WCNSFVMomentumFluxBC

Flux boundary conditions for momentum advection.

The momentum flux is:

var element = document.getElementById("moose-equation-aec8aca7-cf9d-4e17-bb25-399fca2a0274");katex.render("\\phi = \\rho v^2 = \\dfrac{\\dot{m}^2}{\\rho A^2}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

with $var element = document.getElementById("moose-equation-fc695066-2e1e-42ec-8982-59696c4cb02f");katex.render("\\phi", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the momentum flux, $var element = document.getElementById("moose-equation-db32db8d-3431-4a23-8b64-ccd9b130c458");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the density, $var element = document.getElementById("moose-equation-106e024d-36fb-4423-bebf-dc267924f920");katex.render("v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the fluid velocity (assumed normal to the surface), $var element = document.getElementById("moose-equation-79646af8-25c0-4d51-aec3-c4b82be36ed8");katex.render("\\dot{m}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the mass flow rate and $var element = document.getElementById("moose-equation-05259fcb-9071-432a-b0d5-b094c13652ac");katex.render("A", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ the inlet area.

There are two options for specifying the momentum flux:

specifying a mass flow rate postprocessor, which is then divided by the area of the inlet, which may also be a postprocessor.
specifying an inlet velocity postprocessor and a density functor. The functor is usually a functor material property, defined by a GeneralFunctorFluidProps.

The scaling factor may be used if the inlet is not aligned with the X or Y direction, in which case a projection is necessary and this boundary condition should be used for both components of the momentum equation.

This boundary condition works with postprocessors, which may be replaced by constant values in the input. The intended use case for this boundary condition is to be receiving its value from a coupled application, using a Receiver postprocessor.

Example input syntax

In this example input, the inlet boundary condition to the momentum conservation equation is specified using a WCNSFVMomentumFluxBC. The momentum flux is specified using the mass flow rate and the inlet area.

[FVBCs<<<{"href": "../../syntax/FVBCs/index.html"}>>>]
  # Inlet
  [inlet_mass]
    type = WCNSFVMassFluxBC<<<{"description": "Flux boundary conditions for mass advection.", "href": "WCNSFVMassFluxBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = pressure
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    mdot_pp<<<{"description": "Postprocessor with the inlet mass flow rate"}>>> = 'inlet_mdot'
    area_pp<<<{"description": "Inlet area as a postprocessor"}>>> = 'area_pp_left'
    rho<<<{"description": "Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
    vel_x<<<{"description": "The x-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_x
    vel_y<<<{"description": "The y-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_y
  []
  [inlet_u]
    type = WCNSFVMomentumFluxBC<<<{"description": "Flux boundary conditions for momentum advection.", "href": "WCNSFVMomentumFluxBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = vel_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    mdot_pp<<<{"description": "Postprocessor with the inlet mass flow rate"}>>> = 'inlet_mdot'
    area_pp<<<{"description": "Inlet area as a postprocessor"}>>> = 'area_pp_left'
    rho<<<{"description": "Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
    momentum_component<<<{"description": "The component of the momentum equation that this kernel applies to."}>>> = 'x'
    vel_x<<<{"description": "The x-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_x
    vel_y<<<{"description": "The y-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_y
  []
  [inlet_v]
    type = WCNSFVMomentumFluxBC<<<{"description": "Flux boundary conditions for momentum advection.", "href": "WCNSFVMomentumFluxBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = vel_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    mdot_pp<<<{"description": "Postprocessor with the inlet mass flow rate"}>>> = 0
    area_pp<<<{"description": "Inlet area as a postprocessor"}>>> = 'area_pp_left'
    rho<<<{"description": "Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
    momentum_component<<<{"description": "The component of the momentum equation that this kernel applies to."}>>> = 'y'
    vel_x<<<{"description": "The x-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_x
    vel_y<<<{"description": "The y-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_y
  []
  [inlet_T]
    type = WCNSFVEnergyFluxBC<<<{"description": "Flux boundary conditions for energy advection.", "href": "WCNSFVEnergyFluxBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = T_fluid
    T_fluid<<<{"description": "temperature functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = T_fluid
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    temperature_pp<<<{"description": "Postprocessor with the inlet temperature"}>>> = 'inlet_T'
    mdot_pp<<<{"description": "Postprocessor with the inlet mass flow rate"}>>> = 'inlet_mdot'
    area_pp<<<{"description": "Inlet area as a postprocessor"}>>> = 'area_pp_left'
    rho<<<{"description": "Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
    cp<<<{"description": "specific heat capacity functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'cp'
    vel_x<<<{"description": "The x-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_x
    vel_y<<<{"description": "The y-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_y
  []
  [inlet_scalar]
    type = WCNSFVScalarFluxBC<<<{"description": "Flux boundary conditions for scalar quantity advection.", "href": "WCNSFVScalarFluxBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = scalar
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left'
    scalar_value_pp<<<{"description": "Postprocessor with the inlet scalar concentration"}>>> = 'inlet_scalar_value'
    mdot_pp<<<{"description": "Postprocessor with the inlet mass flow rate"}>>> = 'inlet_mdot'
    area_pp<<<{"description": "Inlet area as a postprocessor"}>>> = 'area_pp_left'
    rho<<<{"description": "Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
    vel_x<<<{"description": "The x-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_x
    vel_y<<<{"description": "The y-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = vel_y
    passive_scalar<<<{"description": "passive scalar functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = scalar
  []

