ParsedFunctorMaterial

This functor material computes a functor material property using a mathematical expression provided by a string. The expression may operate on any of the following values:

the spatial point, provided by x, y, and z,
the time, provided by t, and
any functor.

Usage

This functor material creates a functor material property with the name given by "property_name".

The mathematical expression is provided via "expression".

Functors used in this expression are provided via "functor_names". These functors can optionally be assigned alternate (usually simpler) names for use in the expression by providing "functor_symbols". Otherwise their names are used directly in the expression.

For more information on the mathematical operators that can be used in the expression, see the function parser site.

Input Parameters

expressionExpression to parse for the new functor material
C++ Type:FunctionExpression
Unit:(no unit assumed)
Controllable:No
Description:Expression to parse for the new functor material
property_nameName to give the new functor material property
C++ Type:std::string
Controllable:No
Description:Name to give the new functor material property

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
epsilon0Fuzzy comparison tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fuzzy comparison tolerance
execute_onALWAYSThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:ALWAYS
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM, ALWAYS
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
functor_namesFunctors to use in the parsed expression
C++ Type:std::vector<std::string>
Controllable:No
Description:Functors to use in the parsed expression
functor_symbolsSymbolic name to use for each functor in 'functor_names' in the parsed expression. If not provided, then the actual functor names must be used in the parsed expression.
C++ Type:std::vector<std::string>
Controllable:No
Description:Symbolic name to use for each functor in 'functor_names' in the parsed expression. If not provided, then the actual functor names must be used in the parsed expression.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
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
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator

Advanced Parameters

disable_fpoptimizerFalseDisable the function parser algebraic optimizer
Default:False
C++ Type:bool
Controllable:No
Description:Disable the function parser algebraic optimizer
enable_ad_cacheTrueEnable caching of function derivatives for faster startup time
Default:True
C++ Type:bool
Controllable:No
Description:Enable caching of function derivatives for faster startup time
enable_auto_optimizeTrueEnable automatic immediate optimization of derivatives
Default:True
C++ Type:bool
Controllable:No
Description:Enable automatic immediate optimization of derivatives
enable_jitTrueEnable just-in-time compilation of function expressions for faster evaluation
Default:True
C++ Type:bool
Controllable:No
Description:Enable just-in-time compilation of function expressions for faster evaluation
evalerror_behaviornanWhat to do if evaluation error occurs. Options are to pass a nan, pass a nan with a warning, throw a error, or throw an exception
Default:nan
C++ Type:MooseEnum
Options:nan, nan_warning, error, exception
Controllable:No
Description:What to do if evaluation error occurs. Options are to pass a nan, pass a nan with a warning, throw a error, or throw an exception

Parsed Expression Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

(test/tests/executioners/nl_forced_its/nl_forced_its.i)
(test/tests/executioners/nl_divergence_tolerance/nl_abs_divergence_tolerance.i)
(test/tests/postprocessors/side_integral/side_integral_functor_fe.i)
(test/tests/functormaterials/output/output.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/materials/1d_test_cpT.i)
(modules/navier_stokes/test/tests/finite_volume/ins/cht/flow-around-square-linear-fluidonly.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/natural_convection/natural_circulation_pipe.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux-w-interface-area.i)
(test/tests/executioners/nl_divergence_tolerance/nl_divergence_tolerance.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/pressure_driven_growth_transient.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/lid-driven-two-phase.i)
(modules/navier_stokes/test/tests/finite_volume/ins/cht/flow-around-square-linear-fluidonly-physics.i)
(test/tests/kernels/functor_kernel/functor_kernel.i)
(test/tests/functormaterials/parsed_functor_material/parsed_functor_material.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux-transient.i)
(test/tests/convergence/child.i)
(modules/navier_stokes/test/tests/finite_volume/ins/cht/flow-around-square-linear.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h_fp.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/segregated/rayleigh-bernard-two-phase-physics_heated.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/lid-driven/lid-driven-turb-energy.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/materials/2d-steady-wall-balance.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/turbulent_driven_growth.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-advection-slip.i)
(test/tests/convergence/parent.i)
(modules/navier_stokes/test/tests/finite_volume/ins/dittus-boelter/channel.i)
(test/tests/functormaterials/output/output_ad.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/enthalpy_equation.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/segregated/channel-drift-flux.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/pressure_driven_growth.i)

(test/tests/executioners/nl_forced_its/nl_forced_its.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

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

[FVKernels]
  [./diff]
    type = FVDiffusion
    variable = u
    coeff = 1
  [../]
  [force]
    type = FVCoupledForce
    v = v
    variable = u
  []
[]

[FunctorMaterials]
  [parsed]
    type = ADParsedFunctorMaterial
    property_name = 'v'
    functor_names = 'u'
    expression = 'if(u>0.1,1e6,0)'
  []
[]

[FVBCs]
  [./left]
    type = FVDirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = FVDirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  line_search = 'none'
  solve_type = NEWTON
  nl_max_its = 5
  nl_forced_its = 3
  nl_abs_div_tol = 1e+3
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

(test/tests/executioners/nl_divergence_tolerance/nl_abs_divergence_tolerance.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

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

[FVKernels]
  [./diff]
    type = FVDiffusion
    variable = u
    coeff = 1
  [../]
  [force]
    type = FVCoupledForce
    v = v
    variable = u
  []
[]

[FunctorMaterials]
  [parsed]
    type = ADParsedFunctorMaterial
    property_name = 'v'
    functor_names = 'u'
    expression = 'if(u>0.1,1e6,0)'
  []
[]

[FVBCs]
  [./left]
    type = FVDirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = FVDirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  line_search = 'none'
  solve_type = NEWTON
  nl_max_its = 5
  nl_abs_div_tol = 1e+5
  nl_div_tol = 1e+50
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

(test/tests/postprocessors/side_integral/side_integral_functor_fe.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[FunctorMaterials]
  [test_fmat]
    type = ADParsedFunctorMaterial
    property_name = test_prop
    expression = '10'
  []
[]

[Postprocessors]
  [test_pp]
    type = ADSideIntegralFunctorPostprocessor
    boundary = top
    functor = test_prop
    functor_argument = face # results in error due to no face info in mesh
    execute_on = 'INITIAL'
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

(test/tests/functormaterials/output/output.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  nz = 1
  xmin = 0.0
  xmax = 4.0
  ymin = 0.0
  ymax = 6.0
[]

[FunctorMaterials]
  [parsed_fmat]
    type = ParsedFunctorMaterial
    expression = 't + x + y + z'
    property_name = 'prop1'
    outputs = 'exodus'
    output_properties = 'prop1'
  []
  [parsed_vector_fmat]
    type = GenericVectorFunctorMaterial
    prop_names = 'prop1_vec'
    prop_values = '1 2 3'
    outputs = 'exodus'
    output_properties = 'prop1_vec'
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
  # Get the t to be equal to 4
  time = 4.0
[]

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

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
U = 1
dp = 0.01
inlet_phase_2 = 0.1
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 4
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'phase_2'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []
  [u_friction]
    type = PINSFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    is_porous_medium = false
    momentum_component = x
    mu = mu_mixture
    rho = rho_mixture
    variable = vel_x
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'phase_2'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []
  [v_friction]
    type = PINSFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    is_porous_medium = false
    momentum_component = y
    mu = mu_mixture
    rho = rho_mixture
    variable = vel_y
  []

  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_x'
    ghost_layers = 5
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_y'
    ghost_layers = 5
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
    outputs = 'out'
    output_properties = 'phase_1'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = '${rho_d} ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

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

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  print_linear_residuals = true
  print_nonlinear_residuals = true
  [out]
    type = Exodus
    hide = 'Re lin cum_lin'
  []
  [perf]
    type = PerfGraphOutput
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '${rho} * ${l} * ${U}'
  []
  [lin]
    type = NumLinearIterations
  []
  [cum_lin]
    type = CumulativeValuePostprocessor
    postprocessor = lin
  []
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/materials/1d_test_cpT.i)

L = 30
bulk_u = 0.01
p_ref = 101325.0
T_in = 860
q_source = 50000

A_cp = 976.78
B_cp = 1.0634
rho = 2000

advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = 10
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  velocity_interp_method = 'rc'
[]

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

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = ${bulk_u}
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${p_ref}
    two_term_boundary_expansion = false
  []
  [T]
    type = INSFVEnergyVariable
    two_term_boundary_expansion = false
    initial_condition = ${T_in}
  []
[]

[FVKernels]
  [mass]
    type = WCNSFVMassAdvection
    variable = pressure
    rho = 'rho'
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    rho = 'rho'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
  []
  [source]
    type = FVBodyForce
    variable = T
    function = source_func
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u}
  []
  [inlet_T]
    type = FVDirichletBC
    variable = T
    boundary = 'left'
    value = ${T_in}
  []

  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = ${p_ref}
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = '${q_source}'
  []
[]

[FunctorMaterials]
  [converter_to_regular_T]
    type = FunctorADConverter
    ad_props_in = 'T'
    reg_props_out = 'T_nAD'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T'
    rho = 'rho'
    cp = 'cp'

    assumed_constant_cp = false
    h_in = 'h'
    # Alternative to providing 'h': set the fluid property and the pressure parameter
    # fp = 'fp'
    # pressure = 'pressure'
  []

  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    expression = '${rho}'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    expression = '0.7'
  []
  [h]
    type = ADParsedFunctorMaterial
    property_name = 'h'
    functor_names = 'T ${A_cp} ${B_cp}'
    functor_symbols = 'T A_cp B_cp'
    expression = 'A_cp * T + B_cp * T * T / 2'
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T ${A_cp} ${B_cp}'
    functor_symbols = 'T A_cp B_cp'
    expression = 'A_cp+B_cp*T'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'

  nl_abs_tol = 1e-9
  nl_max_its = 50
  line_search = 'none'

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
[]

