GeneralFunctorFluidProps

Creates functor fluid properties using a (P, T) formulation

Overview

This object uses a SinglePhaseFluidProperties derived-object to compute the following properties:

specific heat at constant volume, $var element = document.getElementById("moose-equation-9b140746-26a5-450c-b84e-67e898da78ba");katex.render("c_v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
specific heat at constant pressure, $var element = document.getElementById("moose-equation-4d68dc54-999c-4349-bb97-2bb4d9698420");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
dynamic viscosity, $var element = document.getElementById("moose-equation-c8ef0af4-2aec-42e3-8ee5-5ad93cc299ab");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
thermal conductivity, $var element = document.getElementById("moose-equation-850109d8-1417-4530-a9c8-951d4aeeed4a");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
Prandtl number, $var element = document.getElementById("moose-equation-d33fa533-a327-4ae8-9aa3-ec3b08fda040");katex.render("\\text{Pr}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
pore/particle Reynolds number $var element = document.getElementById("moose-equation-224419a0-41f0-4e72-9221-2f72e402635b");katex.render("\\text{Re}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
hydraulic Reynolds number $var element = document.getElementById("moose-equation-ff1f4971-9931-48b4-86bb-dcca42ad5942");katex.render("\\text{Re}_h", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
interstitial Reynolds number $var element = document.getElementById("moose-equation-7a849421-3c16-473c-bcca-07d5aa53e38c");katex.render("\\text{Re}_i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

the time derivatives of the:

specific heat at constant pressure, $var element = document.getElementById("moose-equation-c6d38150-4586-47fd-bfa3-1d5b52edf32c");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
density $var element = document.getElementById("moose-equation-94558bbf-48d0-46ea-b38e-02dbeb170ad0");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

and the pressure and temperature derivatives of the:

specific heat at constant pressure, $var element = document.getElementById("moose-equation-b6b66d01-6692-4c9c-aa3c-0919bac07e72");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
density $var element = document.getElementById("moose-equation-d98c3c0e-6936-4898-bd86-ce3548548b58");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
dynamic viscosity, $var element = document.getElementById("moose-equation-65ea7cb9-099f-4019-af22-06ec24165b26");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
thermal conductivity, $var element = document.getElementById("moose-equation-454928c2-2d08-48f4-8b1a-48766cae0efe");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
Prandtl number, $var element = document.getElementById("moose-equation-8cbcf28d-8dd9-46a6-81a1-6c6238939633");katex.render("\\text{Pr}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$
pore Reynolds number $var element = document.getElementById("moose-equation-9825f441-77b1-4dc5-9832-4919fee4da3e");katex.render("\\text{Re}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

note

In order to use this with some fluid properties that do not compute the AD version of the density derivatives, such as the Spline Base Table Lookup fluid properties, you can use the "neglect_derivatives_of_density_time_derivative" to neglect the derivatives with regards to the nonlinear variables (usually pressure, temperature) of the time derivative of the density.

Input Parameters

T_fluidFluid temperature. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Fluid temperature. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
characteristic_lengthcharacteristic length for Reynolds number calculation. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:characteristic length for Reynolds number calculation. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
fpFluid properties functor userobject
C++ Type:UserObjectName
Unit:(no unit assumed)
Controllable:No
Description:Fluid properties functor userobject
porosityporosity. A functor is any of the following: a variable, a functor material property, a function, a post-processor, 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 post-processor, or a number.
pressurePressure. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Pressure. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
speedVelocity norm. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Velocity norm. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
execute_onALWAYSThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:ALWAYS
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
force_define_densityFalseWhether to force the definition of a density functor from the fluid properties
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to force the definition of a density functor from the fluid properties
mu_rampdown1A function describing a ramp down of viscosity over time
Default:1
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:A function describing a ramp down of viscosity over time
neglect_derivatives_of_density_time_derivativeFalseWhether to neglect the derivatives with regards to nonlinear variables of the density time derivatives
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to neglect the derivatives with regards to nonlinear variables of the density time derivatives
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.
rhoDensity. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
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
Unit:(no unit assumed)
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.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:No
Description:The seed for the master random number generator

