true
    []
  []
  [Markers]
    [error_frac]
      type = ErrorFractionMarker
      coarsen = 0.15
      indicator = temperature_jump
      refine = 0.7
    []
  []
[]

(modules/heat_conduction/test/tests/joule_heating/transient_ad_jouleheating.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 5
  ymax = 5
[]

[Variables]
  [./T]
    initial_condition = 293.0 #in K
  [../]
  [./elec]
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = ADHeatConduction
    variable = T
  [../]
  [./HeatTdot]
    type = ADHeatConductionTimeDerivative
    variable = T
  [../]
  [./HeatSrc]
    type = ADJouleHeatingSource
    variable = T
    elec = elec
  [../]
  [./electric]
    type = ADHeatConduction
    variable = elec
    thermal_conductivity = electrical_conductivity
  [../]
[]

[BCs]
  [./lefttemp]
    type = ADDirichletBC
    boundary = left
    variable = T
    value = 293 #in K
  [../]
  [./elec_left]
    type = ADDirichletBC
    variable = elec
    boundary = left
    value = 1 #in V
  [../]
  [./elec_right]
    type = ADDirichletBC
    variable = elec
    boundary = right
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '397.48' #copper in W/(m K)
  [../]
  [./cp]
    type = ADGenericConstantMaterial
    prop_names = 'specific_heat'
    prop_values = '385.0' #copper in J/(kg K)
  [../]
  [./rho]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = '8920.0' #copper in kg/(m^3)
  [../]
  [./sigma] #copper is default material
    type = ADElectricalConductivity
    temperature = T
  [../]
[]

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'hypre'
  dt = 1
  end_time = 5
  automatic_scaling = true
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/problems/step6b_transient_inflow.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 200
  ny = 10
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[Functions]
  [inlet_function]
    type = ParsedFunction
    value = 2000*sin(0.466*pi*t) # Inlet signal from Fig. 3
  []
  [outlet_function]
    type = ParsedFunction
    value = 2000*cos(0.466*pi*t) # Outlet signal from Fig. 3
  []
[]

[BCs]
  [inlet]
    type = FunctionDirichletBC
    variable = pressure
    boundary = left
    function = inlet_function
  []
  [outlet]
    type = FunctionDirichletBC
    variable = pressure
    boundary = right
    function = outlet_function
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = left
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    radius = 1
    temperature = temperature
    fluid_viscosity_file = data/water_viscosity.csv
    fluid_density_file = data/water_density.csv
    fluid_thermal_conductivity_file = data/water_thermal_conductivity.csv
    fluid_specific_heat_file = data/water_specific_heat.csv
    outputs = exodus
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true

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

  end_time = 100
  dt = 0.25
  start_time = -1

  steady_state_tolerance = 1e-5
  steady_state_detection = true

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,(2*pi/(0.466*pi))/16)' # dt to always hit the peaks of sine/cosine BC
  []
[]

[Outputs]
  exodus = true
[]

(tutorials/darcy_thermo_mech/step07_adaptivity/problems/step7b_fine.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 30
  ny = 3
  xmax = 0.304 # Length of test chamber
  ymax = 0.0257 # Test chamber radius
  uniform_refine = 3
[]

[Variables]
  [pressure]
  []
  [temperature]
    initial_condition = 300 # Start at room temperature
  []
[]

[AuxVariables]
  [velocity]
    order = CONSTANT
    family = MONOMIAL_VEC
  []
[]

[Kernels]
  [darcy_pressure]
    type = DarcyPressure
    variable = pressure
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_conduction_time_derivative]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat_convection]
    type = DarcyAdvection
    variable = temperature
    pressure = pressure
  []
[]

[AuxKernels]
  [velocity]
    type = DarcyVelocity
    variable = velocity
    execute_on = timestep_end
    pressure = pressure
  []
[]