[Postprocessors]
  [H_in]
    type = VolumetricFlowRate
    vel_x = 'vel_x'
    advected_quantity = 'rho_h'
    boundary = 'left'
  []
  [H_out]
    type = VolumetricFlowRate
    vel_x = 'vel_x'
    advected_quantity = 'rho_h'
    boundary = 'right'
  []
  [Q]
    type = FunctionElementIntegral
    function = 'source_func'
    execute_on = 'initial'
  []
  [balance_in_percent]
    type = ParsedPostprocessor
    expression = '(H_out + H_in - Q) / H_in * 100'
    pp_names = 'H_in H_out Q'
  []

  [T_out]
    type = SideAverageValue
    variable = T
    boundary = 'right'
  []
  [T_analytical_outlet]
    type = Receiver
    default = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
  []
  [error_T]
    type = ParsedPostprocessor
    expression = 'T_out - T_analytical_outlet'
    pp_names = 'T_out T_analytical_outlet'
  []
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/cht/flow-around-square-linear-fluidonly.i)

mu = 0.01
rho = 1.1
k = 0.0005
cp = 10
h_conv = 5

advected_interp_method = 'upwind'

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    ymin = 0
    ymax = 0.1
    xmax = 0.1
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    input = generated_mesh
    block_name = subdomain1
    bottom_left = '0.04 0.04 0'
    block_id = 1
    top_right = '0.06 0.06 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = subdomain1
    primary_block = 0
    paired_block = 1
    new_boundary = interface
  []
  [delete]
    type = BlockDeletionGenerator
    input = interface
    block = 1
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = 0
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.1
    solver_sys = u_system
    block = 0
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.01
    block = 0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
    block = 0
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
    block = 0
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = true
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '0.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []

  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    functor = 300
    boundary = 'left'
  []
  [walls_T]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_fluid
    functor = 0.0
    boundary = 'top bottom'
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T_fluid
    use_two_term_expansion = false
    boundary = right
  []

  [fluid_solid]
    type = LinearFVConvectiveHeatTransferBC
    variable = T_fluid
    T_solid = boundary_value
    T_fluid = T_fluid
    boundary = interface
    h = ${h_conv}
  []
[]

[FunctorMaterials]
  [rhocpT]
    property_name = 'rhocpT'
    type = ParsedFunctorMaterial
    functor_names = 'T_fluid'
    expression = '${rho}*${cp}*T_fluid'
  []
[]

[Functions]
  [boundary_value]
    type = ConstantFunction
    value = 350
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  energy_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.8
  energy_equation_relaxation = 1.0
  pressure_variable_relaxation = 0.3
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/natural_convection/natural_circulation_pipe.i)

# natural convection through a pipe
# Reference solution in "reference_pipe_natural_convection.py"
# Reference mdot: 0.0792 kg/s
# this input
# iy   mdot
# 10   8.302364e-02
# 20   8.111192e-02
# 40   8.007924e-02
# 80   7.954403e-02
# 160  7.927201e-02
# Convergence to the analytical result is observed

height = 10.0
gravity = 9.81
p0 = 1e5
molar_mass = 29.0e-3
T0 = 328
Ru = 8.3145
Ri = '${fparse Ru / molar_mass}'
density = '${fparse p0 / (Ri * T0)}'
head = '${fparse height * density * gravity}'
k = 25.68e-3
gamma = 1.4

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.1'
    ix = '2'
    dy = '${height}'
    iy = '5'
  []
[]

[GlobalParams]
  rhie_chow_user_object = pins_rhie_chow_interpolator
[]

[FluidProperties]
  [air]
    type = IdealGasFluidProperties
    molar_mass = ${molar_mass}
    k = ${k}
    gamma = ${gamma}
  []
[]

[Modules]
  [NavierStokesFV]
    compressibility = 'weakly-compressible'
    add_energy_equation = true
    gravity = '0 -${gravity} 0'
    density = rho
    dynamic_viscosity = mu
    specific_heat = cp
    thermal_conductivity = k
    initial_velocity = '0 1e-6 0'
    initial_pressure = ${p0}
    initial_temperature = ${T0}
    inlet_boundaries = 'bottom'
    momentum_inlet_types = 'fixed-pressure'
    momentum_inlet_function = '${fparse p0 + head}'
    energy_inlet_types = 'fixed-temperature'
    energy_inlet_function = '${T0}'
    energy_scaling = 1e-5
    wall_boundaries = 'left right'
    momentum_wall_types = 'slip slip'
    energy_wall_types = 'heatflux heatflux'
    energy_wall_function = '300 300'
    outlet_boundaries = 'top'
    momentum_outlet_types = 'fixed-pressure'
    pressure_function = '${fparse p0}'
    momentum_advection_interpolation = 'upwind'
    mass_advection_interpolation = 'upwind'
    porous_medium_treatment = true
    porosity = porosity
    energy_advection_interpolation = 'average'
  []
[]

[FVKernels]
  [u_friction]
    type = PINSFVMomentumFriction
    variable = superficial_vel_x
    Darcy_name = linear_friction_coeff
    momentum_component = 'x'
    standard_friction_formulation = false
    rho = rho
  []
  [v_friction]
    type = PINSFVMomentumFriction
    variable = superficial_vel_y
    Darcy_name = linear_friction_coeff
    momentum_component = 'y'
    standard_friction_formulation = false
    rho = rho
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'lu        NONZERO'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-6
  end_time = 1e4
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.1
    growth_factor = 2
    iteration_window = 2
    optimal_iterations = 6
  []
[]

[Functions]
  [mu_rampdown_fn]
    type = PiecewiseLinear
    x = '0    0.5  1   5  10 100 1000 2000'
    y = '1000 1000 100 10 1  1   1    0'
  []
[]

[FunctorMaterials]
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = air
    pressure = pressure
    T_fluid = T_fluid
    speed = speed
    force_define_density = true
    neglect_derivatives_of_density_time_derivative = false
    mu_rampdown = 'mu_rampdown_fn'
    characteristic_length = 1
    porosity = porosity
  []

  [scalar_props]
    type = ADGenericFunctorMaterial
    prop_names = 'porosity loss_coeff'
    prop_values = '1       1.3'
  []

  [linear_friction]
    type = ADParsedFunctorMaterial
    property_name = 'linear_friction'
    expression = 'loss_coeff * rho'
    functor_names = 'loss_coeff rho'
  []

  [linear_friction_coeff]
    type = ADGenericVectorFunctorMaterial
    prop_names = 'linear_friction_coeff'
    prop_values = 'linear_friction linear_friction linear_friction'
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseVariableFVReal
  []

  [cp_var]
    type = MooseVariableFVReal
  []

  [rho_cp_T_fluid_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [rho_var_aux]
    type = FunctorAux
    variable = rho_var
    functor = rho
  []

  [cp_var_aux]
    type = FunctorAux
    variable = cp_var
    functor = cp
  []

  [rho_cp_T_fluid_var_aux]
    type = ParsedAux
    variable = rho_cp_T_fluid_var
    coupled_variables = 'rho_var cp_var T_fluid'
    expression = 'rho_var * cp_var * T_fluid'
  []
[]

[Postprocessors]
  [inlet_mfr]
    type = VolumetricFlowRate
    vel_x = superficial_vel_x
    vel_y = superficial_vel_y
    advected_quantity = rho
    boundary = bottom
    advected_interp_method = average
  []

  [outlet_mfr]
    type = VolumetricFlowRate
    vel_x = superficial_vel_x
    vel_y = superficial_vel_y
    advected_quantity = rho
    boundary = top
    advected_interp_method = average
  []

  [inlet_energy]
    type = VolumetricFlowRate
    vel_x = superficial_vel_x
    vel_y = superficial_vel_y
    advected_quantity = rho_cp_T_fluid_var
    boundary = bottom
    advected_interp_method = average
  []

  [outlet_energy]
    type = VolumetricFlowRate
    vel_x = superficial_vel_x
    vel_y = superficial_vel_y
    advected_quantity = rho_cp_T_fluid_var
    boundary = top
    advected_interp_method = average
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux-w-interface-area.i)

mu = 10.0
rho = 100.0
mu_d = 1.0
rho_d = 1.0
l = 2
U = 1
dp = 0.01
inlet_phase_2 = 0.0
advected_interp_method = 'upwind'
velocity_interp_method = 'rc'
mass_exchange_coeff = 0.01

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

[Problem]
  identify_variable_groups_in_nl = false
[]

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 20
    ny = 5
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
  [interface_area]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]

  inactive = 'u_time v_time phase_2_time interface_area_time'

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [phase_2_time]
    type = FVFunctorTimeKernel
    variable = phase_2
    functor = phase_2
  []
  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_diffusion]
    type = FVDiffusion
    variable = phase_2
    coeff = 1.0
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = ${mass_exchange_coeff}
  []

  [interface_area_time]
    type = FVFunctorTimeKernel
    variable = interface_area
    functor = interface_area
  []
  [interface_area_advection]
    type = INSFVScalarFieldAdvection
    variable = interface_area
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [interface_area_diffusion]
    type = FVDiffusion
    variable = interface_area
    coeff = 0.1
  []
  [interface_area_source_sink]
    type = WCNSFV2PInterfaceAreaSourceSink
    variable = interface_area
    u = 'vel_x'
    v = 'vel_y'
    L = 1.0
    rho = 'rho_mixture'
    rho_d = ${rho_d}
    pressure = 'pressure'
    k_c = ${fparse mass_exchange_coeff * 100.0}
    fd = 'phase_2'
    sigma = 1e-3
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
  [inlet_interface_area]
    type = FVDirichletBC
    boundary = 'left'
    variable = interface_area
    value = 0.0
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = '${rho_d} ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-10
  # dt = 0.1
  # end_time = 1.0
  # nl_max_its = 10
[]

[Debug]
  show_var_residual_norms = true
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    function = '${rho} * ${l} * ${U}'
    pp_names = ''
  []
  [rho_outlet]
    type = SideAverageValue
    boundary = 'right'
    variable = 'rho_mixture_var'
  []
[]

(test/tests/executioners/nl_divergence_tolerance/nl_divergence_tolerance.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

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

[FVKernels]
  [./diff]
    type = FVDiffusion
    variable = u
    coeff = 1
  [../]
  [force]
    type = FVCoupledForce
    v = v
    variable = u
  []
[]

