PINSFVEnergyDiffusion

Description

This kernel implements a diffusion term for the fluid energy equation. The thermal conductivity is isotropic for this kernel. For anisotropic diffusion, use the PINSFVEnergyAnisotropicDiffusion kernel.

$var element = document.getElementById("moose-equation-b50e1000-01ea-4be5-a669-9f5e992666c8");katex.render("\\nabla \\cdot \\left( \\epsilon k \\nabla T \\right) = \\epsilon \\nabla \\cdot k \\nabla T + k \\nabla T \\nabla \\epsilon", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-c4c3cc66-9867-4a94-bd09-260691da5a4b");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the porosity, $var element = document.getElementById("moose-equation-b467c21c-dc00-4e59-8005-9b1f715201aa");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the thermal conductivity, and $var element = document.getElementById("moose-equation-57e91796-b66a-4297-b6e4-61cc5bb6f7e3");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the fluid temperature.

The porosity gradient term creates oscillations in the presence of porosity discontinuities and is generally neglected. It is not computed by this kernel.

note

To switch from using a regular conductivity to an effective conductivity, use the "effective_conductivity" parameter.

note

If the thermal conductivity is null or negative, the harmonic interpolation method for the face value of the thermal conductivity is not well-defined and will be automatically changed to an average interpolation.

Input Parameters

kThermal conductivity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Thermal conductivity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
porosityPorosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Porosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
effective_conductivityFalseWhether the conductivity should be multiplied by porosity, or whether the provided conductivity is an effective conductivity taking porosity effects into account
Default:False
C++ Type:bool
Controllable:No
Description:Whether the conductivity should be multiplied by porosity, or whether the provided conductivity is an effective conductivity taking porosity effects into account
kappa_interp_methodharmonicSwitch that can select face interpolation method for the thermal conductivity.
Default:harmonic
C++ Type:MooseEnum
Options:average, harmonic
Controllable:No
Description:Switch that can select face interpolation method for the thermal conductivity.
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
variable_interp_methodaverageSwitch that can select between face interpolation methods for the variable.
Default:average
C++ Type:MooseEnum
Options:average, skewness-corrected
Controllable:No
Description:Switch that can select between face interpolation methods for the variable.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

boundaries_to_avoidThe set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.
boundaries_to_forceThe set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.
force_boundary_executionFalseWhether to force execution of this object on all external boundaries.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to force execution of this object on all external boundaries.

Boundary Execution Modification 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
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

ghost_layers2The number of layers of elements to ghost.
Default:2
C++ Type:unsigned short
Controllable:No
Description:The number of layers of elements to ghost.
use_point_neighborsFalseWhether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient-gas.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/segregated/2d-heated.i)
(modules/navier_stokes/test/tests/finite_volume/pins/block-restriction/with-empty-block.i)
(modules/navier_stokes/test/tests/finite_volume/pins/block-restriction/segregated/empty-block-segregated.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-disp-system.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-transient.i)
(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-boussinesq.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated.i)

(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient-gas.i)

# Fluid properties
mu = 'mu'
rho = 'rho'
k = 'k'

# Solid properties
cp_s = 2
rho_s = 4
k_s = 1e-2
h_fs = 10

# Operating conditions
u_inlet = 1
T_inlet = 200
p_outlet = 10
top_side_temperature = 150

# Numerical scheme
advected_interp_method = 'upwind'
velocity_interp_method = 'rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 10
    ymin = 0
    ymax = 1
    nx = 20
    ny = 5
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
  []
[]

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${p_outlet}
  []
  [T_fluid]
    type = INSFVEnergyVariable
    initial_condition = ${T_inlet}
  []
  [T_solid]
    type = MooseVariableFVReal
    initial_condition = 100
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
    initial_condition = 0.5
  []
[]

[FVKernels]
  [mass_time]
    type = PWCNSFVMassTimeDerivative
    variable = pressure
    porosity = 'porosity'
    drho_dt = 'drho_dt'
  []
  [mass]
    type = PWCNSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_time]
    type = WCNSFVMomentumTimeDerivative
    variable = superficial_vel_x
    rho = ${rho}
    drho_dt = 'drho_dt'
    momentum_component = 'x'
  []
  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_time]
    type = WCNSFVMomentumTimeDerivative
    variable = superficial_vel_y
    rho = ${rho}
    drho_dt = 'drho_dt'
    momentum_component = 'y'
  []
  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [energy_time]
    type = PINSFVEnergyTimeDerivative
    variable = T_fluid
    h = 'h'
    dh_dt = 'dh_dt'
    rho = ${rho}
    drho_dt = 'drho_dt'
    is_solid = false
    porosity = porosity
  []
  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    variable = T_fluid
    k = ${k}
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_fluid
    is_solid = false
    T_fluid = T_fluid
    T_solid = T_solid
    h_solid_fluid = 'h_cv'
  []