  [outlet_p]
    type = INSFVOutletPressureBC<<<{"description": "Defines a Dirichlet boundary condition for finite volume method.", "href": "INSFVOutletPressureBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = pressure
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
    function<<<{"description": "The boundary pressure as a regular function"}>>> = ${outlet_pressure}
  []

  # Walls
  [no_slip_x]
    type = INSFVNoSlipWallBC<<<{"description": "Implements a no slip boundary condition.", "href": "INSFVNoSlipWallBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = vel_x
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'top bottom'
    function<<<{"description": "The exact solution function."}>>> = 0
  []
  [no_slip_y]
    type = INSFVNoSlipWallBC<<<{"description": "Implements a no slip boundary condition.", "href": "INSFVNoSlipWallBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = vel_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'top bottom'
    function<<<{"description": "The exact solution function."}>>> = 0
  []
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
momentum_componentThe component of the momentum equation that this kernel applies to.
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:The component of the momentum equation that this kernel applies to.
rhie_chow_user_objectThe rhie-chow user-object
C++ Type:UserObjectName
Controllable:No
Description:The rhie-chow user-object
rhoDensity functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this boundary condition applies to
vel_xThe x-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The x-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

Required Parameters

area_ppInlet area as a postprocessor
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Inlet area as a postprocessor
direction0 0 0The direction of the flow at the boundary. This is mainly used for cases when an inlet angle needs to be defined with respect to the normal and when a boundary is defined on an internal face where the normal can point in both directions. Use positive mass flux and velocity magnitude if the flux aligns with this direction vector.
Default:0 0 0
C++ Type:libMesh::Point
Controllable:No
Description:The direction of the flow at the boundary. This is mainly used for cases when an inlet angle needs to be defined with respect to the normal and when a boundary is defined on an internal face where the normal can point in both directions. Use positive mass flux and velocity magnitude if the flux aligns with this direction vector.
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
mdot_ppPostprocessor with the inlet mass flow rate
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor with the inlet mass flow rate
scaling_factor1To scale the mass flux
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:To scale the mass flux
vel_yThe y-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The y-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
vel_zThe z-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The z-axis velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
velocity_ppPostprocessor with the inlet velocity norm
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor with the inlet velocity norm

Optional Parameters

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

Contribution To Tagged Field Data Parameters

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

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

Material Property Retrieval Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_velocity.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/with-direction/errors/flux_bcs.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_reversal.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_mdot.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_direct.i)

Child Objects

(modules/navier_stokes/include/fvbcs/PWCNSFVMomentumFluxBC.h)

(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_mdot.i)

rho = 'rho'
l = 10
inlet_area = 1
velocity_interp_method = 'rc'
advected_interp_method = 'average'