Advanced Parameters

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

Outputs Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/turbulent_driven_growth.i)
(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient-physics.i)
(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient-gas.i)
(modules/navier_stokes/test/tests/finite_volume/materials/ergun/ergun.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/materials/2d-transient.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/natural_convection/natural_circulation_pipe.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/materials/functorfluidprops.i)
(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient.i)
(modules/navier_stokes/test/tests/finite_volume/pwcns/channel-flow/2d-transient-action.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/pressure_driven_growth_transient.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_interface_area_model/pressure_driven_growth.i)

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

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

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

outlet_pressure = 1e5

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

[Problem]
  identify_variable_groups_in_nl = false
  previous_nl_solution_required = true
[]

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

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

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

[FVKernels]

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

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

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

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

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

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

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

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

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

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

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

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

[Debug]
  show_var_residual_norms = true
[]

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

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

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

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

# Solid properties
cp_s = 2
rho_s = 4
k_s = '${fparse 1e-2 / 0.5}'
h_fs = 10

# thermal diffusivity is divided by 0.5 to match the reference using the action

# 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
  []
[]

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

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

[Physics]
  [NavierStokes]
    [Flow]
      [flow]
        compressibility = 'weakly-compressible'
        porous_medium_treatment = true
        define_variables = true

        pressure_variable = 'pressure'

        density = 'rho'
        dynamic_viscosity = 'mu'

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

        inlet_boundaries = 'left'
        momentum_inlet_types = 'fixed-velocity'
        momentum_inlet_function = '${u_inlet} 0'

        wall_boundaries = 'top bottom'
        momentum_wall_types = 'noslip symmetry'

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

        mass_advection_interpolation = 'average'
        momentum_advection_interpolation = 'average'
      []
    []
    [FluidHeatTransfer]
      [fluid]
        thermal_conductivity = 'k'
        effective_conductivity = true
        specific_heat = 'cp'

        initial_temperature = '${T_inlet}'

        # See 'flow' for inlet boundaries
        energy_inlet_types = 'fixed-temperature'
        energy_inlet_function = '${T_inlet}'

        # See 'flow' for wall boundaries
        energy_wall_types = 'heatflux heatflux'
        energy_wall_function = '0 0'

        ambient_convection_alpha = 'h_cv'
        ambient_temperature = 'T_solid'

        energy_advection_interpolation = 'average'
      []
    []

    [SolidHeatTransfer]
      [solid]
        block = 0
        initial_temperature = 100
        transient = true
        # To match the previous test results
        solid_temperature_two_term_bc_expansion = true

        thermal_conductivity_solid = '${k_s}'
        cp_solid = ${cp_s}
        rho_solid = ${rho_s}

        fixed_temperature_boundaries = 'top'
        boundary_temperatures = '${top_side_temperature}'

        ambient_convection_alpha = 'h_cv'
        ambient_convection_temperature = 'T_fluid'
        verbose = true
      []
    []
  []
[]

[FunctorMaterials]
  [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'
    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/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/materials/ergun/ergun.i)

# This file simulates flow of fluid in a porous elbow for the purpose of verifying
# correct implementation of the various different solution variable sets. This input
# tests correct implementation of the primitive superficial variable set. Flow enters on the top
# and exits on the right. Because the purpose is only to test the equivalence of
# different equation sets, no solid energy equation is included.

porosity_left = 0.4
porosity_right = 0.6
pebble_diameter = 0.06

mu = 1.81e-5 # This has been increased to avoid refining the mesh
M = 28.97e-3
R = 8.3144598

