Navier Stokes Flow / WCNSFVFlowPhysics

Define the Navier Stokes weakly-compressible mass and momentum equations

Equations

This Physics object creates the kernels and boundary conditions to solve the mass and momentum Navier Stokes equations for the flow. The time derivatives in the mass equations are omitted for incompressible flow. For regular flow in a non-porous medium:

var element = document.getElementById("moose-equation-6ba25a24-2d6e-422b-91fc-3b15ee91f317");katex.render("\\dfrac{\\partial \\rho}{\\partial t} + \\nabla \\cdot \\rho \\vec{v} = 0", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-f36fd8d6-b14c-484d-8bf5-4fc1ed56d53b");katex.render("\\dfrac{\\partial \\rho \\mathbf{v}}{\\partial t} + \\nabla \\cdot (\\rho \\mathbf{v} \\otimes \\mathbf{v}) = \\nabla \\cdot (\\mu \\nabla \\mathbf{v}) - \\nabla p + (\\mathbf{F}_g + \\mathbf{F}_f)", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

For porous media flow:

var element = document.getElementById("moose-equation-b6da438b-1e33-48b2-9bf7-42500bce06e1");katex.render("\\epsilon \\dfrac{\\partial \\rho}{\\partial t} + \\nabla \\cdot \\rho \\vec{v}_D = 0", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-bc4cc27d-5faf-402c-a0c7-550036c02a10");katex.render("\\dfrac{\\partial \\rho \\mathbf{v}_D}{\\partial t} + \\nabla \\cdot (\\dfrac{\\rho}{\\epsilon} \\mathbf{v}_D \\otimes \\mathbf{v}_D) = \\nabla \\cdot (\\mu \\nabla \\dfrac{\\mathbf{v}_D}{\\epsilon}) - \\epsilon \\nabla p + \\epsilon (\\mathbf{F}_g + \\mathbf{F}_f)", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where:

$var element = document.getElementById("moose-equation-032a4dc5-8259-42dd-98c4-4784bfa1bd02");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the density
$var element = document.getElementById("moose-equation-1658171d-dc6e-4315-8ef9-894a7cda1016");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the dynamic viscosity
$var element = document.getElementById("moose-equation-3ba37a6b-9dd5-4099-9263-fb963e81cf86");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the porosity
$var element = document.getElementById("moose-equation-c702eb2b-31c3-4e77-9811-9b30938639a1");katex.render("\\mathbf{v}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the velocity (non-porous flow)
$var element = document.getElementById("moose-equation-9cb2ddde-07cb-4ab8-99a6-66f0f29ecbce");katex.render("\\mathbf{v}_D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the superficial velocity (porous flow)
$var element = document.getElementById("moose-equation-2c0cc298-1f50-4154-8051-cb1a7019e5ff");katex.render("p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the pressure
$var element = document.getElementById("moose-equation-9c469cef-ba78-44b2-acad-03e5615812bd");katex.render("\\mathbf{F}_g", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the gravity term
$var element = document.getElementById("moose-equation-9f205afe-ffca-40a7-8a7a-1405343e7a20");katex.render("\\mathbf{F}_f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the friction / inter-phase friction term

note

Additional details on porous media flow equations can be found on this page.

The kernels created for free flow for the mass equation:

WCNSFVMassTimeDerivative for weakly-compressible flow in a transient case
INSFVMassAdvection for the mass advection term

for porous media flow:

PWCNSFVMassTimeDerivative for weakly-compressible flow
PINSFVMassAdvection for mass advection

The kernels created for the momentum equation for free flow:

WCNSFVMomentumTimeDerivative for the time derivative for weakly-compressible flow in a transient case
INSFVMomentumTimeDerivative for the time derivative incompressible flow in a transient case
INSFVMomentumAdvection for the momentum advection term
INSFVMomentumDiffusion for the momentum diffusion term
INSFVMomentumPressure for the pressure gradient term
PINSFVMomentumFriction for the friction term if specified
INSFVMomentumGravity for the gravity term if specified

for porous media flow:

PINSFVMomentumTimeDerivative for the time derivative
PINSFVMomentumAdvection for the momentum advection term
PINSFVMomentumDiffusion for the momentum diffusion term
PINSFVMomentumPressure for the pressure gradient term
PINSFVMomentumFriction for the friction term if specified
PINSFVMomentumGravity for the gravity term if specified

Automatically defined variables

The WCNSFVFlowPhysics automatically sets up the variables which are necessary for the solution of a given problem. These variables can then be used to couple fluid flow simulations with other physics. The list of variable names commonly used in the action syntax is presented below:

Velocities for non-porous-medium simulations:

static const std::string velocity_x = "vel_x";
static const std::string velocity_y = "vel_y";
static const std::string velocity_z = "vel_z";

Velocities for porous medium simulations:

static const std::string superficial_velocity_x = "superficial_vel_x";
static const std::string superficial_velocity_y = "superficial_vel_y";
static const std::string superficial_velocity_z = "superficial_vel_z";

Pressure:

static const std::string total_pressure = "pressure_total";

For the default names of other variables used in this action, visit this site.

Coupling with other Physics

The energy advection equation can be solved concurrently with the flow equations using an additional Navier Stokes Fluid Heat Transfer / WCNSFVFluidHeatTransferPhysics. The following input performs this coupling for incompressible flow in a 2D flow channel. No system parameters are passed, so the equations are solved in a fully coupled manner in the same nonlinear system.

[Physics<<<{"href": "../../syntax/Physics/index.html"}>>>]
  [NavierStokes<<<{"href": "../../syntax/Physics/NavierStokes/index.html"}>>>]
    [Flow<<<{"href": "../../syntax/Physics/NavierStokes/Flow/index.html"}>>>]
      [flow]
        compressibility<<<{"description": "Compressibility constraint for the Navier-Stokes equations."}>>> = 'incompressible'

        density<<<{"description": "The name of the density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
        dynamic_viscosity<<<{"description": "The name of the dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'mu'

        initial_velocity<<<{"description": "The initial velocity, assumed constant everywhere"}>>> = '${u_inlet} 1e-12 0'
        initial_pressure<<<{"description": "The initial pressure, assumed constant everywhere"}>>> = 0.0

        inlet_boundaries<<<{"description": "Names of inlet boundaries"}>>> = 'left'
        momentum_inlet_types<<<{"description": "Types of inlet boundaries for the momentum equation."}>>> = 'fixed-velocity'
        momentum_inlet_function = '${u_inlet} 0'
        wall_boundaries<<<{"description": "Names of wall boundaries"}>>> = 'bottom top'
        momentum_wall_types<<<{"description": "Types of wall boundaries for the momentum equation"}>>> = 'symmetry noslip'

        outlet_boundaries<<<{"description": "Names of outlet boundaries"}>>> = 'right'
        momentum_outlet_types<<<{"description": "Types of outlet boundaries for the momentum equation"}>>> = 'fixed-pressure-zero-gradient'
        pressure_function = '${p_outlet}'

        mass_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating density, as an advected quantity, to the face."}>>> = 'average'
        momentum_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating momentum/velocity, as an advected quantity, to the face."}>>> = 'average'
      []
    []

    [FluidHeatTransfer<<<{"href": "../../syntax/Physics/NavierStokes/FluidHeatTransfer/index.html"}>>>]
      [heat]
        thermal_conductivity<<<{"description": "The name of the fluid thermal conductivity for each block. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'k'
        specific_heat<<<{"description": "The name of the specific heat. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'cp'

        fluid_temperature_variable<<<{"description": "Name of the fluid temperature variable"}>>> = 'T_fluid'
        initial_temperature<<<{"description": "The initial temperature, assumed constant everywhere"}>>> = '${T_inlet}'
        energy_inlet_types<<<{"description": "Types for the inlet boundaries for the energy equation."}>>> = 'heatflux'
        energy_inlet_functors<<<{"description": "Functions for fixed-value boundaries in the energy equation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = '${fparse u_inlet * rho * cp * T_inlet}'

        energy_wall_types<<<{"description": "Types for the wall boundaries for the energy equation."}>>> = 'heatflux heatflux'
        energy_wall_functors<<<{"description": "Functions for Dirichlet/Neumann boundaries in the energy equation. For wall types requiring multiple functions, the syntax is <function_1>:<function_2>:... So, 'convection' types are '<Tinf_function>:<htc_function>'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = '0 0'

        ambient_convection_alpha<<<{"description": "The heat exchange coefficients for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'h_cv'
        ambient_temperature<<<{"description": "The ambient temperature for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'T_solid'

        energy_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating energy/temperature, as an advected quantity, to the face."}>>> = 'average'
      []
    []
  []
[]

Other advected scalar equations can be solved concurrently with the flow equations using an additional Navier Stokes Scalar Transport / WCNSFVScalarTransportPhysics. The following input performs this coupling for incompressible flow in a 2D flow channel. No system parameters are passed, so the equations are solved in a fully coupled manner in the same nonlinear system.