  [solid_energy_time]
    type = PINSFVEnergyTimeDerivative
    variable = T_solid
    cp = ${cp_s}
    rho = ${rho_s}
    is_solid = true
    porosity = porosity
  []
  [solid_energy_diffusion]
    type = FVDiffusion
    variable = T_solid
    coeff = ${k_s}
  []
  [solid_energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_solid
    is_solid = true
    T_fluid = T_fluid
    T_solid = T_solid
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    function = 0
  []
  [inlet-T]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T_inlet}
    boundary = 'left'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_x
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_y
    function = 0
  []
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'T_solid'
    value = ${top_side_temperature}
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = ${p_outlet}
  []
[]

[FluidProperties]
  [fp]
    type = IdealGasFluidProperties
    gamma = 1.4
  []
[]

[FunctorMaterials]
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = fp
    pressure = 'pressure'
    T_fluid = 'T_fluid'
    speed = 'speed'

    # To initialize with a high viscosity
    mu_rampdown = 'mu_rampdown'

    # For porous flow
    characteristic_length = 1
    porosity = 'porosity'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    rho = ${rho}
    temperature = 'T_fluid'
  []
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv'
    prop_values = '${h_fs}'
  []
  [speed]
    type = PINSFVSpeedFunctorMaterial
    porosity = 'porosity'
    superficial_vel_x = 'superficial_vel_x'
    superficial_vel_y = 'superficial_vel_y'
  []
[]

[Functions]
  [mu_rampdown]
    type = PiecewiseLinear
    x = '1 2 3 4'
    y = '1e3 1e2 1e1 1'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  automatic_scaling = true

  end_time = 3.0
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = VolumetricFlowRate
    boundary = 'right'
    advected_quantity = '1'
    advected_interp_method = ${advected_interp_method}
    vel_x = 'superficial_vel_x'
    vel_y = 'superficial_vel_y'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = T_fluid
    boundary = 'right'
  []
  [solid-temp]
    type = ElementAverageValue
    variable = T_solid
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/segregated/2d-heated.i)

mu = 1
rho = 1
k = 1e-3
cp = 1
u_inlet = 1
T_inlet = 200
advected_interp_method = 'upwind'
velocity_interp_method = 'rc'

pressure_tag = "pressure_grad"

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '5 5'
    dy = '1.0'
    ix = '10 10'
    iy = '5'
    subdomain_id = '1 2'
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolatorSegregated
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
  []
[]

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

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
    solver_sys = u_system
    two_term_boundary_expansion = false
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
    solver_sys = v_system
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = false
    solver_sys = pressure_system
  []
  [T_fluid]
    type = INSFVEnergyVariable
    two_term_boundary_expansion = false
    solver_sys = energy_system
    initial_condition = 200
  []
  [T_solid]
    type = MooseVariableFVReal
    two_term_boundary_expansion = false
    solver_sys = solid_energy_system
    initial_condition = 200
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
    initial_condition = 0.5
    two_term_boundary_expansion = false
  []
[]

[FVKernels]
  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
    extra_vector_tags = ${pressure_tag}
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
    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
  []

  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    boundaries_to_force = bottom
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    k = ${k}
    variable = T_fluid
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_fluid
    is_solid = false
    T_fluid = 'T_fluid'
    T_solid = 'T_solid'
    h_solid_fluid = 'h_cv'
  []

  [solid_energy_diffusion]
    type = FVDiffusion
    coeff = ${k}
    variable = T_solid
  []
  [solid_energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_solid
    is_solid = true
    T_fluid = 'T_fluid'
    T_solid = 'T_solid'
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    function = 0
  []
  [inlet-T]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T_inlet}
    boundary = 'left'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_x
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_y
    function = 0
  []
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'T_solid'
    value = 250
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0.1
  []
[]

[FunctorMaterials]
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv cp'
    prop_values = '0.1 ${cp}'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    rho = ${rho}
    temperature = 'T_fluid'
  []
[]