[FunctorMaterials]
  [parsed]
    type = ADParsedFunctorMaterial
    property_name = 'v'
    functor_names = 'u'
    expression = 'if(u>0.1,1e6,0)'
  []
[]

[FVBCs]
  [./left]
    type = FVDirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = FVDirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  line_search = 'none'
  solve_type = NEWTON
  nl_max_its = 5
  nl_div_tol = 10
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/pressure_driven_growth_transient.i)

###############################################################################
# Validation test based on Hibiki and Ishii experiment [1] reported in Figure 3
# [1] Hibiki, T., & Ishii, M. (2000). One-group interfacial area transport of bubbly flows in vertical round tubes.
# International Journal of Heat and Mass Transfer, 43(15), 2711-2726.
###############################################################################

mu = 1.0
rho = 1000.0
mu_d = 1.0
rho_d = 1.0
l = ${fparse 50.8/1000.0}
U = 0.491230114
dp = 0.001
inlet_phase_2 = 0.049
advected_interp_method = 'upwind'
velocity_interp_method = 'rc'
mass_exchange_coeff = 0.0
inlet_interface_area = ${fparse 6.0*inlet_phase_2/dp}

outlet_pressure = 1e6

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

[Problem]
  identify_variable_groups_in_nl = false
[]

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

[Mesh]
  coord_type = 'RZ'
  rz_coord_axis = 'X'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 60}'
    ymin = 0
    ymax = '${fparse l / 2}'
    nx = 20
    ny = 5
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
    initial_condition = ${inlet_phase_2}
  []
  [interface_area]
    type = INSFVScalarFieldVariable
    initial_condition = ${inlet_interface_area}
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [phase_2_time]
    type = FVFunctorTimeKernel
    variable = phase_2
    functor = phase_2
  []
  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_x'
    v_slip = 'vel_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_diffusion]
    type = FVDiffusion
    variable = phase_2
    coeff = 1.0
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = ${mass_exchange_coeff}
  []

  [interface_area_time]
    type = FVFunctorTimeKernel
    variable = interface_area
    functor = interface_area
  []
  [interface_area_advection]
    type = INSFVScalarFieldAdvection
    variable = interface_area
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [interface_area_diffusion]
    type = FVDiffusion
    variable = interface_area
    coeff = 0.1
  []
  [interface_area_source_sink]
    type = WCNSFV2PInterfaceAreaSourceSink
    variable = interface_area
    u = 'vel_x'
    v = 'vel_y'
    L = ${fparse l/2}
    rho = 'rho_mixture'
    rho_d = 'rho'
    pressure = 'pressure'
    k_c = '${fparse mass_exchange_coeff}'
    fd = 'phase_2'
    sigma = 1e-3
    cutoff_fraction = 0.0
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '${outlet_pressure}'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
  [inlet_interface_area]
    type = FVDirichletBC
    boundary = 'left'
    variable = interface_area
    value = ${inlet_interface_area}
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = vel_x
    u = vel_x
    v = vel_y
    mu = 'mu_mixture'
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = vel_y
    u = vel_x
    v = vel_y
    mu = 'mu_mixture'
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [symmetry-phase-2]
    type = INSFVSymmetryScalarBC
    boundary = 'bottom'
    variable = phase_2
  []
  [symmetry-interface-area]
    type = INSFVSymmetryScalarBC
    boundary = 'bottom'
    variable = interface_area
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

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

[FunctorMaterials]
  [bubble_properties]
    type = GeneralFunctorFluidProps
    fp = 'fp'
    pressure = 'pressure'
    T_fluid = 300.0
    speed = 1.0
    characteristic_length = 1.0
    porosity = 1.0
    output_properties = 'rho'
    outputs = 'out'
  []
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = 'rho ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  nl_abs_tol = 1e-7
  dt = 0.1
  end_time = 1.0
  nl_max_its = 10
  line_search = 'none'
[]

[Debug]
  show_var_residual_norms = true
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  [out]
    type = Exodus
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '${rho} * ${l} * ${U}'
    pp_names = ''
  []
  [rho_outlet]
    type = SideAverageValue
    boundary = 'right'
    variable = 'rho_mixture_var'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)

L = 30
nx = 600
bulk_u = 0.01
q_source = 50000.
A_cp = 976.78
B_cp = 1.0634
T_in = 860.
p_ref = 101325.0
rho = 2000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

[Problem]
  linear_sys_names = 'u_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*1900.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 860.
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [p_diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = ${q_source}
  []
  [T_analytical]
    type = ParsedFunction
    expression = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    h_from_p_T_functor = h_from_p_T_functor
    T_from_p_h_functor = T_from_p_h_functor
  []
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial
    property_name = 'h_from_p_T_functor'
    functor_names = 'T'
    expression = '${A_cp}*T+${B_cp}/2*(T^2)'
  []
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial
    property_name = 'T_from_p_h_functor'
    functor_names = 'h'
    expression = '(-${A_cp}+sqrt(${A_cp}^2+2*h*${B_cp}))/${B_cp}'
  []
  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    functor_names = 'T'
    expression = ${rho}
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T'
    expression = '${A_cp}+${B_cp}*T'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    functor_names = 'T'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    functor_names = 'T'
    expression = 0.7
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
  [T_out_analytic]
    type = FunctionValuePostprocessor
    function = T_analytical
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/lid-driven-two-phase.i)

mu = 1.0
rho = 1.0e3
mu_d = 0.3
rho_d = 1.0
dp = 0.01
U_lid = 0.1
g = -9.81

[GlobalParams]
  velocity_interp_method = 'rc'
  advected_interp_method = 'upwind'
  rhie_chow_user_object = 'rc'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 5
    ny = 5
  []
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
  []
  [vel_y]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

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

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    rho = 'rho_mixture'
  []
  [mean_zero_pressure]
    type = FVPointValueConstraint
    variable = pressure
    lambda = lambda
    point = '0 0 0'
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []
  [u_buoyant]
    type = INSFVMomentumGravity
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
    gravity = '0 ${g} 0'
  []
  # NOTE: the friction terms for u and v are missing

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []
  [v_buoyant]
    type = INSFVMomentumGravity
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
    gravity = '0 ${g} 0'
  []

  [phase_2_time]
    type = FVFunctorTimeKernel
    variable = phase_2
  []
  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
  []
  [phase_2_diffusion]
    type = FVDiffusion
    variable = phase_2
    coeff = 1e-3
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top'
    function = ${U_lid}
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'left right bottom'
    function = 0
  []

  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'left right top bottom'
    function = 0
  []

  [bottom_phase_2]
    type = FVDirichletBC
    variable = phase_2
    boundary = 'bottom'
    value = 1.0
  []

  [top_phase_2]
    type = FVDirichletBC
    variable = phase_2
    boundary = 'top'
    value = 0.0
  []
[]

[AuxVariables]
  [U]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = vel_x
    y = vel_y
  []
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    gravity = '0 ${g} 0'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    gravity = '0 ${g} 0'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_1_names = '${rho_d} ${mu_d}'
    phase_2_names = '${rho} ${mu}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Postprocessors]
  [average_void]
    type = ElementAverageValue
    variable = 'phase_2'
  []
  [max_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = max
  []
  [min_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = min
  []
  [max_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = max
  []
  [min_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = min
  []
  [max_x_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_x'
    value_type = max
  []
  [max_y_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_y'
    value_type = max
  []
  [max_drag_coefficient]
    type = ElementExtremeFunctorValue
    functor = 'drag_coefficient'
    value_type = max
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'

  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 7
    iteration_window = 2
    growth_factor = 2.0
    cutback_factor = 0.5
    dt = 1e-3
  []
  nl_max_its = 20
  nl_rel_tol = 1e-03
  nl_abs_tol = 1e-9
  l_max_its = 5
  end_time = 1e8
  line_search=none
[]

[Outputs]
  exodus = false
  [CSV]
    type = CSV
    execute_on = 'FINAL'
    execute_scalars_on = NONE
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/cht/flow-around-square-linear-fluidonly-physics.i)

mu = 0.01
rho = 1.1
k = 0.0005
cp = 10
h_conv = 5

inlet_temp = 300
advected_interp_method = 'upwind'

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    ymin = 0
    ymax = 0.1
    xmax = 0.1
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    input = generated_mesh
    block_name = subdomain1
    bottom_left = '0.04 0.04 0'
    block_id = 1
    top_right = '0.06 0.06 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = subdomain1
    primary_block = 0
    paired_block = 1
    new_boundary = interface
  []
  [delete]
    type = BlockDeletionGenerator
    input = interface
    block = 1
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[Physics]
  [NavierStokes]
    [FlowSegregated]
      [flow]
        compressibility = 'weakly-compressible'
        block = '0'

        velocity_variable = 'vel_x vel_y'

        density = ${rho}
        dynamic_viscosity = ${mu}

        initial_velocity = '0.1 0.01 0'
        initial_pressure = '0.2'

        inlet_boundaries = 'left'
        momentum_inlet_types = 'fixed-velocity'
        momentum_inlet_functors = '0.1 0'

        wall_boundaries = 'top bottom interface'
        momentum_wall_types = 'noslip noslip noslip'

        outlet_boundaries = 'right'
        momentum_outlet_types = 'fixed-pressure'
        pressure_functors = '1.4'

        momentum_advection_interpolation = ${advected_interp_method}
        momentum_two_term_bc_expansion = false
        pressure_two_term_bc_expansion = false
        orthogonality_correction = false
      []
    []
    [FluidHeatTransferSegregated]
      [energy]
        coupled_flow_physics = flow
        block = '0'

        thermal_conductivity = '${k}'
        specific_heat = '${cp}'

        initial_temperature = '${inlet_temp}'

        energy_inlet_types = 'fixed-temperature'
        energy_inlet_functors = '${inlet_temp}'
        energy_wall_types = 'heatflux heatflux convection'
        energy_wall_functors = '0 0 boundary_value:htc'

        energy_advection_interpolation = ${advected_interp_method}
        energy_two_term_bc_expansion = false
      []
    []
  []
[]