[Physics<<<{"href": "../../syntax/Physics/index.html"}>>>]
  [NavierStokes<<<{"href": "../../syntax/Physics/NavierStokes/index.html"}>>>]
    [Flow<<<{"href": "../../syntax/Physics/NavierStokes/Flow/index.html"}>>>]
      [flow]
        compressibility<<<{"description": "Compressibility constraint for the Navier-Stokes equations."}>>> = 'incompressible'

        density<<<{"description": "The name of the density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${rho}
        dynamic_viscosity<<<{"description": "The name of the dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${mu}

        inlet_boundaries<<<{"description": "Names of inlet boundaries"}>>> = 'left'
        momentum_inlet_types<<<{"description": "Types of inlet boundaries for the momentum equation."}>>> = 'fixed-velocity'
        momentum_inlet_function = '1 0'

        wall_boundaries<<<{"description": "Names of wall boundaries"}>>> = 'top bottom'
        momentum_wall_types<<<{"description": "Types of wall boundaries for the momentum equation"}>>> = 'noslip noslip'

        outlet_boundaries<<<{"description": "Names of outlet boundaries"}>>> = 'right'
        momentum_outlet_types<<<{"description": "Types of outlet boundaries for the momentum equation"}>>> = 'fixed-pressure'
        pressure_function = '0'

        mass_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating density, as an advected quantity, to the face."}>>> = 'average'
        momentum_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating momentum/velocity, as an advected quantity, to the face."}>>> = 'average'
      []
    []
    [FluidHeatTransfer<<<{"href": "../../syntax/Physics/NavierStokes/FluidHeatTransfer/index.html"}>>>]
      [heat]
        thermal_conductivity<<<{"description": "The name of the fluid thermal conductivity for each block. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${k}
        specific_heat<<<{"description": "The name of the specific heat. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${cp}

        energy_inlet_types<<<{"description": "Types for the inlet boundaries for the energy equation."}>>> = 'fixed-temperature'
        energy_inlet_function = '1'

        energy_wall_types<<<{"description": "Types for the wall boundaries for the energy equation."}>>> = 'heatflux heatflux'
        energy_wall_function = '0 0'

        energy_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating energy/temperature, as an advected quantity, to the face."}>>> = 'average'
      []
    []

    [ScalarTransport<<<{"href": "../../syntax/Physics/NavierStokes/ScalarTransport/index.html"}>>>]
      [heat]
        passive_scalar_names<<<{"description": "Vector containing the names of the advected scalar variables."}>>> = 'scalar'

        passive_scalar_diffusivity<<<{"description": "Functor names for the diffusivities used for the passive scalar fields. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${diff}
        passive_scalar_source<<<{"description": "Passive scalar sources. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 0.1
        passive_scalar_coupled_source<<<{"description": "Coupled variable names for the sources used for the passive scalar fields. If multiple sources for each equation are specified, major (outer) ordering by equation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = U
        passive_scalar_coupled_source_coeff<<<{"description": "Coupled variable multipliers for the sources used for the passive scalar fields. If multiple sources for each equation are specified, major (outer) ordering by equation."}>>> = 0.1

        passive_scalar_inlet_types<<<{"description": "Types for the inlet boundaries for the passive scalar equation."}>>> = 'fixed-value'
        passive_scalar_inlet_function = '1'

        passive_scalar_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating passive scalar field, as an advected quantity, to the face."}>>> = 'average'
      []
    []
  []
[]

Modeling options and implementation details

note

This physics only supports Rhie-Chow interpolation for the determination of face velocities in the advection terms. The face interpolation of the advected quantities (e.g. upwind, average) can be controlled through the *_advection_interpolation physics parameters.

Bernoulli pressure jump treatment

Please see the Bernoulli pressure variable documentation for more information.

Input Parameters

add_flow_equationsTrueWhether to add the flow equations. This parameter is not necessary when using the Physics syntax
Default:True
C++ Type:bool
Controllable:No
Description:Whether to add the flow equations. This parameter is not necessary when using the Physics syntax
blockBlocks (subdomains) that this Physics is active on.
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:Blocks (subdomains) that this Physics is active on.
compressibilityincompressibleCompressibility constraint for the Navier-Stokes equations.
Default:incompressible
C++ Type:MooseEnum
Options:incompressible, weakly-compressible
Controllable:No
Description:Compressibility constraint for the Navier-Stokes equations.
density_for_gravity_termsIf specified, replaces the 'density' for the Boussinesq and gravity momentum kernels. 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:If specified, replaces the 'density' for the Boussinesq and gravity momentum kernels. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
fluid_temperature_variableIf supplied, the system checks for available fluid temperature variable. Otherwise, it is created within the action.
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:If supplied, the system checks for available fluid temperature variable. Otherwise, it is created within the action.
hydraulic_separator_sidesetsSidesets which serve as hydraulic separators.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Sidesets which serve as hydraulic separators.
porosityporosityThe name of the auxiliary variable for the porosity field. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
Default:porosity
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the auxiliary variable for the porosity field. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
porous_medium_treatmentFalseWhether to use porous medium kernels or not.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use porous medium kernels or not.
solve_for_dynamic_pressureFalseWhether to solve for the dynamic pressure instead of the total pressure
Default:False
C++ Type:bool
Controllable:No
Description:Whether to solve for the dynamic pressure instead of the total pressure
system_namesnl0 Name of the solver system(s) for the variables. If a single name is specified, that system is used for all solver variables.
Default:nl0
C++ Type:std::vector<SolverSystemName>
Controllable:No
Description:Name of the solver system(s) for the variables. If a single name is specified, that system is used for all solver variables.
transientsame_as_problemWhether the physics is to be solved as a transient
Default:same_as_problem
C++ Type:MooseEnum
Options:true, false, same_as_problem
Controllable:No
Description:Whether the physics is to be solved as a transient
verboseFalseFlag to facilitate debugging a Physics
Default:False
C++ Type:bool
Controllable:No
Description:Flag to facilitate debugging a Physics

Optional Parameters

active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified only the blocks named will be visited and made active
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.
define_variablesTrueWhether to define variables if the variables with the specified names do not exist. Note that if the variables are defined externally from the Physics, the initial conditions will not be created in the Physics either.
Default:True
C++ Type:bool
Controllable:No
Description:Whether to define variables if the variables with the specified names do not exist. Note that if the variables are defined externally from the Physics, the initial conditions will not be created in the Physics either.
ghost_layers2Number of layers of elements to ghost near process domain boundaries
Default:2
C++ Type:unsigned short
Controllable:No
Description:Number of layers of elements to ghost near process domain boundaries
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.