# inlet mass flowrate, kg/s
mdot = -10.0

# inlet mass flux (superficial)
mflux_in_superficial = ${fparse mdot / (pi * 0.5 * 0.5)}

# inlet mass flux (interstitial)
mflux_in_interstitial = ${fparse mflux_in_superficial / porosity_left}

p_initial = 201325.0
T_initial = 300.0
rho_initial = ${fparse p_initial / T_initial * M / R}

vel_y_initial = ${fparse mflux_in_interstitial / rho_initial}
vel_x_initial = 0.0

superficial_vel_y_initial = ${fparse mflux_in_superficial / rho_initial}
superficial_vel_x_initial = 1e-12

# Computation parameters
velocity_interp_method = 'rc'
advected_interp_method = 'upwind'

# ==============================================================================
# GEOMETRY AND MESH
# ==============================================================================

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = 'ergun_in.e'
  []
  coord_type = RZ
[]

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

[GlobalParams]
  porosity = porosity
  pebble_diameter = ${pebble_diameter}
  fp = fp

  # rho for the kernels. Must match fluid property!
  rho = ${rho_initial}

  fv = true
  velocity_interp_method = ${velocity_interp_method}
  advected_interp_method = ${advected_interp_method}

  # behavior at time of test creation
  two_term_boundary_expansion = false
  rhie_chow_user_object = 'rc'
[]

# ==============================================================================
# VARIABLES AND KERNELS
# ==============================================================================

[Variables]
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${p_initial}
  []
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${superficial_vel_x_initial}
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${superficial_vel_y_initial}
  []
[]

[FVKernels]
  # Mass Equation.
  [mass]
    type = PINSFVMassAdvection
    variable = 'pressure'
  []

  # Momentum x component equation.
  [vel_x_time]
    type = PINSFVMomentumTimeDerivative
    variable = 'superficial_vel_x'
    momentum_component = 'x'
  []
  [vel_x_advection]
    type = PINSFVMomentumAdvection
    variable = 'superficial_vel_x'
    momentum_component = 'x'
  []
  [vel_x_viscosity]
    type = PINSFVMomentumDiffusion
    variable = 'superficial_vel_x'
    momentum_component = 'x'
    mu = 'mu'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = 'superficial_vel_x'
    pressure = pressure
    momentum_component = 'x'
  []
  [u_friction]
    type = PINSFVMomentumFriction
    variable = 'superficial_vel_x'
    Darcy_name = 'Darcy_coefficient'
    Forchheimer_name = 'Forchheimer_coefficient'
    momentum_component = 'x'
    speed = speed
    mu = 'mu'
  []

  # Momentum y component equation.
  [vel_y_time]
    type = PINSFVMomentumTimeDerivative
    variable = 'superficial_vel_y'
    momentum_component = 'y'
  []
  [vel_y_advection]
    type = PINSFVMomentumAdvection
    variable = 'superficial_vel_y'
    momentum_component = 'y'
  []
  [vel_y_viscosity]
    type = PINSFVMomentumDiffusion
    variable = 'superficial_vel_y'
    momentum_component = 'y'
    mu = 'mu'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = 'superficial_vel_y'
    pressure = pressure
    momentum_component = 'y'
  []
  [v_friction]
    type = PINSFVMomentumFriction
    variable = 'superficial_vel_y'
    Darcy_name = 'Darcy_coefficient'
    Forchheimer_name = 'Forchheimer_coefficient'
    momentum_component = 'y'
    mu = 'mu'
    speed = speed
  []
  [gravity]
    type = PINSFVMomentumGravity
    variable = 'superficial_vel_y'
    gravity = '0 -9.81 0'
    momentum_component = 'y'
  []
[]

# ==============================================================================
# AUXVARIABLES AND AUXKERNELS
# ==============================================================================