# Artificial fluid properties
# For a real case, use a GeneralFluidFunctorProperties and a viscosity rampdown
# or initialize very well!
k = 1
cp = 1000
mu = 1e2

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = 1
    nx = 10
    ny = 5
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

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

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_velocity}
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
  []
  [T_fluid]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
  []
  [scalar]
    type = MooseVariableFVReal
    initial_condition = 0.1
  []
[]

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

[FVKernels]
  # Mass equation
  [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}
  []

  # X component momentum equation
  [u_time]
    type = WCNSFVMomentumTimeDerivative
    variable = vel_x
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  # Y component momentum equation
  [v_time]
    type = WCNSFVMomentumTimeDerivative
    variable = vel_y
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  # Energy equation
  [temp_time]
    type = WCNSFVEnergyTimeDerivative
    variable = T_fluid
    rho = rho
    drho_dt = drho_dt
    h = h
    dh_dt = dh_dt
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T_fluid
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [heat_source]
    type = FVCoupledForce
    variable = T_fluid
    v = power_density
  []

  # Scalar concentration equation
  [scalar_time]
    type = FVFunctorTimeKernel
    variable = scalar
  []
  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [scalar_diffusion]
    type = FVDiffusion
    variable = scalar
    coeff = 1.1
  []
  [scalar_source]
    type = FVBodyForce
    variable = scalar
    function = 2.1
  []
[]

[FVBCs]
  # Inlet
  [inlet_mass]
    type = WCNSFVMassFluxBC
    variable = pressure
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_u]
    type = WCNSFVMomentumFluxBC
    variable = vel_x
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'x'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_v]
    type = WCNSFVMomentumFluxBC
    variable = vel_y
    boundary = 'left'
    mdot_pp = 0
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'y'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_T]
    type = WCNSFVEnergyFluxBC
    variable = T_fluid
    T_fluid = T_fluid
    boundary = 'left'
    temperature_pp = 'inlet_T'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    cp = 'cp'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_scalar]
    type = WCNSFVScalarFluxBC
    variable = scalar
    boundary = 'left'
    scalar_value_pp = 'inlet_scalar_value'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
    passive_scalar = scalar
  []

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

  # Walls
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top bottom'
    function = 0
  []
  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'top bottom'
    function = 0
  []
[]

# used for the boundary conditions in this example
[Postprocessors]
  [inlet_mdot]
    type = Receiver
    default = ${fparse 1980 * inlet_velocity * inlet_area}
  []
  [area_pp_left]
    type = AreaPostprocessor
    boundary = 'left'
    execute_on = 'INITIAL'
  []
  [inlet_T]
    type = Receiver
    default = ${inlet_temp}
  []
  [inlet_scalar_value]
    type = Receiver
    default = 0.2
  []
[]

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

[FunctorMaterials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'cp k'
    prop_values = '${cp} ${k}'
  []
  [rho]
    type = RhoFromPTFunctorMaterial
    fp = fp
    temperature = T_fluid
    pressure = pressure
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho}
  []
[]

[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-2
    optimal_iterations = 6
  []
  end_time = 1

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

  automatic_scaling = true
[]

[Outputs]
  exodus = true
  execute_on = FINAL
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_velocity.i)

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

# Artificial fluid properties
# For a real case, use a GeneralFluidFunctorProperties and a viscosity rampdown
# or initialize very well!
k = 1
cp = 1000
mu = 1e2

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = 1
    nx = 10
    ny = 5
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

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

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_velocity}
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
  []
  [T_fluid]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
  []
  [scalar]
    type = MooseVariableFVReal
    initial_condition = 0.1
  []
[]

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

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

  [temp_time]
    type = WCNSFVEnergyTimeDerivative
    variable = T_fluid
    rho = rho
    drho_dt = drho_dt
    h = h
    dh_dt = dh_dt
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T_fluid
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [heat_source]
    type = FVCoupledForce
    variable = T_fluid
    v = power_density
  []

  # Scalar concentration equation
  [scalar_time]
    type = FVFunctorTimeKernel
    variable = scalar
  []
  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [scalar_diffusion]
    type = FVDiffusion
    variable = scalar
    coeff = 1.1
  []
  [scalar_source]
    type = FVBodyForce
    variable = scalar
    function = 2.1
  []
[]