[Executioner]
  type = SIMPLENonlinearAssembly
  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  energy_l_abs_tol = 1e-14
  solid_energy_l_abs_tol = 1e-14
  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'
  pressure_gradient_tag = ${pressure_tag}
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.4
  energy_equation_relaxation = 1.0
  num_iterations = 160
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  energy_absolute_tolerance = 1e-12
  solid_energy_absolute_tolerance = 1e-12
  print_fields = false
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/pins/block-restriction/with-empty-block.i)

mu = 1.2
rho_fluid = 0.2
k_fluid = 1.1
cp_fluid = 2.3
T_cold = 310
alpha = 1e-3
Q = 200

[Problem]
  kernel_coverage_check = false
[]

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

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.3683 0.0127'
    dy = '0.0127 0.2292 2.5146 0.2292 0.0127'
    ix = '2 1'
    iy = '1 2 3 2 1'
    subdomain_id = '0 0
                    1 0
                    2 0
                    1 0
                    0 0
                    '
  []

  [rename_block_name]
    type = RenameBlockGenerator
    input = cmg
    old_block = '0 1 2'
    new_block = 'wall_block spacer_block porous_block'
  []

  [solid_fluid_interface_1]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_block_name
    primary_block = porous_block
    paired_block = wall_block
    new_boundary = 'solid_fluid_interface'
  []

  [solid_fluid_interface_2]
    type = SideSetsBetweenSubdomainsGenerator
    input = solid_fluid_interface_1
    primary_block = spacer_block
    paired_block = wall_block
    new_boundary = 'solid_fluid_interface'
  []

  [wall_left_boundary_1]
    type = SideSetsFromBoundingBoxGenerator
    input = solid_fluid_interface_2
    bottom_left = '0 0 0'
    top_right = '0.1 0.0127 0'
    included_boundaries = left
    boundary_new = wall_left
  []

  [wall_left_boundary_2]
    type = SideSetsFromBoundingBoxGenerator
    input = wall_left_boundary_1
    bottom_left = '0 2.9857 0'
    top_right = '0.1 2.9984 0'
    included_boundaries = left
    boundary_new = wall_left
  []

  [fluid_left_boundary]
    type = SideSetsFromBoundingBoxGenerator
    input = wall_left_boundary_2
    bottom_left = '0 0.0127 0'
    top_right = '0.1 2.9857 0'
    included_boundaries = left
    boundary_new = fluid_left
  []

  coord_type = RZ
  rz_coord_axis = Y
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
    block = 'spacer_block porous_block'
  []
[]

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    block = 'spacer_block porous_block'
  []

  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    block = 'spacer_block porous_block'
  []

  [pressure]
    type = INSFVPressureVariable
    block = 'spacer_block porous_block'
  []

  [T_fluid]
    type = INSFVEnergyVariable
    block = 'spacer_block porous_block'
  []

  [lambda]
    family = SCALAR
    order = FIRST
    block = 'spacer_block porous_block'
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
    block = 'spacer_block porous_block'
  []
[]

[FVKernels]
  # No mass time derivative because imcompressible (derivative = 0)
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    rho = ${rho_fluid}
    block = 'spacer_block porous_block'
  []

  [mean_zero_pressure]
    type = FVIntegralValueConstraint
    variable = pressure
    lambda = lambda
    block = 'spacer_block porous_block'
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    rho = ${rho_fluid}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [u_buoyancy]
    type = PINSFVMomentumBoussinesq
    variable = superficial_vel_x
    T_fluid = T_fluid
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    ref_temperature = ${T_cold}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [u_gravity]
    type = PINSFVMomentumGravity
    variable = superficial_vel_x
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    rho = ${rho_fluid}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_buoyancy]
    type = PINSFVMomentumBoussinesq
    variable = superficial_vel_y
    T_fluid = T_fluid
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    ref_temperature = ${T_cold}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_gravity]
    type = PINSFVMomentumGravity
    variable = superficial_vel_y
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [temp_conduction]
    type = PINSFVEnergyDiffusion
    k = 'k_fluid'
    variable = T_fluid
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [temp_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    block = 'spacer_block porous_block'
  []

  [heat_source]
    type = FVBodyForce
    variable = T_fluid
    function = ${Q}
    block = 'porous_block'
  []
[]

[FVBCs]
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = superficial_vel_x
    boundary = 'solid_fluid_interface'
    function = 0
  []

  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = superficial_vel_y
    boundary = 'solid_fluid_interface'
    function = 0
  []