[AuxVariables]
  [T_fluid]
    initial_condition = ${T_initial}
    order = CONSTANT
    family = MONOMIAL
  []
  [vel_x]
    initial_condition = ${fparse vel_x_initial}
    order = CONSTANT
    family = MONOMIAL
  []
  [vel_y]
    initial_condition = ${fparse vel_y_initial}
    order = CONSTANT
    family = MONOMIAL
  []
  [porosity_out]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [vel_x]
    type = FunctorAux
    variable = vel_x
    functor = vel_x_mat
  []
  [vel_y]
    type = FunctorAux
    variable = vel_y
    functor = vel_y_mat
  []
  [porosity_out]
    type = FunctorAux
    variable = porosity_out
    functor = porosity
  []
[]

# ==============================================================================
# FLUID PROPERTIES, MATERIALS AND USER OBJECTS
# ==============================================================================

[FluidProperties]
  [fp]
    type = IdealGasFluidProperties
    k = 0.0
    mu = ${mu}
    gamma = 1.4
    molar_mass = ${M}
  []
[]

[FunctorMaterials]
  [enthalpy]
    type = INSFVEnthalpyMaterial
    temperature = 'T_fluid'
  []
  [speed]
    type = PINSFVSpeedFunctorMaterial
    superficial_vel_x = 'superficial_vel_x'
    superficial_vel_y = 'superficial_vel_y'
    porosity = porosity
    vel_x = vel_x_mat
    vel_y = vel_y_mat
  []
  [kappa]
    type = FunctorKappaFluid
  []
  [const_Fdrags_mat]
    type = FunctorErgunDragCoefficients
    porosity = porosity
  []
  [fluidprops]
    type = GeneralFunctorFluidProps
    mu_rampdown = mu_func
    porosity = porosity
    characteristic_length = ${pebble_diameter}
    T_fluid = 'T_fluid'
    pressure = 'pressure'
    speed = 'speed'
  []
[]

d = 0.05

[Functions]
  [mu_func]
    type = PiecewiseLinear
    x = '1 3 5 10 15 20'
    y = '1e5 1e4 1e3 1e2 1e1 1'
  []
  [real_porosity_function]
    type = ParsedFunction
    expression = 'if (x < 0.6 - ${d}, ${porosity_left}, if (x > 0.6 + ${d}, ${porosity_right},
        (x-(0.6-${d}))/(2*${d})*(${porosity_right}-${porosity_left}) + ${porosity_left}))'
  []
  [porosity]
    type = ParsedFunction
    expression = 'if (x < 0.6 - ${d}, ${porosity_left}, if (x > 0.6 + ${d}, ${porosity_right},
        (x-(0.6-${d}))/(2*${d})*(${porosity_right}-${porosity_left}) + ${porosity_left}))'
  []
[]

# ==============================================================================
# BOUNDARY CONDITIONS
# ==============================================================================

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

  ## No or Free slip BC
  [free-slip-wall-x]
    type = INSFVNaturalFreeSlipBC
    boundary = 'bottom wall_1 wall_2 left'
    variable = superficial_vel_x
    momentum_component = 'x'
  []
  [free-slip-wall-y]
    type = INSFVNaturalFreeSlipBC
    boundary = 'bottom wall_1 wall_2 left'
    variable = superficial_vel_y
    momentum_component = 'y'
  []

  ## Symmetry
  [symmetry-x]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = 'mu'
    momentum_component = 'x'
  []
  [symmetry-y]
    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'
  []

  ## inlet
  [inlet_vel_x]
    type = INSFVInletVelocityBC
    variable = 'superficial_vel_x'
    function = ${superficial_vel_x_initial}
    boundary = 'top'
  []
  [inlet_vel_y]
    type = INSFVInletVelocityBC
    variable = 'superficial_vel_y'
    function = ${superficial_vel_y_initial}
    boundary = 'top'
  []
[]
# ==============================================================================
# EXECUTION PARAMETERS
# ==============================================================================

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'asm      lu           NONZERO                   200'
  line_search = 'none'