Advanced Parameters

boussinesq_approximationFalseTrue to have Boussinesq approximation
Default:False
C++ Type:bool
Controllable:No
Description:True to have Boussinesq approximation
gravity0 0 0The gravitational acceleration vector.
Default:0 0 0
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:The gravitational acceleration vector.
ref_temperature273.15Value for reference temperature in case of Boussinesq approximation
Default:273.15
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Value for reference temperature in case of Boussinesq approximation
thermal_expansionalphaThe name of the thermal expansion coefficient in the Boussinesq approximation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
Default:alpha
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the thermal expansion coefficient in the Boussinesq approximation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

Gravity Treatment Parameters

characteristic_speedThe characteristic speed. For porous medium simulations, this characteristic speed should correspond to the superficial velocity, not the interstitial.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The characteristic speed. For porous medium simulations, this characteristic speed should correspond to the superficial velocity, not the interstitial.
include_deviatoric_stressFalseWhether to include the full expansion (the transposed term as well) of the stress tensor
Default:False
C++ Type:bool
Controllable:No
Description:Whether to include the full expansion (the transposed term as well) of the stress tensor
mass_advection_interpolationupwindThe numerical scheme to use for interpolating density, as an advected quantity, to the face.
Default:upwind
C++ Type:MooseEnum
Options:average, upwind, sou, min_mod, vanLeer, quick, venkatakrishnan, skewness-corrected
Controllable:No
Description:The numerical scheme to use for interpolating density, as an advected quantity, to the face.
mass_scaling1The scaling factor for the mass variables (for incompressible simulation this is pressure scaling).
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor for the mass variables (for incompressible simulation this is pressure scaling).
momentum_advection_interpolationupwindThe numerical scheme to use for interpolating momentum/velocity, as an advected quantity, to the face.
Default:upwind
C++ Type:MooseEnum
Options:average, upwind, sou, min_mod, vanLeer, quick, venkatakrishnan, skewness-corrected
Controllable:No
Description:The numerical scheme to use for interpolating momentum/velocity, as an advected quantity, to the face.
momentum_face_interpolationaverageThe numerical scheme to interpolate the velocity/momentum to the face (separate from the advected quantity interpolation).
Default:average
C++ Type:MooseEnum
Options:average, skewness-corrected
Controllable:No
Description:The numerical scheme to interpolate the velocity/momentum to the face (separate from the advected quantity interpolation).
momentum_scaling1The scaling factor for the momentum variables.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor for the momentum variables.
momentum_two_term_bc_expansionTrueIf a two-term Taylor expansion is needed for the determination of the boundary valuesof the velocity/momentum.
Default:True
C++ Type:bool
Controllable:No
Description:If a two-term Taylor expansion is needed for the determination of the boundary valuesof the velocity/momentum.
mu_interp_methodharmonicSwitch that can select face interpolation method for the viscosity.
Default:harmonic
C++ Type:MooseEnum
Options:average, harmonic
Controllable:No
Description:Switch that can select face interpolation method for the viscosity.
preconditioningdeferWhich preconditioning to use/add for this Physics, or whether to defer to the Preconditioning block, or another Physics
Default:defer
C++ Type:MooseEnum
Options:default, defer
Controllable:No
Description:Which preconditioning to use/add for this Physics, or whether to defer to the Preconditioning block, or another Physics
pressure_face_interpolationaverageThe numerical scheme to interpolate the pressure to the face (separate from the advected quantity interpolation).
Default:average
C++ Type:MooseEnum
Options:average, skewness-corrected
Controllable:No
Description:The numerical scheme to interpolate the pressure to the face (separate from the advected quantity interpolation).
pressure_two_term_bc_expansionTrueIf a two-term Taylor expansion is needed for the determination of the boundary valuesof the pressure.
Default:True
C++ Type:bool
Controllable:No
Description:If a two-term Taylor expansion is needed for the determination of the boundary valuesof the pressure.
time_derivative_contributes_to_RC_coefficientsTrueWhether the time derivative term should contribute to the Rhie Chow coefficients. This adds stabilization, but makes the solution dependent on the time step size
Default:True
C++ Type:bool
Controllable:No
Description:Whether the time derivative term should contribute to the Rhie Chow coefficients. This adds stabilization, but makes the solution dependent on the time step size
velocity_interpolationrcThe interpolation to use for the velocity. Options are 'average' and 'rc' which stands for Rhie-Chow. The default is Rhie-Chow.
Default:rc
C++ Type:MooseEnum
Options:average, rc
Controllable:No
Description:The interpolation to use for the velocity. Options are 'average' and 'rc' which stands for Rhie-Chow. The default is Rhie-Chow.

Numerical Scheme Parameters

consistent_scalingScaling parameter for the friction correction in the momentum equation (if requested).
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling parameter for the friction correction in the momentum equation (if requested).
porosity_interface_pressure_treatmentautomaticHow to treat pressure at a porosity interface
Default:automatic
C++ Type:MooseEnum
Options:automatic, bernoulli
Controllable:No
Description:How to treat pressure at a porosity interface
porosity_smoothing_layersThe number of interpolation-reconstruction operations to perform on the porosity.
C++ Type:unsigned short
Controllable:No
Description:The number of interpolation-reconstruction operations to perform on the porosity.
pressure_allow_expansion_on_bernoulli_facesFalseSwitch to enable the two-term extrapolation on porosity jump faces. WARNING: Depending on the mesh, enabling this parameter may lead to termination in parallel runs due to insufficient ghosting between processors. An example can be the presence of multiple porosity jumps separated by only one cell while using the Bernoulli pressure treatment. In such cases adjust the `ghost_layers` parameter.
Default:False
C++ Type:bool
Controllable:No
Description:Switch to enable the two-term extrapolation on porosity jump faces. WARNING: Depending on the mesh, enabling this parameter may lead to termination in parallel runs due to insufficient ghosting between processors. An example can be the presence of multiple porosity jumps separated by only one cell while using the Bernoulli pressure treatment. In such cases adjust the `ghost_layers` parameter.
pressure_drop_form_factorsUser-supplied form loss coefficients to be applied over the sidesets listed above
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:User-supplied form loss coefficients to be applied over the sidesets listed above
pressure_drop_sidesetsSidesets over which form loss coefficients are to be applied
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Sidesets over which form loss coefficients are to be applied
use_friction_correctionFalseIf friction correction should be applied in the momentum equation.
Default:False
C++ Type:bool
Controllable:No
Description:If friction correction should be applied in the momentum equation.

Flow Medium Discontinuity Treatment Parameters

coupled_turbulence_physicsTurbulence Physics coupled with the flow
C++ Type:PhysicsName
Controllable:No
Description:Turbulence Physics coupled with the flow

Coupled Physics Parameters

densityrhoThe name of the density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
Default:rho
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
dynamic_viscositymuThe name of the dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
Default:mu
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

Material Properties Parameters

dont_create_aux_kernelsFalseWhether to skip the 'add_aux_kernel' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_aux_kernel' task
dont_create_aux_variablesFalseWhether to skip the 'add_aux_variable' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_aux_variable' task
dont_create_bcsFalseWhether to skip the 'add_bc' task for each boundary condition type
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_bc' task for each boundary condition type
dont_create_correctorsFalseWhether to skip the 'add_correctors' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_correctors' task
dont_create_functionsFalseWhether to skip the 'add_function' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_function' task
dont_create_icsFalseWhether to skip the 'add_ic' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_ic' task
dont_create_kernelsFalseWhether to skip the 'add_kernel' task for each kernel type
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_kernel' task for each kernel type
dont_create_materialsFalseWhether to skip the 'add_material' task for each material type
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_material' task for each material type
dont_create_postprocessorsFalseWhether to skip the 'add_postprocessors' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_postprocessors' task
dont_create_solver_variablesFalseWhether to skip the 'add_variable' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_variable' task
dont_create_user_objectsFalseWhether to skip the 'add_user_object' task. This does not apply to UserObject derived classes being created on a different task (for example: postprocessors, VPPs, correctors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_user_object' task. This does not apply to UserObject derived classes being created on a different task (for example: postprocessors, VPPs, correctors)
dont_create_vectorpostprocessorsFalseWhether to skip the 'add_vectorpostprocessors' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_vectorpostprocessors' task

Reduce Physics Object Creation Parameters

flux_inlet_directionsThe directions which can be used to define the orientation of the flux with respect to the mesh. This can be used to define a flux which is incoming with an angle or to adjust the flux direction with respect to the normal. If the inlet surface is defined on an internal face, this is necessary to ensure the arbitrary orientation of the normal does not result in non-physical results.
C++ Type:std::vector<libMesh::Point>
Controllable:No
Description:The directions which can be used to define the orientation of the flux with respect to the mesh. This can be used to define a flux which is incoming with an angle or to adjust the flux direction with respect to the normal. If the inlet surface is defined on an internal face, this is necessary to ensure the arbitrary orientation of the normal does not result in non-physical results.
flux_inlet_ppsThe name of the postprocessors which compute the mass flow/ velocity magnitude. Mainly used for coupling between different applications.
C++ Type:std::vector<PostprocessorName>
Unit:(no unit assumed)
Controllable:No
Description:The name of the postprocessors which compute the mass flow/ velocity magnitude. Mainly used for coupling between different applications.

