PINSFVEnergyTimeDerivative

Description

This kernel implements a time derivative for the domain $var element = document.getElementById("moose-equation-81688f0c-fe3d-48c3-8a18-1629bcd63035");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ given by

$var element = document.getElementById("moose-equation-92c311fe-524b-4971-b276-5f8a158d1766");katex.render("\\epsilon \\frac{\\partial \\rho c_{pf} T_f}{\\partial t}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for the fluid phase and $var element = document.getElementById("moose-equation-1b3f2a6f-b661-4633-b132-36817b2f09f3");katex.render("(1 - \\epsilon) \\frac{\\partial \\rho_s c_{ps} T_s}{\\partial t}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for the solid phase, where $var element = document.getElementById("moose-equation-1a963c43-9edd-4576-8b2c-c6d38a1437d7");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the porosity, $var element = document.getElementById("moose-equation-4cb78963-95eb-4ae1-a9df-8a71682f80bf");katex.render("\\rho_{f/s}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the fluid/solid material density, $var element = document.getElementById("moose-equation-2405d1fb-1d12-49e8-8cda-9fa2a69f1d8a");katex.render("c_{pf/s}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the fluid/solid specific heat and $var element = document.getElementById("moose-equation-5b009ced-452a-4076-8fb0-f94c7ed386c9");katex.render("T_{f/s}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the fluid/solid temperature.

The time derivatives of density and the specific heat capacity are ignored if "drho_dt" and "dcp_dt" are not provided. For incompressible flows, the former should not be provided.

The variation of the kinetic energy is not considered in this kernel.

Input Parameters

cpSpecific heat capacity
C++ Type:MooseFunctorName
Controllable:No
Description:Specific heat capacity
is_solidFalseWhether this kernel acts on the solid temperature
Default:False
C++ Type:bool
Controllable:No
Description:Whether this kernel acts on the solid temperature
porosityPorosity
C++ Type:MooseFunctorName
Controllable:No
Description:Porosity
rhoDensity
C++ Type:MooseFunctorName
Controllable:No
Description:Density
variableThe name of the finite volume variable this kernel applies to
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the finite volume variable this kernel applies to

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
dcp_dtSpecific heat capacity time derivative functor
C++ Type:MooseFunctorName
Controllable:No
Description:Specific heat capacity time derivative functor
drho_dtDensity time derivative functor
C++ Type:MooseFunctorName
Controllable:No
Description:Density time derivative functor
ghost_layers1The number of layers of elements to ghost.
Default:1
C++ Type:unsigned short
Controllable:No
Description:The number of layers of elements to ghost.
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
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.
scaling1scaling factor to reduce the thermal mass during pseudo transients; this can accelerate convergence to steady state
Default:1
C++ Type:double
Controllable:No
Description:scaling factor to reduce the thermal mass during pseudo transients; this can accelerate convergence to steady state
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.

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
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

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_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Options:nontime, system, time
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

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

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

[Variables]
  [T_solid]
    type = MooseVariableFVReal
    initial_condition = 100
  []
[]

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

[Modules]
  [NavierStokesFV]
    compressibility = 'incompressible'
    porous_medium_treatment = true
    add_energy_equation = true

    density = 'rho'
    dynamic_viscosity = 'mu'
    thermal_conductivity = 'k'
    specific_heat = 'cp'
    porosity = 'porosity'

    initial_velocity = '${u_inlet} 1e-6 0'
    initial_pressure = ${p_outlet}
    initial_temperature = 0.0

    inlet_boundaries = 'left'
    momentum_inlet_types = 'fixed-velocity'
    momentum_inlet_function = '${u_inlet} 0'
    energy_inlet_types = 'heatflux'
    energy_inlet_function = '${fparse u_inlet * rho * cp * T_inlet}'

    wall_boundaries = 'top bottom'
    momentum_wall_types = 'noslip symmetry'
    energy_wall_types = 'heatflux heatflux'
    energy_wall_function = '0 0'

    outlet_boundaries = 'right'
    momentum_outlet_types = 'fixed-pressure'
    pressure_function = '${p_outlet}'

    ambient_convection_alpha = 'h_cv'
    ambient_temperature = 'T_solid'
  []
[]

[FVKernels]
  [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]
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'T_solid'
    value = ${top_side_temperature}
  []
[]

[Materials]
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv cp rho mu k'
    prop_values = '${h_fs} ${cp} ${rho} ${mu} ${k}'
  []
[]

[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 = 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/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}
  []
[]

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

[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 = 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-action.i)

# 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

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

[Variables]
  [T_solid]
    type = MooseVariableFVReal
    initial_condition = 100
  []
[]

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

[Modules]
  [NavierStokesFV]
    compressibility = 'weakly-compressible'
    add_energy_equation = true
    porous_medium_treatment = true

    density = 'rho'
    dynamic_viscosity = 'mu'
    thermal_conductivity = 'k'
    specific_heat = 'cp'

    initial_velocity = '${u_inlet} 1e-6 0'
    initial_pressure = '${p_outlet}'
    initial_temperature = '${T_inlet}'

    inlet_boundaries = 'left'
    momentum_inlet_types = 'fixed-velocity'
    momentum_inlet_function = '${u_inlet} 0'
    energy_inlet_types = 'fixed-temperature'
    energy_inlet_function = '${T_inlet}'

    wall_boundaries = 'top bottom'
    momentum_wall_types = 'noslip symmetry'
    energy_wall_types = 'heatflux heatflux'
    energy_wall_function = '0 0'

    outlet_boundaries = 'right'
    momentum_outlet_types = 'fixed-pressure'
    pressure_function = '${p_outlet}'

    ambient_convection_alpha = 'h_cv'
    ambient_temperature = 'T_solid'
  []
  [FluidProperties]
    [fp]
      type = FlibeFluidProperties
    []
  []
[]

[FVKernels]
  [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]
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'T_solid'
    value = ${top_side_temperature}
  []
[]

[Materials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv'
    prop_values = '${h_fs}'
  []
  [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'
  []
[]

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

[AuxKernels]
  [speed]
    type = ParsedAux
    variable = 'velocity_norm'
    args = 'superficial_vel_x superficial_vel_y porosity'
    function = '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/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 = PINSFVMassAdvection
    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}
    dcp_dt = 'dcp_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}
  []
[]

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

[Materials]
  [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 = INSFVEnthalpyMaterial
    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'
    args = 'superficial_vel_x superficial_vel_y porosity'
    function = '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
[]

Description
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