[FVBCs]
  # Inlet
  [inlet_mass]
    type = WCNSFVMassFluxBC
    variable = pressure
    boundary = 'left'
    velocity_pp = 'inlet_u'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_u]
    type = WCNSFVMomentumFluxBC
    variable = vel_x
    boundary = 'left'
    velocity_pp = 'inlet_u'
    rho = 'rho'
    momentum_component = 'x'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_v]
    type = WCNSFVMomentumFluxBC
    variable = vel_y
    boundary = 'left'
    velocity_pp = 0
    rho = 'rho'
    momentum_component = 'y'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_T]
    type = WCNSFVEnergyFluxBC
    variable = T_fluid
    T_fluid = T_fluid
    boundary = 'left'
    velocity_pp = 'inlet_u'
    temperature_pp = 'inlet_T'
    rho = 'rho'
    cp = 'cp'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_scalar]
    type = WCNSFVScalarFluxBC
    variable = scalar
    boundary = 'left'
    scalar_value_pp = 'inlet_scalar_value'
    velocity_pp = 'inlet_u'
    vel_x = vel_x
    vel_y = vel_y
    rho = rho
    passive_scalar = scalar
  []

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

  # Walls
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top bottom'
    function = 0
  []
  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'top bottom'
    function = 0
  []
[]

# used for the boundary conditions in this example
[Postprocessors]
  [inlet_u]
    type = Receiver
    default = ${inlet_velocity}
  []
  [area_pp_left]
    type = AreaPostprocessor
    boundary = 'left'
    execute_on = 'INITIAL'
  []
  [inlet_T]
    type = Receiver
    default = ${inlet_temp}
  []
  [inlet_scalar_value]
    type = Receiver
    default = 0.2
  []
[]

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

[FunctorMaterials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'cp k'
    prop_values = '${cp} ${k}'
  []
  [rho]
    type = RhoFromPTFunctorMaterial
    fp = fp
    temperature = T_fluid
    pressure = pressure
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho}
  []
[]

[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-2
    optimal_iterations = 6
  []
  end_time = 1

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

  automatic_scaling = true
[]

[Outputs]
  exodus = true
  execute_on = FINAL
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/with-direction/errors/flux_bcs.i)

l = 5
inlet_area = 2
velocity_interp_method = 'rc'
advected_interp_method = 'average'

# Artificial fluid properties
# For a real case, use a GeneralFluidFunctorProperties and a viscosity rampdown
# or initialize very well!
k = 1
cp = 1000
mu = 1e2
rho = 1000

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

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${l} ${l}'
    dy = '${inlet_area}'
    ix = '5 5'
    iy = '2'
    subdomain_id = '1 2'
  []
  [side_set]
    type = SideSetsBetweenSubdomainsGenerator
    input = gen
    primary_block = '1'
    paired_block = '2'
    new_boundary = 'mid-inlet'
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = vel_x
    v = vel_y
    pressure = pressure
    block = 2
  []
[]

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_velocity}
    block = 2
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
    block = 2
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
    block = 2
  []
  [T_fluid]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
    block = 2
  []
  [scalar]
    type = MooseVariableFVReal
    initial_condition = 0.1
    block = 2
  []
  [T_solid]
    type = MooseVariableFVReal
    initial_condition = ${inlet_temp}
  []
[]

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

[FVKernels]
  # Mass equation
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []

  # X component momentum equation
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  # Y component momentum equation
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  # Energy equation
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T_fluid
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [heat_source]
    type = FVCoupledForce
    variable = T_fluid
    v = power_density
  []

  # Scalar concentration equation
  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [scalar_diffusion]
    type = FVDiffusion
    variable = scalar
    coeff = 1.1
  []
  [scalar_source]
    type = FVBodyForce
    variable = scalar
    function = 2.1
  []