  [reflective_x]
    type = INSFVSymmetryVelocityBC
    variable = superficial_vel_x
    boundary = fluid_left
    momentum_component = 'x'
    mu = ${mu}
    u = superficial_vel_x
    v = superficial_vel_y
  []

  [reflective_y]
    type = INSFVSymmetryVelocityBC
    variable = superficial_vel_y
    boundary = fluid_left
    momentum_component = 'y'
    mu = ${mu}
    u = superficial_vel_x
    v = superficial_vel_y
  []

  [reflective_p]
    type = INSFVSymmetryPressureBC
    boundary = fluid_left
    variable = pressure
  []

  [T_reflective]
    type = FVNeumannBC
    variable = T_fluid
    boundary = fluid_left
    value = 0
  []

  [T_cold_boundary]
    type = FVDirichletBC
    variable = T_fluid
    boundary = solid_fluid_interface
    value = ${T_cold}
  []
[]

[ICs]
  [porosity_spacer]
    type = ConstantIC
    variable = porosity
    block = spacer_block
    value = 1.0
  []

  [porosity_fuel]
    type = ConstantIC
    variable = porosity
    block = porous_block
    value = 0.1
  []

  [temp_ic_fluid]
    type = ConstantIC
    variable = T_fluid
    value = ${T_cold}
    block = 'spacer_block porous_block'
  []

  [superficial_vel_x]
    type = ConstantIC
    variable = superficial_vel_x
    value = 1E-5
    block = 'spacer_block porous_block'
  []

  [superficial_vel_y]
    type = ConstantIC
    variable = superficial_vel_y
    value = 1E-5
    block = 'spacer_block porous_block'
  []
[]

[FunctorMaterials]
  [functor_constants_fluid]
    type = ADGenericFunctorMaterial
    prop_names = 'alpha_b cp k_fluid'
    prop_values = '${alpha} ${cp_fluid} ${k_fluid}'
    block = 'spacer_block porous_block'
  []

  [density_fluid]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho_fluid}
    block = 'spacer_block porous_block'
  []

  [functor_constants_steel]
    # We need this to avoid errors for materials not existing on every block
    type = ADGenericFunctorMaterial
    prop_names = 'dummy'
    prop_values = 0.0
    block = wall_block
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = none
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/navier_stokes/test/tests/finite_volume/pins/block-restriction/segregated/empty-block-segregated.i)

mu = 1.2
rho_fluid = 0.2
k_fluid = 1.1
cp_fluid = 2.3
T_cold = 310
alpha = 1e-3
Q = 200

pressure_tag = "pressure_grad"

[Problem]
  kernel_coverage_check = false
[]

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

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.3683 0.0127'
    dy = '0.0127 0.2292 2.5146 0.2292 0.0127'
    ix = '2 1'
    iy = '1 2 3 2 1'
    subdomain_id = '0 0
                    1 0
                    2 0
                    1 0
                    0 0
                    '
  []

  [rename_block_name]
    type = RenameBlockGenerator
    input = cmg
    old_block = '0 1 2'
    new_block = 'wall_block spacer_block porous_block'
  []

  [solid_fluid_interface_1]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_block_name
    primary_block = porous_block
    paired_block = wall_block
    new_boundary = 'solid_fluid_interface'
  []

  [solid_fluid_interface_2]
    type = SideSetsBetweenSubdomainsGenerator
    input = solid_fluid_interface_1
    primary_block = spacer_block
    paired_block = wall_block
    new_boundary = 'solid_fluid_interface'
  []

  [wall_left_boundary_1]
    type = SideSetsFromBoundingBoxGenerator
    input = solid_fluid_interface_2
    bottom_left = '0 0 0'
    top_right = '0.1 0.0127 0'
    included_boundaries = left
    boundary_new = wall_left
  []

  [wall_left_boundary_2]
    type = SideSetsFromBoundingBoxGenerator
    input = wall_left_boundary_1
    bottom_left = '0 2.9857 0'
    top_right = '0.1 2.9984 0'
    included_boundaries = left
    boundary_new = wall_left
  []

  [fluid_left_boundary]
    type = SideSetsFromBoundingBoxGenerator
    input = wall_left_boundary_2
    bottom_left = '0 0.0127 0'
    top_right = '0.1 2.9857 0'
    included_boundaries = left
    boundary_new = fluid_left
  []

  coord_type = RZ
  rz_coord_axis = Y
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolatorSegregated
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
    block = 'spacer_block porous_block'
  []
[]