  # Problem time parameters
  dtmin = 0.01
  dtmax = 2000
  end_time = 3000
  # must be the same as the fluid

  # Iterations parameters
  l_max_its = 50
  l_tol     = 1e-8
  nl_max_its = 25
  # nl_rel_tol = 5e-7
  nl_abs_tol = 2e-7

  # Automatic scaling
  automatic_scaling = true
  verbose = true

  [TimeStepper]
    type = IterationAdaptiveDT
    dt                 = 0.025
    cutback_factor     = 0.5
    growth_factor      = 2.0
  []

  # Steady state detection.
  steady_state_detection = true
  steady_state_tolerance = 1e-7
  steady_state_start_time = 400
[]

# ==============================================================================
# POSTPROCESSORS DEBUG AND OUTPUTS
# ==============================================================================

[Postprocessors]
  [mass_flow_in]
    type = VolumetricFlowRate
    boundary = 'top'
    vel_x = 'superficial_vel_x'
    vel_y = 'superficial_vel_y'
    advected_quantity = ${rho_initial}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [mass_flow_out]
    type = VolumetricFlowRate
    boundary = 'right'
    vel_x = 'superficial_vel_x'
    vel_y = 'superficial_vel_y'
    advected_quantity = ${rho_initial}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_in]
    type = SideAverageValue
    variable = pressure
    boundary = 'top'
  []
  [dP]
    type = LinearCombinationPostprocessor
    pp_names = 'p_in'
    pp_coefs = '1.0'
    b = ${fparse -p_initial}
  []
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/materials/2d-transient.i)

l = 10
velocity_interp_method = 'rc'
advected_interp_method = 'average'

# Operating conditions
inlet_temp = 300
outlet_pressure = 1e5
inlet_v = 0.001

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = 1
    nx = 20
    ny = 10
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  rho = 'rho'
[]

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

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_v}
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
  []
  [T]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
  []
[]

[AuxVariables]
  [velocity_norm]
    type = MooseVariableFVReal
  []
  [power_density]
    type = MooseVariableFVReal
    initial_condition = 1e4
  []
[]

[FVKernels]
  [mass_time]
    type = WCNSFVMassTimeDerivative
    variable = pressure
    drho_dt = drho_dt
  []
  [mass]
    type = WCNSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = 'rho'
  []

  [u_time]
    type = WCNSFVMomentumTimeDerivative
    variable = u
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = 'rho'
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = u
    mu = 'mu'
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_time]
    type = WCNSFVMomentumTimeDerivative
    variable = v
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = 'rho'
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = v
    mu = 'mu'
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [temp_time]
    type = WCNSFVEnergyTimeDerivative
    variable = T
    rho = rho
    drho_dt = drho_dt
    h = h
    dh_dt = dh_dt
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [heat_source]
    type = FVCoupledForce
    variable = T
    v = power_density
  []
[]

[FVBCs]
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top bottom'
    function = 0
  []

  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'top bottom'
    function = 0
  []

  # Inlet
  [inlet_u]
    type = INSFVInletVelocityBC
    variable = u
    boundary = 'left'
    function = ${inlet_v}
  []
  [inlet_v]
    type = INSFVInletVelocityBC
    variable = v
    boundary = 'left'
    function = 0
  []
  [inlet_T]
    type = FVDirichletBC
    variable = T
    boundary = 'left'
    value = ${inlet_temp}
  []

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

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

[FunctorMaterials]
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T'
    rho = 'rho'
  []
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = fp
    pressure = 'pressure'
    T_fluid = 'T'
    speed = 'velocity_norm'

    # even though we provide rho from the parameters, we
    # want to get rho from the fluid properties
    force_define_density = true

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

    # For porous flow
    characteristic_length = 1
    porosity = 1
  []
[]

[AuxKernels]
  [speed]
    type = VectorMagnitudeAux
    variable = 'velocity_norm'
    x = u
    y = v
  []
[]

[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 -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e-3
    optimal_iterations = 6
  []
  end_time = 15

  nl_abs_tol = 1e-12
  nl_max_its = 50
  line_search = 'none'