Boundary Condition Parameters

friction_blocksThe blocks where the friction factors are applied to emulate flow resistances.
C++ Type:std::vector<std::vector<SubdomainName>>
Controllable:No
Description:The blocks where the friction factors are applied to emulate flow resistances.
friction_coeffsThe friction coefficients for every item in 'friction_types'. Note that if 'porous_medium_treatment' is enabled, the coefficients already contain a velocity multiplier but they are not multiplied with density yet!
C++ Type:std::vector<std::vector<std::string>>
Controllable:No
Description:The friction coefficients for every item in 'friction_types'. Note that if 'porous_medium_treatment' is enabled, the coefficients already contain a velocity multiplier but they are not multiplied with density yet!
friction_typesThe types of friction forces for every block in 'friction_blocks'.
C++ Type:std::vector<std::vector<std::string>>
Controllable:No
Description:The types of friction forces for every block in 'friction_blocks'.
standard_friction_formulationTrueFlag to enable the standard friction formulation or its alternative, which is a simplified version (see user documentation for PINSFVMomentumFriction).
Default:True
C++ Type:bool
Controllable:No
Description:Flag to enable the standard friction formulation or its alternative, which is a simplified version (see user documentation for PINSFVMomentumFriction).

Friction Control Parameters

initial_from_file_timestepLATESTGives the time step number (or "LATEST") for which to read the Exodus solution
Default:LATEST
C++ Type:std::string
Controllable:No
Description:Gives the time step number (or "LATEST") for which to read the Exodus solution
initialize_variables_from_mesh_fileFalseDetermines if the variables that are added by the action are initializedfrom the mesh file (only for Exodus format)
Default:False
C++ Type:bool
Controllable:No
Description:Determines if the variables that are added by the action are initializedfrom the mesh file (only for Exodus format)

Restart From Exodus Parameters

initial_pressure1e5The initial pressure, assumed constant everywhere
Default:1e5
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The initial pressure, assumed constant everywhere
initial_velocity1e-15 1e-15 1e-15 The initial velocity, assumed constant everywhere
Default:1e-15 1e-15 1e-15
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The initial velocity, assumed constant everywhere
pressure_variableIf supplied, the system checks for available pressure variable. Otherwise, it is created within the action.
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:If supplied, the system checks for available pressure variable. Otherwise, it is created within the action.
velocity_variableIf supplied, the system checks for available velocity variables. Otherwise, they are created within the action.
C++ Type:std::vector<std::string>
Controllable:No
Description:If supplied, the system checks for available velocity variables. Otherwise, they are created within the action.

Variables Parameters

inlet_boundariesNames of inlet boundaries
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Names of inlet boundaries
momentum_inlet_functorsFunctions for inlet boundary velocities or pressures (for fixed-pressure option). Provide a double vector where the leading dimension corresponds to the number of fixed-velocity and fixed-pressure entries in momentum_inlet_types and the second index runs either over dimensions for fixed-velocity boundaries or is a single function name for pressure inlets. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:std::vector<std::vector<MooseFunctorName>>
Unit:(no unit assumed)
Controllable:No
Description:Functions for inlet boundary velocities or pressures (for fixed-pressure option). Provide a double vector where the leading dimension corresponds to the number of fixed-velocity and fixed-pressure entries in momentum_inlet_types and the second index runs either over dimensions for fixed-velocity boundaries or is a single function name for pressure inlets. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
momentum_inlet_typesTypes of inlet boundaries for the momentum equation.
C++ Type:MultiMooseEnum
Options:fixed-velocity, flux-velocity, flux-mass, fixed-pressure
Controllable:No
Description:Types of inlet boundaries for the momentum equation.

Inlet Boundary Conditions Parameters

momentum_outlet_typesTypes of outlet boundaries for the momentum equation
C++ Type:MultiMooseEnum
Options:fixed-pressure, zero-gradient, fixed-pressure-zero-gradient
Controllable:No
Description:Types of outlet boundaries for the momentum equation
outlet_boundariesNames of outlet boundaries
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Names of outlet boundaries
pressure_functorsFunctions for boundary pressures at outlets. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:std::vector<MooseFunctorName>
Unit:(no unit assumed)
Controllable:No
Description:Functions for boundary pressures at outlets. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

Outlet Boundary Conditions Parameters

momentum_wall_functorsFunctors for each component of the velocity value on walls. This is only necessary for the fixed-velocity momentum wall types. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:std::vector<std::vector<MooseFunctorName>>
Unit:(no unit assumed)
Controllable:No
Description:Functors for each component of the velocity value on walls. This is only necessary for the fixed-velocity momentum wall types. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
momentum_wall_typesTypes of wall boundaries for the momentum equation
C++ Type:MultiMooseEnum
Options:symmetry, noslip, slip, wallfunction
Controllable:No
Description:Types of wall boundaries for the momentum equation
wall_boundariesNames of wall boundaries
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Names of wall boundaries

Wall Boundary Conditions Parameters

pin_pressureFalseSwitch to enable pressure shifting for incompressible simulations.
Default:False
C++ Type:bool
Controllable:No
Description:Switch to enable pressure shifting for incompressible simulations.
pinned_pressure_point0 0 0The XYZ coordinates where pressure needs to be pinned for incompressible simulations.
Default:0 0 0
C++ Type:libMesh::Point
Controllable:No
Description:The XYZ coordinates where pressure needs to be pinned for incompressible simulations.
pinned_pressure_typeaverage-uoTypes for shifting (pinning) the pressure in case of incompressible simulations.
Default:average-uo
C++ Type:MooseEnum
Options:average, point-value, average-uo, point-value-uo
Controllable:No
Description:Types for shifting (pinning) the pressure in case of incompressible simulations.
pinned_pressure_value1e5The value used for pinning the pressure (point value/domain average).
Default:1e5
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The value used for pinning the pressure (point value/domain average).

Incompressible Flow Pressure Constraint Parameters

(modules/navier_stokes/include/base/NS.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 <string>
#include "MathUtils.h"
#include "MooseTypes.h"
#include "libmesh/vector_value.h"
#include "HeatConductionNames.h"

namespace NS
{
using namespace HeatConduction;

static const std::string directions[3] = {"x", "y", "z"};

// geometric quantities
static const std::string pebble_diameter = "pebble_diameter";
static const std::string infinite_porosity = "infinite_porosity";
static const std::string axis = "axis";
static const std::string center = "center";
static const std::string wall_porosity = "wall_porosity";
static const std::string wall_distance = "wall_distance";