[Problem]
  nl_sys_names = 'u_system v_system pressure_system t_system'
  previous_nl_solution_required = true
  error_on_jacobian_nonzero_reallocation = true
[]

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    block = 'spacer_block porous_block'
    solver_sys = u_system
  []

  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    block = 'spacer_block porous_block'
    solver_sys = v_system
  []

  [pressure]
    type = INSFVPressureVariable
    block = 'spacer_block porous_block'
    solver_sys = pressure_system
  []

  [T_fluid]
    type = INSFVEnergyVariable
    block = 'spacer_block porous_block'
    solver_sys = t_system
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
    block = 'spacer_block porous_block'
  []
[]

[FVKernels]
  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    rho = ${rho_fluid}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    block = 'spacer_block porous_block'
    porosity = porosity
    extra_vector_tags = ${pressure_tag}
  []

  [u_buoyancy]
    type = PINSFVMomentumBoussinesq
    variable = superficial_vel_x
    T_fluid = T_fluid
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    ref_temperature = ${T_cold}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [u_gravity]
    type = PINSFVMomentumGravity
    variable = superficial_vel_x
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    momentum_component = 'x'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    rho = ${rho_fluid}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    block = 'spacer_block porous_block'
    porosity = porosity
    extra_vector_tags = ${pressure_tag}
  []

  [v_buoyancy]
    type = PINSFVMomentumBoussinesq
    variable = superficial_vel_y
    T_fluid = T_fluid
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    ref_temperature = ${T_cold}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [v_gravity]
    type = PINSFVMomentumGravity
    variable = superficial_vel_y
    gravity = '0 -1 0'
    rho = ${rho_fluid}
    momentum_component = 'y'
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [temp_conduction]
    type = PINSFVEnergyDiffusion
    k = 'k_fluid'
    variable = T_fluid
    block = 'spacer_block porous_block'
    porosity = porosity
  []

  [temp_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    block = 'spacer_block porous_block'
    boundaries_to_force = fluid_left
  []

  [heat_source]
    type = FVBodyForce
    variable = T_fluid
    function = ${Q}
    block = 'porous_block'
  []

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

[FVBCs]
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = superficial_vel_x
    boundary = 'solid_fluid_interface'
    function = 0
  []

  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = superficial_vel_y
    boundary = 'solid_fluid_interface'
    function = 0
  []

  [reflective_x]
    type = INSFVSymmetryVelocityBC
    variable = superficial_vel_x
    boundary = fluid_left
    momentum_component = 'x'
    mu = ${mu}
    u = superficial_vel_x
    v = superficial_vel_y
  []

  [reflective_y]
    type = INSFVSymmetryVelocityBC
    variable = superficial_vel_y
    boundary = fluid_left
    momentum_component = 'y'
    mu = ${mu}
    u = superficial_vel_x
    v = superficial_vel_y
  []

  [reflective_p]
    type = INSFVSymmetryPressureBC
    boundary = fluid_left
    variable = pressure
  []

  [T_reflective]
    type = FVNeumannBC
    variable = T_fluid
    boundary = fluid_left
    value = 0
  []

  [T_cold_boundary]
    type = FVDirichletBC
    variable = T_fluid
    boundary = solid_fluid_interface
    value = ${T_cold}
  []
[]

[ICs]
  [porosity_spacer]
    type = ConstantIC
    variable = porosity
    block = spacer_block
    value = 1.0
  []

  [porosity_fuel]
    type = ConstantIC
    variable = porosity
    block = porous_block
    value = 0.1
  []

  [temp_ic_fluid]
    type = ConstantIC
    variable = T_fluid
    value = ${T_cold}
    block = 'spacer_block porous_block'
  []

  [superficial_vel_x]
    type = ConstantIC
    variable = superficial_vel_x
    value = 1E-5
    block = 'spacer_block porous_block'
  []

  [superficial_vel_y]
    type = ConstantIC
    variable = superficial_vel_y
    value = 1E-5
    block = 'spacer_block porous_block'
  []
[]

[FunctorMaterials]
  [functor_constants_fluid]
    type = ADGenericFunctorMaterial
    prop_names = 'alpha_b cp k_fluid'
    prop_values = '${alpha} ${cp_fluid} ${k_fluid}'
    block = 'spacer_block porous_block'
  []

  [density_fluid]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho_fluid}
    block = 'spacer_block porous_block'
  []

  [functor_constants_steel]
    # We need this to avoid errors for materials not existing on every block
    type = ADGenericFunctorMaterial
    prop_names = 'dummy'
    prop_values = 0.0
    block = wall_block
  []
[]