  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
  compute_scaling_once = false
[]

[Outputs]
  exodus = true
[]

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

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

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

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

[GlobalParams]
  rhie_chow_user_object = pins_rhie_chow_interpolator
[]

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

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

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

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

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

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

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

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

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

[AuxVariables]
  [rho_var]
    type = MooseVariableFVReal
  []

  [cp_var]
    type = MooseVariableFVReal
  []

  [rho_cp_T_fluid_var]
    type = MooseVariableFVReal
  []
[]

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

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

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

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

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

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

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

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
[]

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

# Operating conditions
inlet_temp = 300
outlet_pressure = 1e5
inlet_v = 4

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

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_v}
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 2
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
  []
  [T]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
  []
[]

[FVKernels]
  [u_time]
    type = FVFunctorTimeKernel
    variable = u
  []
  [v_time]
    type = FVFunctorTimeKernel
    variable = v
  []
  [p_time]
    type = FVFunctorTimeKernel
    variable = pressure
  []
  [T_time]
    type = FVFunctorTimeKernel
    variable = T
  []
[]

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

[FunctorMaterials]
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = fp
    pressure = 'pressure'
    T_fluid = 'T'
    speed = 'velocity_norm'

    # For porous flow
    characteristic_length = 2
    porosity = 'porosity'
  []
[]

[AuxVariables]
  [velocity_norm]
    type = MooseVariableFVReal
  []
  [porosity]
    type = MooseVariableFVReal
    initial_condition = 0.4
  []
  [rho_var]
    type = MooseVariableFVReal
  []
  [drho_dp_var]
    type = MooseVariableFVReal
  []
  [drho_dT_var]
    type = MooseVariableFVReal
  []
  [rho_dot_var]
    type = MooseVariableFVReal
  []
  [cp_var]
    type = MooseVariableFVReal
  []
  [dcp_dp_var]
    type = MooseVariableFVReal
  []
  [dcp_dT_var]
    type = MooseVariableFVReal
  []
  [cp_dot_var]
    type = MooseVariableFVReal
  []
  [cv_var]
    type = MooseVariableFVReal
  []
  [mu_var]
    type = MooseVariableFVReal
  []
  [dmu_dp_var]
    type = MooseVariableFVReal
  []
  [dmu_dT_var]
    type = MooseVariableFVReal
  []
  [k_var]
    type = MooseVariableFVReal
  []
  [dk_dp_var]
    type = MooseVariableFVReal
  []
  [dk_dT_var]
    type = MooseVariableFVReal
  []
  [Pr_var]
    type = MooseVariableFVReal
  []
  [dPr_dp_var]
    type = MooseVariableFVReal
  []
  [dPr_dT_var]
    type = MooseVariableFVReal
  []
  [Re_var]
    type = MooseVariableFVReal
  []
  [dRe_dp_var]
    type = MooseVariableFVReal
  []
  [dRe_dT_var]
    type = MooseVariableFVReal
  []
  [Re_h_var]
    type = MooseVariableFVReal
  []
  [Re_i_var]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [speed]
    type = VectorMagnitudeAux
    variable = 'velocity_norm'
    x = u
    y = v
  []