// Names defined in Navier-Stokes
static const std::string density = "rho";
static const std::string superficial_density = "superficial_rho";
static const std::string momentum_x = "rhou";
static const std::string momentum_y = "rhov";
static const std::string momentum_z = "rhow";
static const std::string momentum_vector[3] = {momentum_x, momentum_y, momentum_z};
static const std::string superficial_momentum_x = "superficial_rhou";
static const std::string superficial_momentum_y = "superficial_rhov";
static const std::string superficial_momentum_z = "superficial_rhow";
static const std::string superficial_momentum_vector[3] = {
    superficial_momentum_x, superficial_momentum_y, superficial_momentum_z};

static const std::string velocity = "velocity";
static const std::string velocity_x = "vel_x";
static const std::string velocity_y = "vel_y";
static const std::string velocity_z = "vel_z";
const std::string velocity_vector[3] = {velocity_x, velocity_y, velocity_z};
static const std::string superficial_velocity_x = "superficial_vel_x";
static const std::string superficial_velocity_y = "superficial_vel_y";
static const std::string superficial_velocity_z = "superficial_vel_z";
static const std::string superficial_velocity = "superficial_velocity";
static const std::string superficial_velocity_vector[3] = {
    superficial_velocity_x, superficial_velocity_y, superficial_velocity_z};
static const std::string pressure = "pressure";
// Starting variable name with pressure so it is displayed next to pressure in outputs
static const std::string total_pressure = "pressure_total";
static const std::string temperature = "temperature";

static const std::string internal_energy = "internal_energy";
static const std::string specific_internal_energy = "e";
static const std::string specific_total_energy = "et";
static const std::string internal_energy_density = "rho_e";
static const std::string total_energy_density = "rho_et";
static const std::string superficial_total_energy_density = "superficial_rho_et";

static const std::string specific_enthalpy = "h";
static const std::string specific_total_enthalpy = "ht";
static const std::string enthalpy_density = "rho_h";
static const std::string total_enthalpy_density = "rho_ht";
static const std::string superficial_total_enthalpy_density = "superficial_rho_ht";

static const std::string mixing_length = "mixing_length";
static const std::string wall_shear_stress = "wall_shear_stress";
static const std::string wall_yplus = "wall_yplus";
static const std::string eddy_viscosity = "eddy_viscosity";
static const std::string total_viscosity = "total_viscosity";

static const std::string mach_number = "Mach";
static const std::string specific_volume = "specific_volume";

static const std::string momentum = "momentum";
static const std::string v = "v";
static const std::string acceleration = "acceleration";

static const std::string fluid = "fp";

// for Navier-Stokes material props representing gradients of nonlin+aux vars
inline std::string
grad(const std::string & var)
{
  return MathUtils::gradName(var);
}
// for Navier-Stokes material props representing time derivatives of nonlin+aux vars
inline std::string
time_deriv(const std::string & var)
{
  return MathUtils::timeDerivName(var);
}

// Navier-Stokes Variables
// Relating to porous media
static const std::string porosity = "porosity";
static const std::string smoothed_porosity = "smoothed_porosity";
static const std::string T_fluid = "T_fluid";
static const std::string T_solid = "T_solid";
static const std::string heat_source = "heat_source";

// Navier-Stokes Materials
static const std::string cL = "Darcy_coefficient";
static const std::string cQ = "Forchheimer_coefficient";
static const std::string alpha_boussinesq = "alpha_b";
static const std::string drhos_dTs = "drhos_dTs";
static const std::string dks_dTs = "dks_dTs";
static const std::string kappa = "kappa";
static const std::string kappa_s = "kappa_s";
static const std::string rho_s = "rho_s";
static const std::string cp_s = "cp_s";
static const std::string k_s = "k_s";
static const std::string cp = "cp";
static const std::string cv = "cv";
static const std::string mu = "mu";
// Turbulent dynamic viscosity
static const std::string mu_t = "mu_t";
// Turbulent dynamic scalar viscosity
static const std::string mu_t_passive_scalar = "mu_t_passive_scalar";
// Effective viscosity = sum of viscosities
static const std::string mu_eff = "mu_eff";
static const std::string k = "k";
// Turbulence 'conductivity'
static const std::string k_t = "k_t";
static const std::string thermal_diffusivity = "thermal_diffusivity";
static const std::string alpha = "alpha";
static const std::string alpha_wall = "alpha_wall";
static const std::string solid = "solid";
static const std::string Prandtl = "Pr";
static const std::string turbulent_Prandtl = "Pr_t";
static const std::string Reynolds = "Re";
static const std::string Reynolds_hydraulic = "Re_h";
static const std::string Reynolds_interstitial = "Re_i";
static const std::string c = "c";
static const std::string speed = "speed";
static const std::string sound_speed = "sound_speed";

// Two phase mixture materials
static const std::string latent_heat = "latent_heat";
static const std::string T_liquidus = "T_liquidus";
static const std::string T_solidus = "T_solidus";
static const std::string alpha_exchange = "alpha_exchange";

// other Navier-Stokes terms
static const std::string component = "component";
static const std::string source_scaling = "source_scaling";

// SUPG terms
static const std::string matrix_tau = "matrix_tau";
static const std::string vector_tau = "vector_tau";
static const std::string scalar_tau = "scalar_tau";
static const std::string diagonal_tau = "diagonal_tau";
static const std::string A = "A";
static const std::string R = "R";
static const std::string S = "S";
static const std::string dS_dTs = "dS_dTs";
static const std::string F = "F";
static const std::string G = "G";
static const std::string dUdt = "dUdt";
static const std::string C = "C";
static const std::string Z = "Z";
static const std::string K = "K";
static const std::string mass_flux = "mass_flux";

// Turbulence

// Turbulence variables
static const std::string TKE = "tke";
static const std::string TKED = "epsilon";

/**
 * Wall treatment options
 */
enum class WallTreatmentEnum
{
  EQ_NEWTON = 0,
  EQ_INCREMENTAL = 1,
  EQ_LINEARIZED = 2,
  NEQ = 3
};

// Turbulence constants
static constexpr Real von_karman_constant = 0.4187;
static constexpr Real E_turb_constant = 9.793;
// Lower limit for mu_t
static constexpr Real mu_t_low_limit = 1.0e-8;
// Lower limit for epsilon in the k-epsilon
static constexpr Real epsilon_low_limit = 1.0e-8;
// Lower limit for y_plus
static constexpr Real min_y_plus = 1e-10;
}

namespace NS_DEFAULT_VALUES
{
static const Real infinite_porosity = 0.4;
static const int bed_axis = 2;
static const Real wall_porosity = 1.0;

static const Real k_epsilon = 1e-6;
static const Real vel_epsilon = 1e-8;

static const RealVectorValue center(0.0, 0.0, 0.0);
static const RealVectorValue acceleration(0.0, 0.0, 0.0);

// assumed that the RZ geometry is not annular unless otherwise specified
static const Real inner_radius = 0.0;
}

namespace NS_CONSTANTS
{
using namespace HeatConduction::Constants;
}

(modules/navier_stokes/include/base/NS.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 <string>
#include "MathUtils.h"
#include "MooseTypes.h"
#include "libmesh/vector_value.h"
#include "HeatConductionNames.h"

namespace NS
{
using namespace HeatConduction;

static const std::string directions[3] = {"x", "y", "z"};

// geometric quantities
static const std::string pebble_diameter = "pebble_diameter";
static const std::string infinite_porosity = "infinite_porosity";
static const std::string axis = "axis";
static const std::string center = "center";
static const std::string wall_porosity = "wall_porosity";
static const std::string wall_distance = "wall_distance";

// Names defined in Navier-Stokes
static const std::string density = "rho";
static const std::string superficial_density = "superficial_rho";
static const std::string momentum_x = "rhou";
static const std::string momentum_y = "rhov";
static const std::string momentum_z = "rhow";
static const std::string momentum_vector[3] = {momentum_x, momentum_y, momentum_z};
static const std::string superficial_momentum_x = "superficial_rhou";
static const std::string superficial_momentum_y = "superficial_rhov";
static const std::string superficial_momentum_z = "superficial_rhow";
static const std::string superficial_momentum_vector[3] = {
    superficial_momentum_x, superficial_momentum_y, superficial_momentum_z};

static const std::string velocity = "velocity";
static const std::string velocity_x = "vel_x";
static const std::string velocity_y = "vel_y";
static const std::string velocity_z = "vel_z";
const std::string velocity_vector[3] = {velocity_x, velocity_y, velocity_z};
static const std::string superficial_velocity_x = "superficial_vel_x";
static const std::string superficial_velocity_y = "superficial_vel_y";
static const std::string superficial_velocity_z = "superficial_vel_z";
static const std::string superficial_velocity = "superficial_velocity";
static const std::string superficial_velocity_vector[3] = {
    superficial_velocity_x, superficial_velocity_y, superficial_velocity_z};
static const std::string pressure = "pressure";
// Starting variable name with pressure so it is displayed next to pressure in outputs
static const std::string total_pressure = "pressure_total";
static const std::string temperature = "temperature";

static const std::string internal_energy = "internal_energy";
static const std::string specific_internal_energy = "e";
static const std::string specific_total_energy = "et";
static const std::string internal_energy_density = "rho_e";
static const std::string total_energy_density = "rho_et";
static const std::string superficial_total_energy_density = "superficial_rho_et";

static const std::string specific_enthalpy = "h";
static const std::string specific_total_enthalpy = "ht";
static const std::string enthalpy_density = "rho_h";
static const std::string total_enthalpy_density = "rho_ht";
static const std::string superficial_total_enthalpy_density = "superficial_rho_ht";

static const std::string mixing_length = "mixing_length";
static const std::string wall_shear_stress = "wall_shear_stress";
static const std::string wall_yplus = "wall_yplus";
static const std::string eddy_viscosity = "eddy_viscosity";
static const std::string total_viscosity = "total_viscosity";

static const std::string mach_number = "Mach";
static const std::string specific_volume = "specific_volume";

static const std::string momentum = "momentum";
static const std::string v = "v";
static const std::string acceleration = "acceleration";

static const std::string fluid = "fp";