[Executioner]
  type = SIMPLENonlinearAssembly
  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  energy_l_abs_tol = 1e-14
  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 = 't_system'
  pressure_gradient_tag = ${pressure_tag}
  momentum_equation_relaxation = 0.85
  energy_equation_relaxation = 0.95
  pressure_variable_relaxation = 0.45
  num_iterations = 150
  pressure_absolute_tolerance = 1e-13
  momentum_absolute_tolerance = 1e-13
  pin_pressure = true
  pressure_pin_point = '0.2 1.5 0.0'
  pressure_pin_value = 0
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-disp-system.i)

mu = 1
rho = 1
k = 1e-3
cp = 1
u_inlet = 1
T_inlet = 200
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '5 5'
    dy = '1.0'
    ix = '50 50'
    iy = '20'
    subdomain_id = '1 2'
  []
  displacements = 'disp_x disp_y'
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  use_displaced_mesh = true
[]

[AuxVariables]
  [disp_x][]
  [disp_y][]
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
    disp_x = disp_x
    disp_y = disp_y
  []
[]

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [T_fluid]
    type = INSFVEnergyVariable
  []
[]

[AuxVariables]
  [T_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
    initial_condition = 100
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.5
  []
[]

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

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    k = ${k}
    variable = T_fluid
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_fluid
    is_solid = false
    T_fluid = 'T_fluid'
    T_solid = 'T_solid'
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    function = 0
  []
  [inlet-T]
    type = FVNeumannBC
    variable = T_fluid
    value = '${fparse u_inlet * rho * cp * T_inlet}'
    boundary = 'left'
  []
  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_x
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_y
    function = 0
  []
  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  nl_rel_tol = 1e-12
  num_steps = 1
  dtmin = 1
[]

[FunctorMaterials]
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv'
    prop_values = '1'
  []
  [functor_constants]
    type = ADGenericFunctorMaterial
    prop_names = 'cp'
    prop_values = '${cp}'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    rho = ${rho}
    temperature = 'T_fluid'
  []
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideAverageValue
    variable = superficial_vel_x
    boundary = 'right'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = T_fluid
    boundary = 'right'
  []
  [solid-temp]
    type = ElementAverageValue
    variable = T_solid
  []
[]

[Outputs]
  hide = 'disp_x disp_y'
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-transient.i)

# Fluid properties
mu = 1
rho = 1
cp = 1
k = 1e-3

# Solid properties
cp_s = 2
rho_s = 4
k_s = 1e-2
h_fs = 10

# Operating conditions
u_inlet = 1
T_inlet = 200
p_outlet = 10
top_side_temperature = 150

# Numerical scheme
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 10
    ymin = 0
    ymax = 1
    nx = 100
    ny = 20
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
  []
[]

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${p_outlet}
  []
  [T_fluid]
    type = INSFVEnergyVariable
  []
  [T_solid]
    type = MooseVariableFVReal
    initial_condition = 100
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
    initial_condition = 0.5
  []
[]

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

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = superficial_vel_x
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = superficial_vel_y
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [energy_time]
    type = PINSFVEnergyTimeDerivative
    variable = T_fluid
    cp = ${cp}
    rho = ${rho}
    is_solid = false
    porosity = porosity
  []
  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    variable = T_fluid
    k = ${k}
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_fluid
    is_solid = false
    T_fluid = 'T_fluid'
    T_solid = 'T_solid'
    h_solid_fluid = 'h_cv'
  []

  [solid_energy_time]
    type = PINSFVEnergyTimeDerivative
    variable = T_solid
    cp = ${cp_s}
    rho = ${rho_s}
    is_solid = true
    porosity = porosity
  []
  [solid_energy_diffusion]
    type = FVDiffusion
    variable = T_solid
    coeff = ${k_s}
  []
  [solid_energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_solid
    is_solid = true
    T_fluid = 'T_fluid'
    T_solid = 'T_solid'
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    function = 0
  []
  [inlet-T]
    type = FVNeumannBC
    variable = T_fluid
    value = '${fparse u_inlet * rho * cp * T_inlet}'
    boundary = 'left'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_x
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_y
    function = 0
  []
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'T_solid'
    value = ${top_side_temperature}
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = ${p_outlet}
  []
[]

[FunctorMaterials]
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv'
    prop_values = '${h_fs}'
  []
  [functor_constants]
    type = ADGenericFunctorMaterial
    prop_names = 'cp'
    prop_values = '${cp}'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    rho = ${rho}
    temperature = 'T_fluid'
  []
[]