[FunctorMaterials]
  [rhocpT]
    property_name = 'rhocpT'
    type = ParsedFunctorMaterial
    functor_names = 'T_fluid'
    expression = '${rho}*${cp}*T_fluid'
  []
  [conv_data]
    type = GenericFunctorMaterial
    prop_names = 'htc        boundary_value'
    prop_values = '${h_conv} 350'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  energy_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.8
  energy_equation_relaxation = 1.0
  pressure_variable_relaxation = 0.3
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
[]

(test/tests/kernels/functor_kernel/functor_kernel.i)

# Heat conduction with fixed temperature on left and convection BC on right.
# Source is temperature-dependent:
#   S(T)    = B   - A   * (T - T_inf)^2 [W]
#   S'''(T) = B/V - A/V * (T - T_inf)^2 [W/m^3]
# Assume volume V = 1 m^3, so
#   S'''(T) = B   - A   * (T - T_inf)^2 [W/m^3]

k = 15.0
htc = 100.0
T_ambient = 300.0
source_coef_A = 0.1
source_coef_B = 1e4

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[Variables]
  [T]
  []
[]

[FunctorMaterials]
  [source_mat]
    type = ADParsedFunctorMaterial
    expression = 'B - A * (T - T_inf)^2'
    functor_symbols = 'T T_inf A B'
    functor_names = 'T ${T_ambient} ${source_coef_A} ${source_coef_B}'
    property_name = 'source_term'
  []
  [heat_flux_mat]
    type = ADParsedFunctorMaterial
    expression = 'htc * (T - T_inf)'
    functor_symbols = 'T T_inf htc'
    functor_names = 'T ${T_ambient} ${htc}'
    property_name = 'heat_flux'
  []
[]

[Kernels]
  [diff]
    type = FunctionDiffusion
    variable = T
    function = ${k}
  []
  [source]
    type = FunctorKernel
    variable = T
    functor = source_term
    functor_on_rhs = true
  []
[]

[BCs]
  [left_bc]
    type = DirichletBC
    variable = T
    boundary = left
    value = ${T_ambient}
  []
  [right_bc]
    type = FunctorNeumannBC
    variable = T
    boundary = right
    functor = heat_flux
    flux_is_inward = false
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_max_its = 10
  l_tol = 1e-3
[]

[Outputs]
  exodus = true
[]

(test/tests/functormaterials/parsed_functor_material/parsed_functor_material.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 2
  ny = 2
  nz = 2
  xmin = 0.0
  xmax = 4.0
  ymin = 0.0
  ymax = 6.0
  zmin = 0.0
  zmax = 10.0
[]

[Functions]
  [fn1]
    type = ParsedFunction
    # The max value on elements should be:
    # 2 * 3 + 0.5 * 4.5 + 7.5 - 4 = 11.75
    expression = '2 * x + 0.5 * y + z - t'
  []
  [fn2]
    type = ConstantFunction
    value = 3
  []
[]

[FunctorMaterials]
  [parsed_fmat]
    type = ParsedFunctorMaterial
    expression = 'A * B^2 + 2 + pi + e + t + x + y + z'
    functor_names = 'fn1 fn2'
    functor_symbols = 'A B'
    property_name = 'prop1'
  []
[]

[Postprocessors]
  # The value should be:
  # 11.75 * 3^2 + 2 + pi + e + 4 + 3 + 4.5 + 7.5 = 132.60987448204884
  [get_prop1]
    type = ElementExtremeFunctorValue
    functor = prop1
    value_type = max
    execute_on = 'INITIAL'
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
  time = 4.0
[]

[Outputs]
  csv = true
  execute_on = 'INITIAL'
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-drift-flux-transient.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
U = 1
dp = 0.01
inlet_phase_2 = 0.1
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 4
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_x
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'phase_2'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []
  [u_friction]
    type = PINSFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    is_porous_medium = false
    momentum_component = x
    mu = mu_mixture
    rho = rho_mixture
    variable = vel_x
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = vel_y
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'phase_2'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []
  [v_friction]
    type = PINSFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    is_porous_medium = false
    momentum_component = y
    mu = mu_mixture
    rho = rho_mixture
    variable = vel_y
  []

  [phase_2_time]
    type = FVFunctorTimeKernel
    variable = phase_2
    functor = phase_2
  []
  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
  [vel_slip_x_var]
    type = MooseVariableFVReal
  []
  [vel_slip_y_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
  [populate_vx_slip_var]
    type = FunctorAux
    variable = vel_slip_x_var
    functor = 'vel_slip_x'
  []
  [populate_vy_slip_var]
    type = FunctorAux
    variable = vel_slip_y_var
    functor = 'vel_slip_y'
  []
[]

[FunctorMaterials]
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = '${rho_d} ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-10
  dt = 0.1
  end_time = 1.0
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  exodus = false
  [CSV]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '${rho} * ${l} * ${U}'
  []
  [rho_outlet]
    type = SideAverageValue
    boundary = 'right'
    variable = 'rho_mixture_var'
  []
  [vslip_x]
    type = SideExtremeValue
    boundary = 'left'
    variable = 'vel_slip_x_var'
  []
  [vslip_y]
    type = SideExtremeValue
    boundary = 'left'
    variable = 'vel_slip_y_var'
  []
  [vslip_value]
    type = ParsedPostprocessor
    expression = 'sqrt(vslip_x*vslip_x + vslip_y*vslip_y)*vslip_x/abs(vslip_x)'
    pp_names = 'vslip_x vslip_y'
  []
[]

(test/tests/convergence/child.i)

# Solves the nonlinear equation
#   S(T) = B - A * (T - T_inf)^2
# on each node.

T_ambient = 300.0
source_coef_A = 0.1
source_coef_B = 1e4

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [S]
  []
[]

[AuxVariables]
  [T_child]
  []
[]

[FunctorMaterials]
  [equation_mat]
    type = ADParsedFunctorMaterial
    expression = 'B - A * (T - T_inf)^2 - S'
    functor_symbols = 'T T_inf A B S'
    functor_names = 'T_child ${T_ambient} ${source_coef_A} ${source_coef_B} S'
    property_name = 'equation'
  []
[]

[Kernels]
  [equation_kernel]
    type = FunctorKernel
    variable = S
    functor = equation
    functor_on_rhs = true
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_max_its = 10
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  l_tol = 1e-3
[]

(modules/navier_stokes/test/tests/finite_volume/ins/cht/flow-around-square-linear.i)

mu = 0.01
rho = 1.1
k = 0.0005
cp = 10
k_s = 3.0
h_conv = 5

power_density = 10000

advected_interp_method = 'upwind'

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    ymin = 0
    ymax = 0.1
    xmax = 0.1
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    input = generated_mesh
    block_name = subdomain1
    bottom_left = '0.04 0.04 0'
    block_id = 1
    top_right = '0.06 0.06 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = subdomain1
    primary_block = 0
    paired_block = 1
    new_boundary = interface
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system solid_energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = 0
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.1
    solver_sys = u_system
    block = 0
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.01
    block = 0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
    block = 0
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
    block = 0
  []
  [T_solid]
    type = MooseLinearVariableFVReal
    solver_sys = solid_energy_system
    initial_condition = 500
    block = 1
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = true
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = true
  []

  [solid-conduction]
    type = LinearFVDiffusion
    variable = T_solid
    diffusion_coeff = ${k_s}
    use_nonorthogonal_correction = true
  []
  [solid-source]
    type = LinearFVSource
    variable = T_solid
    source_density = ${power_density}
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '0.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []

  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    functor = 300
    boundary = 'left'
  []
  [walls_T]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_fluid
    functor = 0.0
    boundary = 'top bottom'
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T_fluid
    use_two_term_expansion = false
    boundary = right
  []

  [fluid_solid]
    type = LinearFVConvectiveHeatTransferBC
    variable = T_fluid
    T_solid = T_solid
    T_fluid = T_fluid
    boundary = interface
    h = ${h_conv}
  []
  [solid_fluid]
    type = LinearFVConvectiveHeatTransferBC
    variable = T_solid
    T_solid = T_solid
    T_fluid = T_fluid
    boundary = interface
    h = ${h_conv}
  []
[]

[FunctorMaterials]
  [rhocpT]
    property_name = 'rhocpT'
    type = ParsedFunctorMaterial
    functor_names = 'T_fluid'
    expression = '${rho}*${cp}*T_fluid'
  []
[]

[Postprocessors]
  [h_in]
    type = VolumetricFlowRate
    boundary = left
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    subtract_mesh_velocity = false
  []
  [h_out]
    type = VolumetricFlowRate
    boundary = right
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    advected_interp_method = upwind
    subtract_mesh_velocity = false
  []
  [power]
    type = ElementIntegralFunctorPostprocessor
    functor = ${power_density}
    block = 1
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  energy_l_abs_tol = 1e-13
  solid_energy_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  solid_energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  solid_energy_system = 'solid_energy_system'
  momentum_equation_relaxation = 0.8
  energy_equation_relaxation = 1.0
  pressure_variable_relaxation = 0.3
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  solid_energy_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  solid_energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  solid_energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h_fp.i)

L = 30
nx = 600
bulk_u = 0.01
p_ref = 101325.0
T_in = 860.
q_source = 20000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

[Problem]
  linear_sys_names = 'u_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*240.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [alpha_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = ${T_in}
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [p_diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u}
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[FluidProperties]
  [lead]
    type = LeadFluidProperties
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    fp = lead
  []
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = lead
    pressure = ${p_ref}
    T_fluid = 'T'
    speed = 1
    porosity = 1
    characteristic_length = 1
  []
  [source_func]
    type = ADParsedFunctorMaterial
    property_name = source_func
    functor_names = 'rho'
    expression = ${q_source}
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/segregated/rayleigh-bernard-two-phase-physics_heated.i)

mu = 1.0
rho = 1e3
mu_d = 0.3
rho_d = 1.0
dp = 0.01
U_lid = 0.0
g = -9.81
advected_interp_method = 'upwind'

T_fluid_top = 1

# Currently required
k = 1
k_d = 1
cp = 1
cp_d = 1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 10
    ny = 11
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system phi_system'
[]