  # Solid temperature
  [solid_temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T_solid
  []
[]

[FVBCs]
  # Inlet
  [inlet_mass]
    type = WCNSFVMassFluxBC
    variable = pressure
    boundary = 'mid-inlet'
    velocity_pp = 'inlet_velocity'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_u]
    type = WCNSFVMomentumFluxBC
    variable = vel_x
    boundary = 'mid-inlet'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'x'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_v]
    type = WCNSFVMomentumFluxBC
    variable = vel_y
    boundary = 'mid-inlet'
    mdot_pp = 0
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'y'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_T]
    type = WCNSFVEnergyFluxBC
    variable = T_fluid
    T_fluid = T_fluid
    boundary = 'mid-inlet'
    temperature_pp = 'inlet_T'
    velocity_pp = 'inlet_velocity'
    area_pp = 'area_pp_left'
    rho = 'rho'
    cp = 'cp'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_scalar]
    type = WCNSFVScalarFluxBC
    variable = scalar
    boundary = 'mid-inlet'
    scalar_value_pp = 'inlet_scalar_value'
    velocity_pp = 'inlet_velocity'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
    passive_scalar = scalar
  []

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

  # Walls
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top bottom'
    function = 0
  []
  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'top bottom'
    function = 0
  []
[]

# used for the boundary conditions in this example
[Postprocessors]
  [inlet_mdot]
    type = Receiver
    default = '${fparse 1980 * inlet_velocity * inlet_area}'
  []
  [inlet_velocity]
    type = Receiver
    default = ${inlet_velocity}
  []
  [area_pp_left]
    type = AreaPostprocessor
    boundary = 'left'
    execute_on = 'INITIAL'
  []
  [inlet_T]
    type = Receiver
    default = ${inlet_temp}
  []
  [inlet_scalar_value]
    type = Receiver
    default = 0.2
  []
[]

[FunctorMaterials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'cp k rho'
    prop_values = '${cp} ${k} ${rho}'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho}
  []
[]

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

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

  automatic_scaling = true
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_reversal.i)

rho = 'rho'
l = 10
inlet_area = 1
velocity_interp_method = 'rc'
advected_interp_method = 'average'

# Artificial fluid properties
# For a real case, use a GeneralFluidFunctorProperties and a viscosity rampdown
# or initialize very well!
k = 1
cp = 1000
mu = 1e2

# Operating conditions
inlet_temp = 300
outlet_pressure = 1e5
inlet_velocity = 0.1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = 1
    nx = 6
    ny = 3
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

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

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_velocity}
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
  []
  [T_fluid]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
  []
  [scalar]
    type = MooseVariableFVReal
    initial_condition = 0.1
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[AuxVariables]
  [power_density]
    type = MooseVariableFVReal
    initial_condition = 1e6
  []
[]

[FVKernels]
  # Mass equation
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVIntegralValueConstraint
    variable = pressure
    lambda = lambda
    phi0 = 0.0
  []

  # X component momentum equation
  [u_time]
    type = WCNSFVMomentumTimeDerivative
    variable = vel_x
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  # Y component momentum equation
  [v_time]
    type = WCNSFVMomentumTimeDerivative
    variable = vel_y
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  # Energy equation
  [temp_time]
    type = WCNSFVEnergyTimeDerivative
    variable = T_fluid
    rho = rho
    drho_dt = drho_dt
    dh_dt = dh_dt
    h = h
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T_fluid
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [heat_source]
    type = FVCoupledForce
    variable = T_fluid
    v = power_density
  []

  # Scalar concentration equation
  [scalar_time]
    type = FVFunctorTimeKernel
    variable = scalar
  []
  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [scalar_diffusion]
    type = FVDiffusion
    variable = scalar
    coeff = 1.1
  []
  [scalar_source]
    type = FVBodyForce
    variable = scalar
    function = 2.1
  []
[]