// for Navier-Stokes material props representing gradients of nonlin+aux vars
inline std::string
grad(const std::string & var)
{
  return MathUtils::gradName(var);
}
// for Navier-Stokes material props representing time derivatives of nonlin+aux vars
inline std::string
time_deriv(const std::string & var)
{
  return MathUtils::timeDerivName(var);
}

// Navier-Stokes Variables
// Relating to porous media
static const std::string porosity = "porosity";
static const std::string smoothed_porosity = "smoothed_porosity";
static const std::string T_fluid = "T_fluid";
static const std::string T_solid = "T_solid";
static const std::string heat_source = "heat_source";

// Navier-Stokes Materials
static const std::string cL = "Darcy_coefficient";
static const std::string cQ = "Forchheimer_coefficient";
static const std::string alpha_boussinesq = "alpha_b";
static const std::string drhos_dTs = "drhos_dTs";
static const std::string dks_dTs = "dks_dTs";
static const std::string kappa = "kappa";
static const std::string kappa_s = "kappa_s";
static const std::string rho_s = "rho_s";
static const std::string cp_s = "cp_s";
static const std::string k_s = "k_s";
static const std::string cp = "cp";
static const std::string cv = "cv";
static const std::string mu = "mu";
// Turbulent dynamic viscosity
static const std::string mu_t = "mu_t";
// Turbulent dynamic scalar viscosity
static const std::string mu_t_passive_scalar = "mu_t_passive_scalar";
// Effective viscosity = sum of viscosities
static const std::string mu_eff = "mu_eff";
static const std::string k = "k";
// Turbulence 'conductivity'
static const std::string k_t = "k_t";
static const std::string thermal_diffusivity = "thermal_diffusivity";
static const std::string alpha = "alpha";
static const std::string alpha_wall = "alpha_wall";
static const std::string solid = "solid";
static const std::string Prandtl = "Pr";
static const std::string turbulent_Prandtl = "Pr_t";
static const std::string Reynolds = "Re";
static const std::string Reynolds_hydraulic = "Re_h";
static const std::string Reynolds_interstitial = "Re_i";
static const std::string c = "c";
static const std::string speed = "speed";
static const std::string sound_speed = "sound_speed";

// Two phase mixture materials
static const std::string latent_heat = "latent_heat";
static const std::string T_liquidus = "T_liquidus";
static const std::string T_solidus = "T_solidus";
static const std::string alpha_exchange = "alpha_exchange";

// other Navier-Stokes terms
static const std::string component = "component";
static const std::string source_scaling = "source_scaling";

// SUPG terms
static const std::string matrix_tau = "matrix_tau";
static const std::string vector_tau = "vector_tau";
static const std::string scalar_tau = "scalar_tau";
static const std::string diagonal_tau = "diagonal_tau";
static const std::string A = "A";
static const std::string R = "R";
static const std::string S = "S";
static const std::string dS_dTs = "dS_dTs";
static const std::string F = "F";
static const std::string G = "G";
static const std::string dUdt = "dUdt";
static const std::string C = "C";
static const std::string Z = "Z";
static const std::string K = "K";
static const std::string mass_flux = "mass_flux";

// Turbulence

// Turbulence variables
static const std::string TKE = "tke";
static const std::string TKED = "epsilon";

/**
 * Wall treatment options
 */
enum class WallTreatmentEnum
{
  EQ_NEWTON = 0,
  EQ_INCREMENTAL = 1,
  EQ_LINEARIZED = 2,
  NEQ = 3
};

// Turbulence constants
static constexpr Real von_karman_constant = 0.4187;
static constexpr Real E_turb_constant = 9.793;
// Lower limit for mu_t
static constexpr Real mu_t_low_limit = 1.0e-8;
// Lower limit for epsilon in the k-epsilon
static constexpr Real epsilon_low_limit = 1.0e-8;
// Lower limit for y_plus
static constexpr Real min_y_plus = 1e-10;
}

namespace NS_DEFAULT_VALUES
{
static const Real infinite_porosity = 0.4;
static const int bed_axis = 2;
static const Real wall_porosity = 1.0;

static const Real k_epsilon = 1e-6;
static const Real vel_epsilon = 1e-8;

static const RealVectorValue center(0.0, 0.0, 0.0);
static const RealVectorValue acceleration(0.0, 0.0, 0.0);

// assumed that the RZ geometry is not annular unless otherwise specified
static const Real inner_radius = 0.0;
}

namespace NS_CONSTANTS
{
using namespace HeatConduction::Constants;
}

(modules/navier_stokes/include/base/NS.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 <string>
#include "MathUtils.h"
#include "MooseTypes.h"
#include "libmesh/vector_value.h"
#include "HeatConductionNames.h"

namespace NS
{
using namespace HeatConduction;

static const std::string directions[3] = {"x", "y", "z"};

// geometric quantities
static const std::string pebble_diameter = "pebble_diameter";
static const std::string infinite_porosity = "infinite_porosity";
static const std::string axis = "axis";
static const std::string center = "center";
static const std::string wall_porosity = "wall_porosity";
static const std::string wall_distance = "wall_distance";

// Names defined in Navier-Stokes
static const std::string density = "rho";
static const std::string superficial_density = "superficial_rho";
static const std::string momentum_x = "rhou";
static const std::string momentum_y = "rhov";
static const std::string momentum_z = "rhow";
static const std::string momentum_vector[3] = {momentum_x, momentum_y, momentum_z};
static const std::string superficial_momentum_x = "superficial_rhou";
static const std::string superficial_momentum_y = "superficial_rhov";
static const std::string superficial_momentum_z = "superficial_rhow";
static const std::string superficial_momentum_vector[3] = {
    superficial_momentum_x, superficial_momentum_y, superficial_momentum_z};

static const std::string velocity = "velocity";
static const std::string velocity_x = "vel_x";
static const std::string velocity_y = "vel_y";
static const std::string velocity_z = "vel_z";
const std::string velocity_vector[3] = {velocity_x, velocity_y, velocity_z};
static const std::string superficial_velocity_x = "superficial_vel_x";
static const std::string superficial_velocity_y = "superficial_vel_y";
static const std::string superficial_velocity_z = "superficial_vel_z";
static const std::string superficial_velocity = "superficial_velocity";
static const std::string superficial_velocity_vector[3] = {
    superficial_velocity_x, superficial_velocity_y, superficial_velocity_z};
static const std::string pressure = "pressure";
// Starting variable name with pressure so it is displayed next to pressure in outputs
static const std::string total_pressure = "pressure_total";
static const std::string temperature = "temperature";

static const std::string internal_energy = "internal_energy";
static const std::string specific_internal_energy = "e";
static const std::string specific_total_energy = "et";
static const std::string internal_energy_density = "rho_e";
static const std::string total_energy_density = "rho_et";
static const std::string superficial_total_energy_density = "superficial_rho_et";

static const std::string specific_enthalpy = "h";
static const std::string specific_total_enthalpy = "ht";
static const std::string enthalpy_density = "rho_h";
static const std::string total_enthalpy_density = "rho_ht";
static const std::string superficial_total_enthalpy_density = "superficial_rho_ht";

static const std::string mixing_length = "mixing_length";
static const std::string wall_shear_stress = "wall_shear_stress";
static const std::string wall_yplus = "wall_yplus";
static const std::string eddy_viscosity = "eddy_viscosity";
static const std::string total_viscosity = "total_viscosity";

static const std::string mach_number = "Mach";
static const std::string specific_volume = "specific_volume";

static const std::string momentum = "momentum";
static const std::string v = "v";
static const std::string acceleration = "acceleration";

static const std::string fluid = "fp";