# We are using a Materials block to order the functor creation.
# See #30827
[Materials]
  [T_from_p_h]
    type = ParsedFunctorMaterial
    property_name = 'T_from_p_h_functor'
    expression = 'h / cp_mixture'
    functor_names = 'h cp_mixture'
  []
  [h_from_p_T]
    type = ParsedFunctorMaterial
    property_name = 'h_from_p_T_functor'
    expression = 'cp_mixture * T_fluid'
    functor_names = 'T_fluid cp_mixture'
  []
  [density_1]
    type = ParsedFunctorMaterial
    property_name = 'rho'
    expression = '${rho} * (1. - 0.9 * T_fluid)'
    functor_names = 'T_fluid'
  []
  [density_2]
    type = ParsedFunctorMaterial
    property_name = 'rho_d'
    expression = '${rho_d} * (1. - 0.9 * T_fluid)'
    functor_names = 'T_fluid'
  []
[]

[Physics]
  [NavierStokes]
    [FlowSegregated]
      [flow]
        compressibility = 'weakly-compressible'

        density = 'rho_mixture'
        dynamic_viscosity = 'mu_mixture'
        gravity = '0 ${g} 0'

        # Initial conditions
        initial_velocity = '1e-12 1e-12 0'
        initial_pressure = 0.2

        wall_boundaries = 'top left right bottom'
        momentum_wall_types = 'noslip noslip noslip noslip'
        momentum_wall_functors = '${U_lid} 0; 0 0; 0 0; 0 0'

        orthogonality_correction = false
        pressure_two_term_bc_expansion = true
        momentum_advection_interpolation = ${advected_interp_method}
      []
    []
    [FluidHeatTransferSegregated]
      [heat]
        system_names = 'energy_system'
        # allows non-constant cp
        solve_for_enthalpy = true
        initial_temperature = ${T_fluid_top}

        thermal_conductivity = 'k_mixture'
        specific_heat = 'cp_mixture'

        energy_wall_boundaries = 'top          bottom'
        energy_wall_types = 'fixed-temperature fixed-temperature'
        energy_wall_functors = '0              1'

        use_nonorthogonal_correction = false
        energy_two_term_bc_expansion = true
        energy_advection_interpolation = ${advected_interp_method}
      []
    []
    [TwoPhaseMixtureSegregated]
      [mixture]
        system_names = 'phi_system'
        phase_1_fraction_name = 'phase_1'
        phase_2_fraction_name = 'phase_2'

        # not fully mixed initialization
        initial_phase_fraction = 'unstable'

        add_phase_transport_equation = true
        phase_advection_interpolation = '${advected_interp_method}'
        phase_fraction_diffusivity = 1e-3

        fluid_heat_transfer_physics = heat

        # Base phase material properties
        phase_1_density_name = 'rho'
        phase_1_viscosity_name = ${mu}
        phase_1_specific_heat_name = ${cp}
        phase_1_thermal_conductivity_name = ${k}

        # Other phase material properties
        phase_2_density_name = 'rho_d'
        phase_2_viscosity_name = ${mu_d}
        phase_2_specific_heat_name = ${cp_d}
        phase_2_thermal_conductivity_name = ${k_d}
        output_all_properties = true

        # Friction model, not actually used!
        use_dispersed_phase_drag_model = true
        particle_diameter = ${dp}
        add_advection_slip_term = false
        # To match Rayleigh Bernard nonlinear test setup
        add_gravity_term_in_slip_velocity = false
      []
    []
  []
[]

[Functions]
  [unstable]
    type = ParsedFunction
    expression = 'if(y > 0.05, 1, 0)'
  []
[]

[Executioner]
  type = PIMPLE
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'

  end_time = 1e8
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 10
    iteration_window = 2
    growth_factor = 2
    cutback_factor = 0.5
    dt = 1e-3
  []

  # Systems
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  active_scalar_systems = 'phi_system'
  momentum_equation_relaxation = 0.8
  active_scalar_equation_relaxation = '0.7'
  energy_equation_relaxation = '0.5'
  pressure_variable_relaxation = 0.3

  # We need to converge the problem to show conservation
  num_iterations = 200
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  active_scalar_absolute_tolerance = '1e-10'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  active_scalar_petsc_options_iname = '-pc_type -pc_factor_shift_type' # -pc_hypre_type'
  active_scalar_petsc_options_value = 'lu NONZERO'
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  energy_l_abs_tol = 1e-13
  active_scalar_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  active_scalar_l_tol = 0
  # print_fields = true
  continue_on_max_its = true

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.0 0.0 0.0'
[]

[Outputs]
  exodus = false
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

[AuxVariables]
  [U]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[Postprocessors]
  [average_void]
    type = ElementAverageValue
    variable = 'phase_2'
  []
  [max_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = max
  []
  [min_y_velocity]
    type = ElementExtremeValue
    variable = 'vel_y'
    value_type = min
  []
  [max_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = max
  []
  [min_x_velocity]
    type = ElementExtremeValue
    variable = 'vel_x'
    value_type = min
  []
  [max_x_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_x'
    value_type = max
  []
  [max_y_slip_velocity]
    type = ElementExtremeFunctorValue
    functor = 'vel_slip_y'
    value_type = max
  []
  [max_drag_coefficient_x]
    type = ElementExtremeFunctorValue
    functor = 'Darcy_coefficient_vec_out_x'
    value_type = max
  []
  [max_drag_coefficient_y]
    type = ElementExtremeFunctorValue
    functor = 'Darcy_coefficient_vec_out_y'
    value_type = max
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/lid-driven/lid-driven-turb-energy.i)

##########################################################
# Lid-driven cavity test
# Reynolds: 5,000
# Author: Dr. Mauricio Tano
# Last Update: November, 2023
# Turbulent model using:
# k-epsilon model with energy transport
# Standard wall functions without temperature wall functions
# SIMPLE Solve
##########################################################

### Thermophysical Properties ###
mu = 2e-5
rho = 1.0
k = 0.01
cp = 10.0
Pr_t = 0.9

### Operation Conditions ###
lid_velocity = 1.0
side_length = 0.1

### Initial Conditions ###
intensity = 0.01
k_init = '${fparse 1.5*(intensity * lid_velocity)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / side_length}'

### k-epsilon Closure Parameters ###
sigma_k = 1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'left top right bottom'
wall_treatment = 'eq_newton' # Options: eq_newton, eq_incremental, eq_linearized, neq

pressure_tag = "pressure_grad"

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = 'upwind'
  velocity_interp_method = 'rc'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${side_length}
    ymin = 0
    ymax = ${side_length}
    nx = 12
    ny = 12
  []
[]

[Problem]
  nl_sys_names = 'u_system v_system pressure_system energy_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolatorSegregated
    u = vel_x
    v = vel_y
    pressure = pressure
  []
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0.0
    solver_sys = u_system
    two_term_boundary_expansion = false
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0.0
    solver_sys = v_system
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    solver_sys = pressure_system
    initial_condition = 0.2
    two_term_boundary_expansion = false
  []
  [T_fluid]
    type = INSFVEnergyVariable
    solver_sys = energy_system
    initial_condition = 1.0
    two_term_boundary_expansion = false
  []
  [TKE]
    type = INSFVEnergyVariable
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = INSFVEnergyVariable
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVKernels]
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_viscosity_turbulent]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_t'
    momentum_component = 'x'
    complete_expansion = true
    u = vel_x
    v = vel_y
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
    extra_vector_tags = ${pressure_tag}
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_viscosity_turbulent]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_t'
    momentum_component = 'y'
    complete_expansion = true
    u = vel_x
    v = vel_y
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
    extra_vector_tags = ${pressure_tag}
  []

  [p_diffusion]
    type = FVAnisotropicDiffusion
    variable = pressure
    coeff = "Ainv"
    coeff_interp_method = 'average'
  []
  [p_source]
    type = FVDivergence
    variable = pressure
    vector_field = "HbyA"
    force_boundary_execution = true
  []

  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T_fluid
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = ${k}
    variable = T_fluid
  []
  [temp_turb_conduction]
    type = FVDiffusion
    coeff = 'k_t'
    variable = T_fluid
  []

  [TKE_advection]
    type = INSFVTurbulentAdvection
    variable = TKE
    rho = ${rho}
  []
  [TKE_diffusion]
    type = INSFVTurbulentDiffusion
    variable = TKE
    coeff = ${mu}
  []
  [TKE_diffusion_turbulent]
    type = INSFVTurbulentDiffusion
    variable = TKE
    coeff = 'mu_t'
    scaling_coef = ${sigma_k}
  []
  [TKE_source_sink]
    type = INSFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
  []

  [TKED_advection]
    type = INSFVTurbulentAdvection
    variable = TKED
    rho = ${rho}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = INSFVTurbulentDiffusion
    variable = TKED
    coeff = ${mu}
    walls = ${walls}
  []
  [TKED_diffusion_turbulent]
    type = INSFVTurbulentDiffusion
    variable = TKED
    coeff = 'mu_t'
    scaling_coef = ${sigma_eps}
    walls = ${walls}
  []
  [TKED_source_sink]
    type = INSFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    k = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top'
    function = ${lid_velocity}
  []
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'left right bottom'
    function = 0
  []
  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'left right top bottom'
    function = 0
  []
  [T_hot]
    type = FVDirichletBC
    variable = T_fluid
    boundary = 'top'
    value = 1
  []
  [T_cold]
    type = FVDirichletBC
    variable = T_fluid
    boundary = 'bottom'
    value = 0
  []
  [walls_mu_t]
    type = INSFVTurbulentViscosityWallFunction
    boundary = 'left right top bottom'
    variable = mu_t
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    k = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
    two_term_boundary_expansion = false
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    k = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
[]

[FunctorMaterials]
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho}
    cp = ${cp}
  []
  [k_t]
    type = ADParsedFunctorMaterial
    expression = 'mu_t * cp / Pr_t'
    functor_names = 'mu_t ${cp} ${Pr_t}'
    functor_symbols = 'mu_t cp Pr_t'
    property_name = 'k_t'
  []
[]