[FVBCs]
  # Inlet
  [inlet_mass]
    type = WCNSFVMassFluxBC
    variable = pressure
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_u]
    type = WCNSFVMomentumFluxBC
    variable = vel_x
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'x'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_v]
    type = WCNSFVMomentumFluxBC
    variable = vel_y
    boundary = 'left'
    mdot_pp = 0
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'y'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_T]
    type = WCNSFVEnergyFluxBC
    variable = T_fluid
    T_fluid = T_fluid
    boundary = 'left'
    temperature_pp = 'inlet_T'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    cp = 'cp'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_scalar]
    type = WCNSFVScalarFluxBC
    variable = scalar
    boundary = 'left'
    scalar_value_pp = 'inlet_scalar_value'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
    passive_scalar = scalar
  []

  [outlet_mass]
    type = WCNSFVMassFluxBC
    variable = pressure
    boundary = 'right'
    mdot_pp = 'outlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
  []

  [outlet_u]
    type = WCNSFVMomentumFluxBC
    variable = vel_x
    boundary = 'right'
    mdot_pp = 'outlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'x'
    vel_x = vel_x
    vel_y = vel_y
  []
  [outlet_v]
    type = WCNSFVMomentumFluxBC
    variable = vel_y
    boundary = 'right'
    mdot_pp = 0
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'y'
    vel_x = vel_x
    vel_y = vel_y
  []

  [outlet_T]
    type = WCNSFVEnergyFluxBC
    variable = T_fluid
    T_fluid = T_fluid
    boundary = 'right'
    temperature_pp = 'inlet_T'
    mdot_pp = 'outlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    cp = 'cp'
    vel_x = vel_x
    vel_y = vel_y
  []

  [outlet_scalar]
    type = WCNSFVScalarFluxBC
    variable = scalar
    boundary = 'right'
    scalar_value_pp = 'inlet_scalar_value'
    mdot_pp = 'outlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
    passive_scalar = scalar
  []

  # Walls
  [no_slip_x]
    type = INSFVNaturalFreeSlipBC
    variable = vel_x
    momentum_component = x
    boundary = 'top bottom'
  []
  [no_slip_y]
    type = INSFVNaturalFreeSlipBC
    variable = vel_y
    momentum_component = y
    boundary = 'top bottom'
  []
[]

# used for the boundary conditions in this example
[Postprocessors]
  [inlet_mdot]
    type = Receiver
    default = ${fparse 1980 * inlet_velocity * inlet_area}
    #outputs = none
  []
  [outlet_mdot]
    type = Receiver
    default = ${fparse -1980 * inlet_velocity * inlet_area}
    outputs = none
  []
  [area_pp_left]
    type = AreaPostprocessor
    boundary = 'left'
    execute_on = 'INITIAL'
    outputs = none
  []
  [inlet_T]
    type = Receiver
    default = ${inlet_temp}
    outputs = none
  []
  [inlet_scalar_value]
    type = Receiver
    default = 0.2
    outputs = none
  []

  [left_mdot]
    type = VolumetricFlowRate
    vel_x = vel_x
    vel_y = vel_y
    advected_quantity = rho
    boundary = left
    #advected_interp_method = ${advected_interp_method}
  []

  [right_mdot]
    type = VolumetricFlowRate
    vel_x = vel_x
    vel_y = vel_y
    advected_quantity = rho
    boundary = right
    advected_interp_method = upwind #${advected_interp_method}
  []
[]

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

[FunctorMaterials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'cp k rho'
    prop_values = '${cp} ${k} 1980'
  []
  #[rho]
  #  type = RhoFromPTFunctorMaterial
  #  fp = fp
  #  temperature = T_fluid
  #  pressure = pressure
  #[]
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho}
  []
[]

[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-1
    optimal_iterations = 6
    growth_factor = 4
  []
  end_time = 500000

  nl_abs_tol = 1e-7
  nl_max_its = 50
  line_search = 'none'

  automatic_scaling = true
[]

[Outputs]
  exodus = true
  execute_on = FINAL
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_mdot.i)

rho = 'rho'
l = 10
inlet_area = 1
velocity_interp_method = 'rc'
advected_interp_method = 'average'

# Artificial fluid properties
# For a real case, use a GeneralFluidFunctorProperties and a viscosity rampdown
# or initialize very well!
k = 1
cp = 1000
mu = 1e2

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = 1
    nx = 10
    ny = 5
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