// for Navier-Stokes material props representing gradients of nonlin+aux vars
inline std::string
grad(const std::string & var)
{
  return MathUtils::gradName(var);
}
// for Navier-Stokes material props representing time derivatives of nonlin+aux vars
inline std::string
time_deriv(const std::string & var)
{
  return MathUtils::timeDerivName(var);
}

// Navier-Stokes Variables
// Relating to porous media
static const std::string porosity = "porosity";
static const std::string smoothed_porosity = "smoothed_porosity";
static const std::string T_fluid = "T_fluid";
static const std::string T_solid = "T_solid";
static const std::string heat_source = "heat_source";

// Navier-Stokes Materials
static const std::string cL = "Darcy_coefficient";
static const std::string cQ = "Forchheimer_coefficient";
static const std::string alpha_boussinesq = "alpha_b";
static const std::string drhos_dTs = "drhos_dTs";
static const std::string dks_dTs = "dks_dTs";
static const std::string kappa = "kappa";
static const std::string kappa_s = "kappa_s";
static const std::string rho_s = "rho_s";
static const std::string cp_s = "cp_s";
static const std::string k_s = "k_s";
static const std::string cp = "cp";
static const std::string cv = "cv";
static const std::string mu = "mu";
// Turbulent dynamic viscosity
static const std::string mu_t = "mu_t";
// Turbulent dynamic scalar viscosity
static const std::string mu_t_passive_scalar = "mu_t_passive_scalar";
// Effective viscosity = sum of viscosities
static const std::string mu_eff = "mu_eff";
static const std::string k = "k";
// Turbulence 'conductivity'
static const std::string k_t = "k_t";
static const std::string thermal_diffusivity = "thermal_diffusivity";
static const std::string alpha = "alpha";
static const std::string alpha_wall = "alpha_wall";
static const std::string solid = "solid";
static const std::string Prandtl = "Pr";
static const std::string turbulent_Prandtl = "Pr_t";
static const std::string Reynolds = "Re";
static const std::string Reynolds_hydraulic = "Re_h";
static const std::string Reynolds_interstitial = "Re_i";
static const std::string c = "c";
static const std::string speed = "speed";
static const std::string sound_speed = "sound_speed";

// Two phase mixture materials
static const std::string latent_heat = "latent_heat";
static const std::string T_liquidus = "T_liquidus";
static const std::string T_solidus = "T_solidus";
static const std::string alpha_exchange = "alpha_exchange";

// other Navier-Stokes terms
static const std::string component = "component";
static const std::string source_scaling = "source_scaling";

// SUPG terms
static const std::string matrix_tau = "matrix_tau";
static const std::string vector_tau = "vector_tau";
static const std::string scalar_tau = "scalar_tau";
static const std::string diagonal_tau = "diagonal_tau";
static const std::string A = "A";
static const std::string R = "R";
static const std::string S = "S";
static const std::string dS_dTs = "dS_dTs";
static const std::string F = "F";
static const std::string G = "G";
static const std::string dUdt = "dUdt";
static const std::string C = "C";
static const std::string Z = "Z";
static const std::string K = "K";
static const std::string mass_flux = "mass_flux";

// Turbulence

// Turbulence variables
static const std::string TKE = "tke";
static const std::string TKED = "epsilon";

/**
 * Wall treatment options
 */
enum class WallTreatmentEnum
{
  EQ_NEWTON = 0,
  EQ_INCREMENTAL = 1,
  EQ_LINEARIZED = 2,
  NEQ = 3
};

// Turbulence constants
static constexpr Real von_karman_constant = 0.4187;
static constexpr Real E_turb_constant = 9.793;
// Lower limit for mu_t
static constexpr Real mu_t_low_limit = 1.0e-8;
// Lower limit for epsilon in the k-epsilon
static constexpr Real epsilon_low_limit = 1.0e-8;
// Lower limit for y_plus
static constexpr Real min_y_plus = 1e-10;
}

namespace NS_DEFAULT_VALUES
{
static const Real infinite_porosity = 0.4;
static const int bed_axis = 2;
static const Real wall_porosity = 1.0;

static const Real k_epsilon = 1e-6;
static const Real vel_epsilon = 1e-8;

static const RealVectorValue center(0.0, 0.0, 0.0);
static const RealVectorValue acceleration(0.0, 0.0, 0.0);

// assumed that the RZ geometry is not annular unless otherwise specified
static const Real inner_radius = 0.0;
}

namespace NS_CONSTANTS
{
using namespace HeatConduction::Constants;
}

(modules/navier_stokes/include/base/NS.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 <string>
#include "MathUtils.h"
#include "MooseTypes.h"
#include "libmesh/vector_value.h"
#include "HeatConductionNames.h"

namespace NS
{
using namespace HeatConduction;

static const std::string directions[3] = {"x", "y", "z"};

// geometric quantities
static const std::string pebble_diameter = "pebble_diameter";
static const std::string infinite_porosity = "infinite_porosity";
static const std::string axis = "axis";
static const std::string center = "center";
static const std::string wall_porosity = "wall_porosity";
static const std::string wall_distance = "wall_distance";

// Names defined in Navier-Stokes
static const std::string density = "rho";
static const std::string superficial_density = "superficial_rho";
static const std::string momentum_x = "rhou";
static const std::string momentum_y = "rhov";
static const std::string momentum_z = "rhow";
static const std::string momentum_vector[3] = {momentum_x, momentum_y, momentum_z};
static const std::string superficial_momentum_x = "superficial_rhou";
static const std::string superficial_momentum_y = "superficial_rhov";
static const std::string superficial_momentum_z = "superficial_rhow";
static const std::string superficial_momentum_vector[3] = {
    superficial_momentum_x, superficial_momentum_y, superficial_momentum_z};

static const std::string velocity = "velocity";
static const std::string velocity_x = "vel_x";
static const std::string velocity_y = "vel_y";
static const std::string velocity_z = "vel_z";
const std::string velocity_vector[3] = {velocity_x, velocity_y, velocity_z};
static const std::string superficial_velocity_x = "superficial_vel_x";
static const std::string superficial_velocity_y = "superficial_vel_y";
static const std::string superficial_velocity_z = "superficial_vel_z";
static const std::string superficial_velocity = "superficial_velocity";
static const std::string superficial_velocity_vector[3] = {
    superficial_velocity_x, superficial_velocity_y, superficial_velocity_z};
static const std::string pressure = "pressure";
// Starting variable name with pressure so it is displayed next to pressure in outputs
static const std::string total_pressure = "pressure_total";
static const std::string temperature = "temperature";

static const std::string internal_energy = "internal_energy";
static const std::string specific_internal_energy = "e";
static const std::string specific_total_energy = "et";
static const std::string internal_energy_density = "rho_e";
static const std::string total_energy_density = "rho_et";
static const std::string superficial_total_energy_density = "superficial_rho_et";

static const std::string specific_enthalpy = "h";
static const std::string specific_total_enthalpy = "ht";
static const std::string enthalpy_density = "rho_h";
static const std::string total_enthalpy_density = "rho_ht";
static const std::string superficial_total_enthalpy_density = "superficial_rho_ht";

static const std::string mixing_length = "mixing_length";
static const std::string wall_shear_stress = "wall_shear_stress";
static const std::string wall_yplus = "wall_yplus";
static const std::string eddy_viscosity = "eddy_viscosity";
static const std::string total_viscosity = "total_viscosity";

static const std::string mach_number = "Mach";
static const std::string specific_volume = "specific_volume";

static const std::string momentum = "momentum";
static const std::string v = "v";
static const std::string acceleration = "acceleration";

static const std::string fluid = "fp";