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

  end_time = 1.5
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideAverageValue
    variable = superficial_vel_x
    boundary = 'right'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = T_fluid
    boundary = 'right'
  []
  [solid-temp]
    type = ElementAverageValue
    variable = T_solid
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient.i)

# Fluid properties
mu = 'mu'
rho = 'rho'
cp = 'cp'
k = 'k'

# Solid properties
cp_s = 2
rho_s = 4
k_s = 1e-2
h_fs = 10

# Operating conditions
u_inlet = 1
T_inlet = 200
p_outlet = 10
top_side_temperature = 150

# Numerical scheme
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 10
    ymin = 0
    ymax = 1
    nx = 20
    ny = 5
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
  []
[]

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${p_outlet}
  []
  [T_fluid]
    type = INSFVEnergyVariable
    initial_condition = ${T_inlet}
  []
  [T_solid]
    type = MooseVariableFVReal
    initial_condition = 100
  []
[]

[AuxVariables]
  [porosity]
    type = MooseVariableFVReal
    initial_condition = 0.5
  []
  [velocity_norm]
    type = MooseVariableFVReal
  []
[]

[FVKernels]
  [mass_time]
    type = PWCNSFVMassTimeDerivative
    variable = pressure
    porosity = 'porosity'
    drho_dt = 'drho_dt'
  []
  [mass]
    type = PWCNSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_time]
    type = WCNSFVMomentumTimeDerivative
    variable = superficial_vel_x
    rho = ${rho}
    drho_dt = 'drho_dt'
    momentum_component = 'x'
  []
  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_time]
    type = WCNSFVMomentumTimeDerivative
    variable = superficial_vel_y
    rho = ${rho}
    drho_dt = 'drho_dt'
    momentum_component = 'y'
  []
  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [energy_time]
    type = PINSFVEnergyTimeDerivative
    variable = T_fluid
    cp = ${cp}
    rho = ${rho}
    drho_dt = 'drho_dt'
    is_solid = false
    porosity = porosity
  []
  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    variable = T_fluid
    k = ${k}
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_fluid
    is_solid = false
    T_fluid = T_fluid
    T_solid = T_solid
    h_solid_fluid = 'h_cv'
  []

  [solid_energy_time]
    type = PINSFVEnergyTimeDerivative
    variable = T_solid
    cp = ${cp_s}
    rho = ${rho_s}
    is_solid = true
    porosity = porosity
  []
  [solid_energy_diffusion]
    type = FVDiffusion
    variable = T_solid
    coeff = ${k_s}
  []
  [solid_energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_solid
    is_solid = true
    T_fluid = T_fluid
    T_solid = T_solid
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    function = 0
  []
  [inlet-T]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T_inlet}
    boundary = 'left'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_x
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_y
    function = 0
  []
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'T_solid'
    value = ${top_side_temperature}
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = ${p_outlet}
  []
[]

[FluidProperties]
  [fp]
    type = FlibeFluidProperties
  []
[]

[FunctorMaterials]
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = fp
    pressure = 'pressure'
    T_fluid = 'T_fluid'
    speed = 'velocity_norm'

    # To initialize with a high viscosity
    mu_rampdown = 'mu_rampdown'

    # For porous flow
    characteristic_length = 1
    porosity = 'porosity'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    rho = ${rho}
    temperature = 'T_fluid'
  []
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv'
    prop_values = '${h_fs}'
  []
[]

[Functions]
  [mu_rampdown]
    type = PiecewiseLinear
    x = '1 2 3 4'
    y = '1e3 1e2 1e1 1'
  []
[]

[AuxKernels]
  [speed]
    type = ParsedAux
    variable = 'velocity_norm'
    coupled_variables = 'superficial_vel_x superficial_vel_y porosity'
    expression = 'sqrt(superficial_vel_x*superficial_vel_x + superficial_vel_y*superficial_vel_y) / '
               'porosity'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12

  end_time = 3.0
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideAverageValue
    variable = superficial_vel_x
    boundary = 'right'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = T_fluid
    boundary = 'right'
  []
  [solid-temp]
    type = ElementAverageValue
    variable = T_solid
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-boussinesq.i)

mu = 1
rho = 1
k = 1e-3
cp = 1
v_inlet = 1
T_inlet = 200
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    nx = 20
    ny = 100
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
  []
[]