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

[Variables]
  [vel_x]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_velocity}
  []
  [vel_y]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
  []
  [T_fluid]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
  []
  [scalar]
    type = MooseVariableFVReal
    initial_condition = 0.1
  []
[]

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

[FVKernels]
  # Mass equation
  [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}
  []

  # X component momentum equation
  [u_time]
    type = WCNSFVMomentumTimeDerivative
    variable = vel_x
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = vel_x
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_x
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = vel_x
    momentum_component = 'x'
    pressure = pressure
  []

  # Y component momentum equation
  [v_time]
    type = WCNSFVMomentumTimeDerivative
    variable = vel_y
    drho_dt = drho_dt
    rho = rho
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = vel_y
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = vel_y
    momentum_component = 'y'
    pressure = pressure
  []

  # Energy equation
  [temp_time]
    type = WCNSFVEnergyTimeDerivative
    variable = T_fluid
    rho = rho
    drho_dt = drho_dt
    h = h
    dh_dt = dh_dt
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T_fluid
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T_fluid
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [heat_source]
    type = FVCoupledForce
    variable = T_fluid
    v = power_density
  []

  # Scalar concentration equation
  [scalar_time]
    type = FVFunctorTimeKernel
    variable = scalar
  []
  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [scalar_diffusion]
    type = FVDiffusion
    variable = scalar
    coeff = 1.1
  []
  [scalar_source]
    type = FVBodyForce
    variable = scalar
    function = 2.1
  []
[]

[FVBCs]
  # Inlet
  [inlet_mass]
    type = WCNSFVMassFluxBC
    variable = pressure
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_u]
    type = WCNSFVMomentumFluxBC
    variable = vel_x
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'x'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_v]
    type = WCNSFVMomentumFluxBC
    variable = vel_y
    boundary = 'left'
    mdot_pp = 0
    area_pp = 'area_pp_left'
    rho = 'rho'
    momentum_component = 'y'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_T]
    type = WCNSFVEnergyFluxBC
    variable = T_fluid
    T_fluid = T_fluid
    boundary = 'left'
    temperature_pp = 'inlet_T'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    cp = 'cp'
    vel_x = vel_x
    vel_y = vel_y
  []
  [inlet_scalar]
    type = WCNSFVScalarFluxBC
    variable = scalar
    boundary = 'left'
    scalar_value_pp = 'inlet_scalar_value'
    mdot_pp = 'inlet_mdot'
    area_pp = 'area_pp_left'
    rho = 'rho'
    vel_x = vel_x
    vel_y = vel_y
    passive_scalar = scalar
  []

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

  # Walls
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = vel_x
    boundary = 'top bottom'
    function = 0
  []
  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = vel_y
    boundary = 'top bottom'
    function = 0
  []
[]

# used for the boundary conditions in this example
[Postprocessors]
  [inlet_mdot]
    type = Receiver
    default = ${fparse 1980 * inlet_velocity * inlet_area}
  []
  [area_pp_left]
    type = AreaPostprocessor
    boundary = 'left'
    execute_on = 'INITIAL'
  []
  [inlet_T]
    type = Receiver
    default = ${inlet_temp}
  []
  [inlet_scalar_value]
    type = Receiver
    default = 0.2
  []
[]

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

[FunctorMaterials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'cp k'
    prop_values = '${cp} ${k}'
  []
  [rho]
    type = RhoFromPTFunctorMaterial
    fp = fp
    temperature = T_fluid
    pressure = pressure
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T_fluid'
    rho = ${rho}
  []
[]

[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-2
    optimal_iterations = 6
  []
  end_time = 1

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

  automatic_scaling = true
[]

[Outputs]
  exodus = true
  execute_on = FINAL
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/boundary_conditions/flux_bcs_direct.i)

rho = 'rho'
l = 10
inlet_area = 1
velocity_interp_method = 'rc'
advected_interp_method = 'average'

# Artificial fluid properties
# For a real case, use a GeneralFluidFunctorProperties and a viscosity rampdown
# or initialize very well!
k = 1
cp = 1000
mu = 1e2

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

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = 1
    nx = 10
    ny = 5
  []
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