[Executioner]
  type = SIMPLENonlinearAssembly
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  turbulence_systems = 'TKED_system TKE_system'
  pressure_gradient_tag = ${pressure_tag}
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.5
  energy_equation_relaxation = 0.9
  turbulence_equation_relaxation = '0.8 0.8'
  num_iterations = 500
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  energy_absolute_tolerance = 1e-12
  turbulence_absolute_tolerance = '1e-12 1e-12'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  momentum_l_abs_tol = 1e-14
  energy_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_max_its = 30
  pressure_l_max_its = 30
  momentum_l_tol = 0.0
  energy_l_tol = 0.0
  pressure_l_tol = 0.0
  turbulence_l_tol = 0.0
  print_fields = false
  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.01 0.099 0.0'
  continue_on_max_its = true
[]

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

(modules/navier_stokes/test/tests/finite_volume/wcns/materials/2d-steady-wall-balance.i)

L = 30
bulk_u = 0.01
p_ref = 101325.0
T_in = 860
q_source = 50000
q2_wall = 10000

A_cp = 976.78
B_cp = 1.0634
rho = 2000

advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${L}
    ymin = 1
    ymax = 2.5
    nx = 10
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  velocity_interp_method = 'rc'
[]

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

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = ${bulk_u}
    two_term_boundary_expansion = false
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${p_ref}
    two_term_boundary_expansion = false
  []
  [T]
    type = INSFVEnergyVariable
    two_term_boundary_expansion = false
    initial_condition = ${T_in}
  []
[]

[FVKernels]
  [mass]
    type = WCNSFVMassAdvection
    variable = pressure
    rho = 'rho'
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    rho = 'rho'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    rho = 'rho'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu'
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
  []
  [source]
    type = FVBodyForce
    variable = T
    function = source_func
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = 0
  []
  [inlet_T]
    type = FVDirichletBC
    variable = T
    boundary = 'left'
    value = ${T_in}
  []

  [incoming_heat]
    type = FVNeumannBC
    variable = T
    value = ${q2_wall}
    boundary = 'top'
  []

  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = ${p_ref}
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = '${q_source}'
  []
[]

[FunctorMaterials]
  [converter_to_regular_T]
    type = FunctorADConverter
    ad_props_in = 'T'
    reg_props_out = 'T_nAD'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T'
    rho = 'rho'
    cp = 'cp'

    assumed_constant_cp = false
    h_in = 'h'
    # fp = 'fp'
    # pressure = 'pressure'
  []

  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    expression = '${rho}'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    expression = '0.7'
  []
  [h]
    type = ADParsedFunctorMaterial
    property_name = 'h'
    functor_names = 'T ${A_cp} ${B_cp}'
    functor_symbols = 'T A_cp B_cp'
    expression = 'A_cp * T + B_cp * T * T / 2'
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T ${A_cp} ${B_cp}'
    functor_symbols = 'T A_cp B_cp'
    expression = 'A_cp+B_cp*T'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'

  nl_abs_tol = 1e-9
  nl_max_its = 50
  line_search = 'none'

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
[]

[Postprocessors]
  [H_in]
    type = VolumetricFlowRate
    vel_x = 'vel_x'
    advected_quantity = 'rho_h'
    boundary = 'left'
  []
  [H_out]
    type = VolumetricFlowRate
    vel_x = 'vel_x'
    advected_quantity = 'rho_h'
    boundary = 'right'
  []
  [Q]
    type = FunctionElementIntegral
    function = 'source_func'
    execute_on = 'initial'
  []
  [Q_wall]
    type = FunctionSideIntegral
    function = ${q2_wall}
    boundary = 'top'
  []
  [balance_in_percent]
    type = ParsedPostprocessor
    expression = '(H_out + H_in - Q - Q_wall) / H_in * 100'
    pp_names = 'H_in H_out Q Q_wall'
  []
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/turbulent_driven_growth.i)

###############################################################################
# Validation test based on Hibiki and Ishii experiment [1] reported in Figure 5
# [1] Hibiki, T., & Ishii, M. (2000). One-group interfacial area transport of
# bubbly flows in vertical round tubes.
# International Journal of Heat and Mass Transfer, 43(15), 2711-2726.
###############################################################################

mu = 1.0
rho = 1000.0
mu_d = 1.0
rho_d = 1.0
l = ${fparse 50.8/1000.0}
U = 5.031429
dp = 0.005
inlet_phase_2 = 0.442
advected_interp_method = 'upwind'
velocity_interp_method = 'rc'
mass_exchange_coeff = 0.0
inlet_interface_area = ${fparse 6.0*inlet_phase_2/dp}

outlet_pressure = 1e5

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

[Problem]
  identify_variable_groups_in_nl = false
  previous_nl_solution_required = true
[]

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

[Mesh]
  coord_type = 'RZ'
  rz_coord_axis = 'X'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 60}'
    ymin = 0
    ymax = '${fparse l / 2}'
    nx = 20
    ny = 5
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
    initial_condition = ${inlet_phase_2}
  []
  [interface_area]
    type = INSFVScalarFieldVariable
    initial_condition = ${inlet_interface_area}
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_x'
    v_slip = 'vel_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_diffusion]
    type = FVDiffusion
    variable = phase_2
    coeff = 1.0
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = ${mass_exchange_coeff}
  []

  [interface_area_advection]
    type = INSFVScalarFieldAdvection
    variable = interface_area
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [interface_area_diffusion]
    type = FVDiffusion
    variable = interface_area
    coeff = 0.1
  []
  [interface_area_source_sink]
    type = WCNSFV2PInterfaceAreaSourceSink
    variable = interface_area
    u = 'vel_x'
    v = 'vel_y'
    L = ${fparse l/2}
    rho = 'rho_mixture'
    rho_d = 'rho'
    pressure = 'pressure'
    k_c = '${fparse mass_exchange_coeff}'
    fd = 'phase_2'
    sigma = 1e-3
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '${outlet_pressure}'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
  [inlet_interface_area]
    type = FVDirichletBC
    boundary = 'left'
    variable = interface_area
    value = ${inlet_interface_area}
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = vel_x
    u = vel_x
    v = vel_y
    mu = 'mu_mixture'
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = vel_y
    u = vel_x
    v = vel_y
    mu = 'mu_mixture'
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [symmetry-phase-2]
    type = INSFVSymmetryScalarBC
    boundary = 'bottom'
    variable = phase_2
  []
  [symmetry-interface-area]
    type = INSFVSymmetryScalarBC
    boundary = 'bottom'
    variable = interface_area
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

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

[FunctorMaterials]
  [bubble_properties]
    type = GeneralFunctorFluidProps
    fp = 'fp'
    pressure = 'pressure'
    T_fluid = 300.0
    speed = 1.0
    characteristic_length = 1.0
    porosity = 1.0
    output_properties = 'rho'
    outputs = 'out'
  []
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = 'rho ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-10
  line_search = 'none'
[]

[Debug]
  show_var_residual_norms = true
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  [out]
    type = Exodus
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '${rho} * ${l} * ${U}'
    pp_names = ''
  []
  [rho_outlet]
    type = SideAverageValue
    boundary = 'right'
    variable = 'rho_mixture_var'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/channel-advection-slip.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
U = 1
dp = 0.01
inlet_phase_2 = 0.1
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[GlobalParams]
  rhie_chow_user_object = 'rc'
  mu_interp_method = 'average'
[]

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 6
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_advection_slip]
    type = WCNSFV2PMomentumAdvectionSlip
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    rho_d = ${rho_d}
    fd = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []
  [u_friction]
    type = PINSFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    is_porous_medium = false
    momentum_component = x
    mu = mu_mixture
    rho = rho_mixture
    variable = vel_x
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_advection_slip]
    type = WCNSFV2PMomentumAdvectionSlip
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    rho_d = ${rho_d}
    fd = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []
  [v_friction]
    type = PINSFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    is_porous_medium = false
    momentum_component = y
    mu = mu_mixture
    rho = rho_mixture
    variable = vel_y
  []

  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

[FunctorMaterials]
  [phase_1]
    property_name = 'phase_1'
    type = ADParsedFunctorMaterial
    functor_names = 'phase_2'
    expression = '1 - phase_2'
    outputs = 'out'
    output_properties = 'phase_1'
  []
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_x'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
    outputs = 'out'
    output_properties = 'vel_slip_y'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = '${rho_d} ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

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

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  [out]
    type = Exodus
    hide = 'Re lin cum_lin'
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '${rho} * ${l} * ${U}'
  []
  [lin]
    type = NumLinearIterations
  []
  [cum_lin]
    type = CumulativeValuePostprocessor
    postprocessor = lin
  []
[]

(test/tests/convergence/parent.i)

# Heat conduction with fixed temperature on left and convection BC on right:
#
#   d/dx(-k dT/dx) = S'''(T)    (0,1)X(0,1)
#   T = T_inf                    x = 0
#   -k dT/dx = htc (T - T_inf)   x = 1
#
# Source is temperature-dependent and is calculated in the child app:
#   S(T) = B - A * (T - T_inf)^2

k = 15.0
htc = 100.0
T_ambient = 300.0

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [T]
  []
[]

[AuxVariables]
  [S_parent]
  []
[]

[FunctorMaterials]
  [heat_flux_mat]
    type = ADParsedFunctorMaterial
    expression = 'htc * (T - T_inf)'
    functor_symbols = 'T T_inf htc'
    functor_names = 'T ${T_ambient} ${htc}'
    property_name = 'heat_flux'
  []
[]

[Kernels]
  [diff]
    type = FunctionDiffusion
    variable = T
    function = ${k}
  []
  [source]
    type = CoupledForce
    variable = T
    v = S_parent
  []
[]

[BCs]
  [left_bc]
    type = DirichletBC
    variable = T
    boundary = left
    value = ${T_ambient}
  []
  [right_bc]
    type = FunctorNeumannBC
    variable = T
    boundary = right
    functor = heat_flux
    flux_is_inward = false
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_max_its = 10
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-8
  l_tol = 1e-3

  multiapp_fixed_point_convergence = fp_conv
[]

[MultiApps]
  [source_app]
    type = FullSolveMultiApp
    positions = '0 0 0'
    input_files = child.i
    execute_on = 'TIMESTEP_END'
  []
[]