[BCs]
  [inlet]
    type = DirichletBC
    variable = pressure
    boundary = left
    value = 4000 # (Pa) From Figure 2 from paper.  First data point for 1mm spheres.
  []
  [outlet]
    type = DirichletBC
    variable = pressure
    boundary = right
    value = 0 # (Pa) Gives the correct pressure drop from Figure 2 for 1mm spheres
  []
  [inlet_temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = left
    function = 'if(t<0,350+50*t,350)'
  []
  [outlet_temperature]
    type = HeatConductionOutflow
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [column]
    type = PackedColumn
    radius = 1
    temperature = temperature
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = X
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true

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

  end_time = 100
  dt = 0.25
  start_time = -1

  steady_state_tolerance = 1e-5
  steady_state_detection = true

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<0,0.1,0.25)'
  []
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/ad_power_law_creep/power_law_creep.i)

# 1x1x1 unit cube with uniform pressure on top face

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 3
[]

[Variables]
  [./temp]
    initial_condition = 1000.0
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = FINITE
    incremental = true
    add_variables = true
    generate_output = 'stress_yy creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_yy'
    use_automatic_differentiation = true
  [../]
[]

[Kernels]
  [./heat]
    type = ADHeatConduction
    variable = temp
  [../]
  [./heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  [../]
[]

[BCs]
  [./u_top_pull]
    type = ADPressure
    variable = disp_y
    component = 1
    boundary = top
    constant = -10.0e6
  [../]
  [./u_bottom_fix]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./u_yz_fix]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./u_xy_fix]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./temp_fix]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top'
    value = 1000.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 2e11
    poissons_ratio = 0.3
    constant_on = SUBDOMAIN
  [../]
  [./radial_return_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'power_law_creep'
  [../]
  [./power_law_creep]
    type = ADPowerLawCreepStressUpdate
    coefficient = 1.0e-15
    n_exponent = 4
    activation_energy = 3.0e5
    temperature = temp
  [../]

  [./thermal]
    type = ADHeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 100.
  [../]
  [./density]
    type = ADDensity
    density = 1.0
  [../]
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 20
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.0
  end_time = 1.0
  num_steps = 10
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/ad_power_law_creep/power_law_creep_restart1.i)

# 1x1x1 unit cube with uniform pressure on top face

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000.0
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = FINITE
    incremental = true
    add_variables = true
    generate_output = 'stress_yy creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_yy'
    use_automatic_differentiation = true
  [../]
[]

[Functions]
  [./top_pull]
    type = PiecewiseLinear
    x = '0 1'
    y = '1 1'
  [../]
[]

[Kernels]
  [./heat]
    type = ADHeatConduction
    variable = temp
  [../]
  [./heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  [../]
[]

[BCs]
  [./u_top_pull]
    type = ADPressure
    variable = disp_y
    component = 1
    boundary = top
    constant = -10.0e6
    function = top_pull
  [../]
  [./u_bottom_fix]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./u_yz_fix]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./u_xy_fix]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./temp_fix]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top'
    value = 1000.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 2e11
    poissons_ratio = 0.3
    constant_on = SUBDOMAIN
  [../]
  [./radial_return_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'power_law_creep'
  [../]
  [./power_law_creep]
    type = ADPowerLawCreepStressUpdate
    coefficient = 1.0e-15
    n_exponent = 4
    activation_energy = 3.0e5
    temperature = temp
  [../]

  [./thermal]
    type = ADHeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 100.
  [../]
  [./density]
    type = ADDensity
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 20
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.0
  end_time = 1.0
  num_steps = 6
  dt = 0.1
[]

[Outputs]
  exodus = true
  csv = true
  [./out]
    type = Checkpoint
    num_files = 1
  [../]
[]

Description
Input Parameters
Input Files

Install MOOSE

New Users

Examples and Tutorials

Application Usage

Physics and Syntax

Application Development

Framework Development

MOOSEDocs

Infrastructure

Questions

Information and Tools

INL Applications and Remote Access