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

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = ${inlet_velocity}
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${outlet_pressure}
  []
  [T]
    type = INSFVEnergyVariable
    initial_condition = ${inlet_temp}
  []
  [scalar]
    type = MooseVariableFVReal
    initial_condition = 0.1
  []
[]

[AuxVariables]
  [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
  []

  # Scalar concentration equation
  [scalar_time]
    type = FVFunctorTimeKernel
    variable = scalar
  []
  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
  [scalar_diffusion]
    type = FVDiffusion
    variable = scalar
    coeff = 1.1
  []
  [scalar_source]
    type = FVBodyForce
    variable = scalar
    function = 2.1
  []
[]

[FVBCs]
  # Inlet
  [inlet_mass]
    type = WCNSFVMassFluxBC
    variable = pressure
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'surface_inlet'
    vel_x = u
    vel_y = v
    rho = 'rho'
  []
  [inlet_u]
    type = WCNSFVMomentumFluxBC
    variable = u
    boundary = 'left'
    mdot_pp = 'inlet_mdot'
    area_pp = 'surface_inlet'
    rho = 'rho'
    momentum_component = 'x'
    vel_x = u
    vel_y = v
  []
  [inlet_v]
    type = WCNSFVMomentumFluxBC
    variable = v
    boundary = 'left'
    mdot_pp = 0
    area_pp = 'surface_inlet'
    rho = 'rho'
    momentum_component = 'y'
    vel_x = u
    vel_y = v
  []
  [inlet_T]
    type = WCNSFVEnergyFluxBC
    variable = T
    T_fluid = T
    boundary = 'left'
    energy_pp = 'inlet_Edot'
    area_pp = 'surface_inlet'
    vel_x = u
    vel_y = v
    rho = 'rho'
    cp = cp
  []
  [inlet_scalar]
    type = WCNSFVScalarFluxBC
    variable = scalar
    boundary = 'left'
    scalar_flux_pp = 'inlet_scalar_flux'
    area_pp = 'surface_inlet'
    vel_x = u
    vel_y = v
    rho = 'rho'
    passive_scalar = scalar
  []

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

  # Walls
  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top bottom'
    function = 0
  []
  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'top bottom'
    function = 0
  []
[]

# used for the boundary conditions in this example
[Postprocessors]
  [inlet_mdot]
    type = Receiver
    default = ${fparse 1980 * inlet_velocity * inlet_area}
  []
  [surface_inlet]
    type = AreaPostprocessor
    boundary = 'left'
    execute_on = 'INITIAL'
  []
  [inlet_Edot]
    type = Receiver
    default = ${fparse 1980 * inlet_velocity * 2530 * inlet_temp * inlet_area}
  []
  [inlet_scalar_flux]
    type = Receiver
    default = ${fparse inlet_velocity * 0.2 * inlet_area}
  []
[]

[FluidProperties]
  [fp]
    type = SimpleFluidProperties
    density0 = 1980
    cp = 2530
  []
[]

[FunctorMaterials]
  [const_functor]
    type = ADGenericFunctorMaterial
    prop_names = 'cp k'
    prop_values = '${cp} ${k}'
  []
  [rho]
    type = RhoFromPTFunctorMaterial
    fp = fp
    temperature = T
    pressure = pressure
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T'
    rho = ${rho}
  []
[]

[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-2
    optimal_iterations = 6
  []
  end_time = 1

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

  automatic_scaling = true
[]

[Outputs]
  exodus = true
  execute_on = FINAL
[]

(modules/navier_stokes/include/fvbcs/PWCNSFVMomentumFluxBC.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "WCNSFVMomentumFluxBC.h"

/**
 * Flux boundary conditions for the porous weakly compressible momentum equation
 */
class PWCNSFVMomentumFluxBC : public WCNSFVMomentumFluxBC
{
public:
  static InputParameters validParams();
  PWCNSFVMomentumFluxBC(const InputParameters & params);

protected:
  ADReal computeQpResidual() override;

  /// Porosity functor
  const Moose::Functor<ADReal> & _eps;
};

Example input syntax
Input Parameters
Input Files
Child Objects