  # To output the functor material properties
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'timestep_begin'
  []
  [drho_dp_out]
    type = FunctorAux
    functor = 'drho/dpressure'
    variable = 'drho_dp_var'
    execute_on = 'timestep_begin'
  []
  [drho_dT_out]
    type = FunctorAux
    functor = 'drho/dT_fluid'
    variable = 'drho_dT_var'
    execute_on = 'timestep_begin'
  []
  [drho_dt_out]
    type = FunctorAux
    functor = 'drho_dt'
    variable = 'rho_dot_var'
    execute_on = 'timestep_begin'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'timestep_begin'
  []
  [dcp_dp_out]
    type = FunctorAux
    functor = 'dcp/dpressure'
    variable = 'dcp_dp_var'
    execute_on = 'timestep_begin'
  []
  [dcp_dT_out]
    type = FunctorAux
    functor = 'dcp/dT_fluid'
    variable = 'dcp_dT_var'
    execute_on = 'timestep_begin'
  []
  [dcp_dt_out]
    type = FunctorAux
    functor = 'dcp_dt'
    variable = 'cp_dot_var'
    execute_on = 'timestep_begin'
  []
  [cv_out]
    type = FunctorAux
    functor = 'cv'
    variable = 'cv_var'
    execute_on = 'timestep_begin'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'timestep_begin'
  []
  [dmu_dp_out]
    type = FunctorAux
    functor = 'dmu/dpressure'
    variable = 'dmu_dp_var'
    execute_on = 'timestep_begin'
  []
  [dmu_dT_out]
    type = FunctorAux
    functor = 'dmu/dT_fluid'
    variable = 'dmu_dT_var'
    execute_on = 'timestep_begin'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'timestep_begin'
  []
  [dk_dp_out]
    type = FunctorAux
    functor = 'dk/dpressure'
    variable = 'dk_dp_var'
    execute_on = 'timestep_begin'
  []
  [dk_dT_out]
    type = FunctorAux
    functor = 'dk/dT_fluid'
    variable = 'dk_dT_var'
    execute_on = 'timestep_begin'
  []
  [Pr_out]
    type = FunctorAux
    functor = 'Pr'
    variable = 'Pr_var'
    execute_on = 'timestep_begin'
  []
  [dPr_dp_out]
    type = FunctorAux
    functor = 'dPr/dpressure'
    variable = 'dPr_dp_var'
    execute_on = 'timestep_begin'
  []
  [dPr_dT_out]
    type = FunctorAux
    functor = 'dPr/dT_fluid'
    variable = 'dPr_dT_var'
    execute_on = 'timestep_begin'
  []
  [Re_out]
    type = FunctorAux
    functor = 'Re'
    variable = 'Re_var'
    execute_on = 'timestep_begin'
  []
  [dRe_dp_out]
    type = FunctorAux
    functor = 'dRe/dpressure'
    variable = 'dRe_dp_var'
    execute_on = 'timestep_begin'
  []
  [dRe_dT_out]
    type = FunctorAux
    functor = 'dRe/dT_fluid'
    variable = 'dRe_dT_var'
    execute_on = 'timestep_begin'
  []
  [Re_h_out]
    type = FunctorAux
    functor = 'Re_h'
    variable = 'Re_h_var'
    execute_on = 'timestep_begin'
  []
  [Re_i_out]
    type = FunctorAux
    functor = 'Re_i'
    variable = 'Re_i_var'
    execute_on = 'timestep_begin'
  []
[]

[Executioner]
  type = Transient
  end_time = 0.1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(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/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 = INSFVEnergyVariable
    initial_condition = 100
  []
[]

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

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

[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'

    mass_advection_interpolation = 'average'
    momentum_advection_interpolation = 'average'
    energy_advection_interpolation = 'average'
  []
[]

[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
    # this should use eps * k instead of k
    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}
  []
[]

[FunctorMaterials]
  [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'
    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/two_phase/mixture_interface_area_model/pressure_driven_growth_transient.i)

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

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

outlet_pressure = 1e6

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

[Problem]
  identify_variable_groups_in_nl = false
[]

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

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

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

[FVKernels]

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

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

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

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

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

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

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

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

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

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

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

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

[Debug]
  show_var_residual_norms = true
[]

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

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

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

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

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

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

outlet_pressure = 1e5

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

[Problem]
  identify_variable_groups_in_nl = false
  previous_nl_solution_required = true
[]

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

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

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

[FVKernels]

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

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

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

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

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

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

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

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

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

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

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

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

[Debug]
  show_var_residual_norms = true
[]

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

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

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

Overview
Input Parameters
Input Files