// for Navier-Stokes material props representing gradients of nonlin+aux vars
inline std::string
grad(const std::string & var)
{
  return MathUtils::gradName(var);
}
// for Navier-Stokes material props representing time derivatives of nonlin+aux vars
inline std::string
time_deriv(const std::string & var)
{
  return MathUtils::timeDerivName(var);
}

// Navier-Stokes Variables
// Relating to porous media
static const std::string porosity = "porosity";
static const std::string smoothed_porosity = "smoothed_porosity";
static const std::string T_fluid = "T_fluid";
static const std::string T_solid = "T_solid";
static const std::string heat_source = "heat_source";

// Navier-Stokes Materials
static const std::string cL = "Darcy_coefficient";
static const std::string cQ = "Forchheimer_coefficient";
static const std::string alpha_boussinesq = "alpha_b";
static const std::string drhos_dTs = "drhos_dTs";
static const std::string dks_dTs = "dks_dTs";
static const std::string kappa = "kappa";
static const std::string kappa_s = "kappa_s";
static const std::string rho_s = "rho_s";
static const std::string cp_s = "cp_s";
static const std::string k_s = "k_s";
static const std::string cp = "cp";
static const std::string cv = "cv";
static const std::string mu = "mu";
// Turbulent dynamic viscosity
static const std::string mu_t = "mu_t";
// Turbulent dynamic scalar viscosity
static const std::string mu_t_passive_scalar = "mu_t_passive_scalar";
// Effective viscosity = sum of viscosities
static const std::string mu_eff = "mu_eff";
static const std::string k = "k";
// Turbulence 'conductivity'
static const std::string k_t = "k_t";
static const std::string thermal_diffusivity = "thermal_diffusivity";
static const std::string alpha = "alpha";
static const std::string alpha_wall = "alpha_wall";
static const std::string solid = "solid";
static const std::string Prandtl = "Pr";
static const std::string turbulent_Prandtl = "Pr_t";
static const std::string Reynolds = "Re";
static const std::string Reynolds_hydraulic = "Re_h";
static const std::string Reynolds_interstitial = "Re_i";
static const std::string c = "c";
static const std::string speed = "speed";
static const std::string sound_speed = "sound_speed";

// Two phase mixture materials
static const std::string latent_heat = "latent_heat";
static const std::string T_liquidus = "T_liquidus";
static const std::string T_solidus = "T_solidus";
static const std::string alpha_exchange = "alpha_exchange";

// other Navier-Stokes terms
static const std::string component = "component";
static const std::string source_scaling = "source_scaling";

// SUPG terms
static const std::string matrix_tau = "matrix_tau";
static const std::string vector_tau = "vector_tau";
static const std::string scalar_tau = "scalar_tau";
static const std::string diagonal_tau = "diagonal_tau";
static const std::string A = "A";
static const std::string R = "R";
static const std::string S = "S";
static const std::string dS_dTs = "dS_dTs";
static const std::string F = "F";
static const std::string G = "G";
static const std::string dUdt = "dUdt";
static const std::string C = "C";
static const std::string Z = "Z";
static const std::string K = "K";
static const std::string mass_flux = "mass_flux";

// Turbulence

// Turbulence variables
static const std::string TKE = "tke";
static const std::string TKED = "epsilon";

/**
 * Wall treatment options
 */
enum class WallTreatmentEnum
{
  EQ_NEWTON = 0,
  EQ_INCREMENTAL = 1,
  EQ_LINEARIZED = 2,
  NEQ = 3
};

// Turbulence constants
static constexpr Real von_karman_constant = 0.4187;
static constexpr Real E_turb_constant = 9.793;
// Lower limit for mu_t
static constexpr Real mu_t_low_limit = 1.0e-8;
// Lower limit for epsilon in the k-epsilon
static constexpr Real epsilon_low_limit = 1.0e-8;
// Lower limit for y_plus
static constexpr Real min_y_plus = 1e-10;
}

namespace NS_DEFAULT_VALUES
{
static const Real infinite_porosity = 0.4;
static const int bed_axis = 2;
static const Real wall_porosity = 1.0;

static const Real k_epsilon = 1e-6;
static const Real vel_epsilon = 1e-8;

static const RealVectorValue center(0.0, 0.0, 0.0);
static const RealVectorValue acceleration(0.0, 0.0, 0.0);

// assumed that the RZ geometry is not annular unless otherwise specified
static const Real inner_radius = 0.0;
}

namespace NS_CONSTANTS
{
using namespace HeatConduction::Constants;
}

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

# Fluid properties
mu = 1.1
rho = 1.1
cp = 1.1
k = 1e-3

# Operating conditions
u_inlet = 1
T_inlet = 200
T_solid = 190
p_outlet = 10
h_fs = 0.01

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 5
    ymin = -1
    ymax = 1
    nx = 50
    ny = 20
  []
[]

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

        density = 'rho'
        dynamic_viscosity = 'mu'

        initial_velocity = '${u_inlet} 1e-12 0'
        initial_pressure = 0.0

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

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

        mass_advection_interpolation = 'average'
        momentum_advection_interpolation = 'average'
      []
    []
  []
[]
# This separation is introduced for documentation purposes.
# Both Physics could be nested under Physics/NavierStokes
[Physics/NavierStokes]
  [FluidHeatTransfer]
    [heat]
      thermal_conductivity = 'k'
      specific_heat = 'cp'

      fluid_temperature_variable = 'T_fluid'
      initial_temperature = '${T_inlet}'
      energy_inlet_types = 'heatflux'
      energy_inlet_functors = '${fparse u_inlet * rho * cp * T_inlet}'

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

      ambient_convection_alpha = 'h_cv'
      ambient_temperature = 'T_solid'

      energy_advection_interpolation = 'average'
    []
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 7e-13
  dt = 0.4
  end_time = 0.8
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-scalar-transport-physics.i)

mu = 1
rho = 1
k = 1e-3
diff = 1e-3
cp = 1

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

[Variables]
  inactive = 'vel_x vel_y pressure T_fluid scalar'
  [vel_x]
    type = 'INSFVVelocityVariable'
    initial_condition = 1
  []
  [vel_y]
    type = 'INSFVVelocityVariable'
    initial_condition = 1
  []
  [pressure]
    type = 'INSFVPressureVariable'
    initial_condition = 0
  []
  [T_fluid]
    type = 'INSFVEnergyVariable'
    initial_condition = 0
  []
  [scalar]
    type = MooseVariableFVReal
    initial_condition = 0
  []
[]

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

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

        inlet_boundaries = 'left'
        momentum_inlet_types = 'fixed-velocity'
        momentum_inlet_function = '1 0'

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

        outlet_boundaries = 'right'
        momentum_outlet_types = 'fixed-pressure'
        pressure_function = '0'

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

        energy_inlet_types = 'fixed-temperature'
        energy_inlet_function = '1'

        energy_wall_types = 'heatflux heatflux'
        energy_wall_function = '0 0'

        energy_advection_interpolation = 'average'
      []
    []
  []
[]
# This separation is introduced for documentation purposes.
# Both could be nested under Physics/NavierStokes
[Physics/NavierStokes]
  [ScalarTransport]
    [heat]
      passive_scalar_names = 'scalar'

      passive_scalar_diffusivity = ${diff}
      passive_scalar_source = 0.1
      passive_scalar_coupled_source = U
      passive_scalar_coupled_source_coeff = 0.1

      passive_scalar_inlet_types = 'fixed-value'
      passive_scalar_inlet_function = '1'

      passive_scalar_advection_interpolation = 'average'
    []
  []
[]

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

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = vel_x
    y = vel_y
  []
[]

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

[Outputs]
  exodus = true
  csv = true
[]

Equations
Automatically defined variables
Coupling with other Physics
Modeling options and implementation details
Input Parameters