[Variables]
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${v_inlet}
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [T_fluid]
    type = INSFVEnergyVariable
  []
[]

[AuxVariables]
  [T_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
    initial_condition = 100
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.4
  []
[]

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

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []
  [u_gravity]
    type = PINSFVMomentumGravity
    variable = superficial_vel_x
    rho = ${rho}
    gravity = '0 -9.81 0'
    momentum_component = 'x'
    porosity = porosity
  []
  [u_boussinesq]
    type = PINSFVMomentumBoussinesq
    variable = superficial_vel_x
    T_fluid = 'T_fluid'
    rho = ${rho}
    ref_temperature = 150
    gravity = '0 -9.81 0'
    momentum_component = 'x'
    alpha_name = 'alpha_b'
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []
  [v_gravity]
    type = PINSFVMomentumGravity
    variable = superficial_vel_y
    rho = ${rho}
    gravity = '-0 -9.81 0'
    momentum_component = 'y'
    porosity = porosity
  []
  [v_boussinesq]
    type = PINSFVMomentumBoussinesq
    variable = superficial_vel_y
    T_fluid = 'T_fluid'
    rho = ${rho}
    ref_temperature = 150
    gravity = '0 -9.81 0'
    momentum_component = 'y'
    alpha_name = 'alpha_b'
    porosity = porosity
  []

  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    k = ${k}
    variable = T_fluid
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_fluid
    is_solid = false
    T_fluid = T_fluid
    T_solid = T_solid
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_x
    function = 0
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_y
    function = ${v_inlet}
  []
  [inlet-T]
    type = FVNeumannBC
    variable = T_fluid
    value = '${fparse v_inlet * rho * cp * T_inlet}'
    boundary = 'bottom'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = superficial_vel_x
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = superficial_vel_y
    function = 0
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 0
  []
[]

[FunctorMaterials]
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv alpha_b'
    prop_values = '1e-3 8e-4'
  []
  [functor_constants]
    type = ADGenericFunctorMaterial
    prop_names = 'cp'
    prop_values = '${cp}'
  []

  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    rho = ${rho}
    temperature = 'T_fluid'
  []
[]

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

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'top'
  []
  [outlet-v]
    type = SideAverageValue
    variable = superficial_vel_y
    boundary = 'top'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = T_fluid
    boundary = 'top'
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated.i)

mu = 1
rho = 1
k = 1e-3
cp = 1
u_inlet = 1
T_inlet = 200
advected_interp_method = 'average'
velocity_interp_method = 'rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '5 5'
    dy = '1.0'
    ix = '50 50'
    iy = '20'
    subdomain_id = '1 2'
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
  []
[]

[Variables]
  inactive = 'T_solid'
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [T_fluid]
    type = INSFVEnergyVariable
  []
  [T_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
  []
[]

[AuxVariables]
  [T_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
    initial_condition = 100
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.5
  []
[]

[FVKernels]
  inactive = 'solid_energy_diffusion solid_energy_convection'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_x
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_x
    mu = ${mu}
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_x
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = superficial_vel_y
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = superficial_vel_y
    mu = ${mu}
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = superficial_vel_y
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    k = ${k}
    variable = T_fluid
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_fluid
    is_solid = false
    T_fluid = 'T_fluid'
    T_solid = 'T_solid'
    h_solid_fluid = 'h_cv'
  []

  [solid_energy_diffusion]
    type = FVDiffusion
    coeff = ${k}
    variable = T_solid
  []
  [solid_energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = T_solid
    is_solid = true
    T_fluid = 'T_fluid'
    T_solid = 'T_solid'
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  inactive = 'heated-side'
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    function = 0
  []
  [inlet-T]
    type = FVNeumannBC
    variable = T_fluid
    value = '${fparse u_inlet * rho * cp * T_inlet}'
    boundary = 'left'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_x
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = superficial_vel_y
    function = 0
  []
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'T_solid'
    value = 150
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'x'
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0.1
  []
[]

[FunctorMaterials]
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv'
    prop_values = '1'
  []
  [functor_constants]
    type = ADGenericFunctorMaterial
    prop_names = 'cp'
    prop_values = '${cp}'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    rho = ${rho}
    temperature = 'T_fluid'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  nl_rel_tol = 1e-14
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideAverageValue
    variable = superficial_vel_x
    boundary = 'right'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = T_fluid
    boundary = 'right'
  []
  [solid-temp]
    type = ElementAverageValue
    variable = T_solid
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

Description
Input Parameters
Input Files