[Transfers]
  [T_to_child]
    type = MultiAppCopyTransfer
    to_multi_app = source_app
    source_variable = T
    variable = T_child
    execute_on = 'SAME_AS_MULTIAPP'
  []
  [S_from_child]
    type = MultiAppCopyTransfer
    from_multi_app = source_app
    source_variable = S
    variable = S_parent
    execute_on = 'SAME_AS_MULTIAPP'
  []
[]

[Postprocessors]
  [n_fp_its]
    type = NumFixedPointIterations
    execute_on = 'TIMESTEP_END'
  []
[]

[Outputs]
  csv = true
  execute_on = 'FINAL'
[]

(modules/navier_stokes/test/tests/finite_volume/ins/dittus-boelter/channel.i)

# Waterish Fluid properties
mu = 1.79e-3
rho = 1e3
cp = 4.186e3
k = .561
D_h = .05
num_axial_elements = 50
num_radial_elements = 10
h = '${fparse D_h/2/num_radial_elements}'

# Operating conditions
u_inlet = 1
T_inlet = 300
T_wall = 350
p_outlet = 0

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse h * num_axial_elements}'
    ymin = 0
    ymax = '${fparse h * num_radial_elements}'
    nx = ${num_axial_elements}
    ny = ${num_radial_elements}
  []
[]

[Physics]
  [NavierStokes]
    [Flow]
      [flow]
        compressibility = 'incompressible'

        density = 'rho'
        dynamic_viscosity = 'mu'

        initial_velocity = '${u_inlet} 0 0'
        initial_pressure = 0.0

        inlet_boundaries = 'left'
        momentum_inlet_types = 'fixed-velocity'
        momentum_inlet_functors = '${u_inlet} 0'
        wall_boundaries = 'bottom top'
        momentum_wall_types = 'symmetry slip'

        outlet_boundaries = 'right'
        momentum_outlet_types = 'fixed-pressure-zero-gradient'
        pressure_functors = '${p_outlet}'

        mass_advection_interpolation = 'average'
        momentum_advection_interpolation = 'average'
      []
    []
    [FluidHeatTransfer]
      [heat]
        thermal_conductivity = 'k'
        specific_heat = 'cp'

        fluid_temperature_variable = 'T_fluid'
        initial_temperature = '${T_inlet}'
        energy_inlet_types = 'FIXED-TEMPERATURE'
        energy_inlet_functors = '${T_inlet}'

        energy_wall_types = 'heatflux heatflux'
        energy_wall_functors = '0 q'

        energy_advection_interpolation = 'average'
      []
    []
  []
[]

[FluidProperties]
  [simple]
    type = SimpleFluidProperties
    thermal_conductivity = ${k}
    cp = ${cp}
    viscosity = ${mu}
    density0 = ${rho}
  []
[]

[UserObjects]
  [layered_speed]
    execute_on = 'linear nonlinear'
    type = LayeredAverageFunctor
    direction = 'x'
    functor = 'speed'
    num_layers = ${num_axial_elements}
  []
  [layered_T_fluid]
    execute_on = 'linear nonlinear'
    type = LayeredAverageFunctor
    direction = 'x'
    num_layers = ${num_axial_elements}
    functor = 'T_fluid'
  []
[]

[FunctorMaterials]
  [converter]
    type = FunctorADConverter
    ad_props_in = 'pressure'
    reg_props_out = 'nonad_pressure'
  []
  [functor_props]
    type = NonADGeneralFunctorFluidProps
    T_fluid = layered_T_fluid
    characteristic_length = ${D_h}
    fp = simple
    porosity = 1
    pressure = nonad_pressure
    speed = layered_speed
  []
  [dittus]
    type = DittusBoelterFunctorMaterial
    D_h = ${D_h}
    Hw = Hw
    Pr = Pr
    Re = Re
    T_fluid = layered_T_fluid
    T_wall = ${T_wall}
    k = k
  []
  [q]
    type = ParsedFunctorMaterial
    expression = 'Hw * (T_wall - T_fluid)'
    functor_symbols = 'Hw T_fluid T_wall'
    functor_names = 'Hw layered_T_fluid ${T_wall}'
    property_name = 'q'
  []
[]

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

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
[]

(test/tests/functormaterials/output/output_ad.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  nz = 1
  xmin = 0.0
  xmax = 4.0
  ymin = 0.0
  ymax = 6.0
[]

[FunctorMaterials]
  [parsed_fmat]
    type = ADParsedFunctorMaterial
    expression = 't + x + y + z'
    property_name = 'prop1'
    outputs = 'exodus'
    output_properties = 'prop1'
  []
  [parsed_vector_fmat]
    type = ADGenericVectorFunctorMaterial
    prop_names = 'prop1_vec'
    prop_values = '1 2 3'
    outputs = 'exodus'
    output_properties = 'prop1_vec'
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
  # Get the t to be equal to 4
  time = 4.0
[]

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

(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/enthalpy_equation.i)

H = 0.015 #halfwidth of the channel, 10 cm of channel height
L = 1
bulk_u = 0.01
p_ref = 101325.0

advected_interp_method = 'upwind'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${L}
    ymin = -${H}
    ymax = ${H}
    nx = 30
    ny = 15
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 44000 # 1900 is an approx of cp(T)
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 777.
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
    u = vel_x
    v = vel_y
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    mu = 'mu'
    momentum_component = 'y'
    use_nonorthogonal_correction = false
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
    u = vel_x
    v = vel_y
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [temp_conduction]
    type = LinearFVDiffusion
    diffusion_coeff = 'alpha'
    variable = h
  []
  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = 0
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = h_from_p_T # ${fparse 1900.*860.}
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = 860.
  []

  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'top bottom'
    functor = 0.
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = 'top bottom'
    functor = 0.
  []
  [walls_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'top bottom'
    functor = h_from_p_T # ${fparse 1900. * 950}
  []
  [walls_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'top bottom'
    functor = 950.
  []
  [walls_p]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top bottom'
    variable = pressure
    use_two_term_expansion = false
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[FluidProperties]
  [lead]
    type = LeadFluidProperties
  []
[]

[FunctorMaterials]
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = lead
    pressure = ${p_ref}
    T_fluid = 'T'
    speed = 1
    porosity = 1
    characteristic_length = 1
  []
  [alpha]
    type = ADParsedFunctorMaterial
    property_name = 'alpha'
    functor_names = 'k cp'
    expression = 'k/cp'
  []
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    fp = lead
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-6
  pressure_l_abs_tol = 1e-6
  energy_l_abs_tol = 1e-8
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.9
  num_iterations = 200
  pressure_absolute_tolerance = 1e-6
  momentum_absolute_tolerance = 1e-6
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 1000

  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = 'TIMESTEP_BEGIN FINAL'
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/segregated/channel-drift-flux.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
# 'average' leads to slight oscillations, upwind may be preferred
# This method is selected for consistency with the original nonlinear input
advected_interp_method = 'average'

# TODO remove need for those
cp = 1
k = 1
cp_d = 1
k_d = 1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 4
  []
  uniform_refine = 0
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system phi_system'
  previous_nl_solution_required = true
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = 1
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
  []
  [phase_2]
    type = MooseLinearVariableFVReal
    solver_sys = phi_system
  []
[]

[LinearFVKernels]
  [flow_p_diffusion]
    type = LinearFVAnisotropicDiffusion
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
    variable = pressure
  []
  [flow_HbyA_divergence]
    type = LinearFVDivergence
    face_flux = HbyA
    force_boundary_execution = true
    variable = pressure
  []
  [flow_ins_momentum_flux_x]
    type = LinearWCNSFVMomentumFlux
    advected_interp_method = ${advected_interp_method}
    momentum_component = x
    mu = mu_mixture
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u = vel_x
    use_deviatoric_terms = false
    use_nonorthogonal_correction = false
    v = vel_y
    variable = vel_x
  []
  [flow_ins_momentum_flux_y]
    type = LinearWCNSFVMomentumFlux
    advected_interp_method = ${advected_interp_method}
    momentum_component = y
    mu = mu_mixture
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u = vel_x
    use_deviatoric_terms = false
    use_nonorthogonal_correction = false
    v = vel_y
    variable = vel_y
  []
  [mixture_drift_flux_x]
    type = LinearWCNSFV2PMomentumDriftFlux
    density_interp_method = average
    fraction_dispersed = phase_2
    momentum_component = x
    rhie_chow_user_object = ins_rhie_chow_interpolator
    rho_d = ${rho_d}
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = vel_x
  []
  [mixture_drift_flux_y]
    type = LinearWCNSFV2PMomentumDriftFlux
    density_interp_method = average
    fraction_dispersed = phase_2
    momentum_component = y
    rhie_chow_user_object = ins_rhie_chow_interpolator
    rho_d = ${rho_d}
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = vel_y
  []
  [flow_ins_momentum_pressure_x]
    type = LinearFVMomentumPressure
    momentum_component = x
    pressure = pressure
    variable = vel_x
  []
  [flow_ins_momentum_pressure_y]
    type = LinearFVMomentumPressure
    momentum_component = y
    pressure = pressure
    variable = vel_y
  []
  [flow_momentum_friction_0_x]
    type = LinearFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    momentum_component = x
    mu = mu_mixture
    variable = vel_x
  []
  [flow_momentum_friction_0_y]
    type = LinearFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    momentum_component = y
    mu = mu_mixture
    variable = vel_y
  []

  # Mixture phase equation
  [mixture_ins_phase_2_advection]
    type = LinearFVScalarAdvection
    advected_interp_method = upwind
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = phase_2
  []
  [mixture_phase_interface_reaction]
    type = LinearFVReaction
    coeff = 0.1
    variable = phase_2
  []
  [mixture_phase_interface_source]
    type = LinearFVSource
    scaling_factor = 0.1
    source_density = phase_1
    variable = phase_2
  []
[]

[LinearFVBCs]
  [vel_x_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 1
    variable = vel_x
  []
  [vel_y_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 0
    variable = vel_y
  []
  [pressure_extrapolation_inlet_left]
    type = LinearFVExtrapolatedPressureBC
    boundary = left
    use_two_term_expansion = true
    variable = pressure
  []
  [vel_x_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = vel_x
  []
  [vel_y_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = vel_y
  []
  [pressure_right]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = right
    functor = 0
    variable = pressure
  []
  [vel_x_bottom]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = bottom
    functor = 0
    variable = vel_x
  []
  [vel_y_bottom]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = bottom
    functor = 0
    variable = vel_y
  []
  [vel_x_top]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = top
    functor = 0
    variable = vel_x
  []
  [vel_y_top]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = top
    functor = 0
    variable = vel_y
  []
  [pressure_extrapolation_top_bottom]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top bottom'
    use_two_term_expansion = true
    variable = pressure
  []

  [phase_2_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 0.1
    variable = phase_2
  []
  [phase_2_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = phase_2
  []
[]

[FunctorMaterials]
  [flow_ins_speed_material]
    type = ADVectorMagnitudeFunctorMaterial
    execute_on = ALWAYS
    outputs = none
    vector_magnitude_name = speed
    x_functor = vel_x
    y_functor = vel_y
  []

  [mixture_phase_1_fraction]
    type = ParsedFunctorMaterial
    execute_on = ALWAYS
    expression = '1 - phase_2'
    functor_names = phase_2
    output_properties = phase_1
    outputs = all
    property_name = phase_1
  []
  [mixture_mixture_material]
    type = WCNSLinearFVMixtureFunctorMaterial
    execute_on = ALWAYS
    limit_phase_fraction = true
    outputs = all
    phase_1_fraction = phase_2
    phase_1_names = '${rho_d} ${mu_d} ${cp_d} ${k_d}'
    phase_2_names = '${rho}   ${mu}   ${cp}   ${k}'
    prop_names = 'rho_mixture mu_mixture cp_mixture k_mixture'
  []
  [mixture_slip_x]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    execute_on = ALWAYS
    gravity = '0 0 0'
    linear_coef_name = Darcy_coefficient
    momentum_component = x
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = ${rho}
    rho_d = ${rho_d}
    slip_velocity_name = vel_slip_x
    u = vel_x
    v = vel_y
  []
  [mixture_slip_y]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    execute_on = ALWAYS
    gravity = '0 0 0'
    linear_coef_name = Darcy_coefficient
    momentum_component = y
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = ${rho}
    rho_d = ${rho_d}
    slip_velocity_name = vel_slip_y
    u = vel_x
    v = vel_y
  []
  [mixture_dispersed_drag]
    type = NSFVDispersePhaseDragFunctorMaterial
    drag_coef_name = Darcy_coefficient
    execute_on = ALWAYS
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = rho_mixture
    u = vel_x
    v = vel_y
  []
[]

[UserObjects]
  [ins_rhie_chow_interpolator]
    type = RhieChowMassFlux
    p_diffusion_kernel = flow_p_diffusion
    pressure = pressure
    rho = rho_mixture
    u = vel_x
    v = vel_y
  []
[]

[Executioner]
  type = SIMPLE
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'

  # Systems
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  active_scalar_systems = 'phi_system'
  momentum_equation_relaxation = 0.8
  active_scalar_equation_relaxation = '0.7'
  pressure_variable_relaxation = 0.3

  # We need to converge the problem to show conservation
  num_iterations = 200
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  active_scalar_absolute_tolerance = '1e-10'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  active_scalar_petsc_options_iname = '-pc_type -pc_hypre_type'
  active_scalar_petsc_options_value = 'hypre boomeramg'
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  active_scalar_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  active_scalar_l_tol = 0
  # print_fields = true
  continue_on_max_its = true
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '10.0 * 2 * 1'
  []
  [average_phase2]
    type = ElementAverageValue
    variable = phase_2
  []
  [dp]
    type = PressureDrop
    boundary = 'left right'
    downstream_boundary = right
    pressure = pressure
    upstream_boundary = left
  []
  [max_phase2]
    type = ElementExtremeValue
    variable = phase_2
  []
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/pressure_driven_growth.i)

###############################################################################
# Validation test based on Hibiki and Ishii experiment [1] reported in Figure 3
# [1] Hibiki, T., & Ishii, M. (2000). One-group interfacial area transport of bubbly flows in vertical round tubes.
# International Journal of Heat and Mass Transfer, 43(15), 2711-2726.
###############################################################################

mu = 1.0
rho = 1000.0
mu_d = 1.0
rho_d = 1.0
l = ${fparse 50.8/1000.0}
U = 0.491230114
dp = 0.001
inlet_phase_2 = 0.049
advected_interp_method = 'upwind'
velocity_interp_method = 'rc'
mass_exchange_coeff = 0.0
inlet_interface_area = ${fparse 6.0*inlet_phase_2/dp}

outlet_pressure = 1e5

[GlobalParams]
  rhie_chow_user_object = 'rc'
  density_interp_method = 'average'
  mu_interp_method = 'average'
[]

[Problem]
  identify_variable_groups_in_nl = false
  previous_nl_solution_required = true
[]

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

[Mesh]
  coord_type = 'RZ'
  rz_coord_axis = 'X'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 60}'
    ymin = 0
    ymax = '${fparse l / 2}'
    nx = 20
    ny = 5
  []
  uniform_refine = 0
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [phase_2]
    type = INSFVScalarFieldVariable
    initial_condition = ${inlet_phase_2}
  []
  [interface_area]
    type = INSFVScalarFieldVariable
    initial_condition = ${inlet_interface_area}
  []
[]

[FVKernels]

  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'x'
  []
  [u_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_x
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho_mixture'
    momentum_component = 'y'
  []
  [v_drift]
    type = WCNSFV2PMomentumDriftFlux
    variable = vel_y
    rho_d = ${rho_d}
    fd = 'rho_mixture_var'
    u_slip = 'vel_slip_x'
    v_slip = 'vel_slip_y'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = 'mu_mixture'
    limit_interpolation = true
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  [phase_2_advection]
    type = INSFVScalarFieldAdvection
    variable = phase_2
    u_slip = 'vel_x'
    v_slip = 'vel_y'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [phase_2_diffusion]
    type = FVDiffusion
    variable = phase_2
    coeff = 1.0
  []
  [phase_2_src]
    type = NSFVMixturePhaseInterface
    variable = phase_2
    phase_coupled = phase_1
    alpha = ${mass_exchange_coeff}
  []

  [interface_area_advection]
    type = INSFVScalarFieldAdvection
    variable = interface_area
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = 'upwind'
  []
  [interface_area_diffusion]
    type = FVDiffusion
    variable = interface_area
    coeff = 0.1
  []
  [interface_area_source_sink]
    type = WCNSFV2PInterfaceAreaSourceSink
    variable = interface_area
    u = 'vel_x'
    v = 'vel_y'
    L = ${fparse l/2}
    rho = 'rho_mixture'
    rho_d = 'rho'
    pressure = 'pressure'
    k_c = '${fparse mass_exchange_coeff}'
    fd = 'phase_2'
    sigma = 1e-3
    cutoff_fraction = 0.0
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_x
    functor = '${U}'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = vel_y
    functor = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = vel_x
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = vel_y
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '${outlet_pressure}'
  []
  [inlet_phase_2]
    type = FVDirichletBC
    boundary = 'left'
    variable = phase_2
    value = ${inlet_phase_2}
  []
  [inlet_interface_area]
    type = FVDirichletBC
    boundary = 'left'
    variable = interface_area
    value = ${inlet_interface_area}
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = vel_x
    u = vel_x
    v = vel_y
    mu = 'mu_mixture'
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = vel_y
    u = vel_x
    v = vel_y
    mu = 'mu_mixture'
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [symmetry-phase-2]
    type = INSFVSymmetryScalarBC
    boundary = 'bottom'
    variable = phase_2
  []
  [symmetry-interface-area]
    type = INSFVSymmetryScalarBC
    boundary = 'bottom'
    variable = interface_area
  []
[]

[AuxVariables]
  [drag_coefficient]
    type = MooseVariableFVReal
  []
  [rho_mixture_var]
    type = MooseVariableFVReal
  []
  [mu_mixture_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [populate_cd]
    type = FunctorAux
    variable = drag_coefficient
    functor = 'Darcy_coefficient'
  []
  [populate_rho_mixture_var]
    type = FunctorAux
    variable = rho_mixture_var
    functor = 'rho_mixture'
  []
  [populate_mu_mixture_var]
    type = FunctorAux
    variable = mu_mixture_var
    functor = 'mu_mixture'
  []
[]

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

[FunctorMaterials]
  [bubble_properties]
    type = GeneralFunctorFluidProps
    fp = 'fp'
    pressure = 'pressure'
    T_fluid = 300.0
    speed = 1.0
    characteristic_length = 1.0
    porosity = 1.0
    output_properties = 'rho'
    outputs = 'out'
  []
  [populate_u_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_x'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [populate_v_slip]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    slip_velocity_name = 'vel_slip_y'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
    rho = ${rho}
    mu = 'mu_mixture'
    rho_d = ${rho_d}
    particle_diameter = ${dp}
    linear_coef_name = 'Darcy_coefficient'
  []
  [compute_phase_1]
    type = ADParsedFunctorMaterial
    property_name = phase_1
    functor_names = 'phase_2'
    expression = '1 - phase_2'
  []
  [CD]
    type = NSFVDispersePhaseDragFunctorMaterial
    rho = 'rho_mixture'
    mu = mu_mixture
    u = 'vel_x'
    v = 'vel_y'
    particle_diameter = ${dp}
  []
  [mixing_material]
    type = NSFVMixtureFunctorMaterial
    phase_2_names = '${rho} ${mu}'
    phase_1_names = 'rho ${mu_d}'
    prop_names = 'rho_mixture mu_mixture'
    phase_1_fraction = 'phase_2'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_rel_tol = 1e-10
  line_search = 'none'
[]

[Debug]
  show_var_residual_norms = true
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_shift_type'
    petsc_options_value = 'lu       NONZERO'
  []
[]

[Outputs]
  [out]
    type = Exodus
  []
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '${rho} * ${l} * ${U}'
    pp_names = ''
  []
  [rho_outlet]
    type = SideAverageValue
    boundary = 'right'
    variable = 'rho_mixture_var'
  []
[]

Usage
Input Parameters
Input Files