PCNSFVStrongBC

Computes the residual of advective term using finite volume method.

Overview

This object accepts functions describing boundary values for pressure, fluid temperature, and superficial velocity. The superficial velocity functions can also be used to supply superficial momentum information instead by setting velocity_function_includes_rho = true. If no function is provided for a quantity, the boundary value of that quantity will be determined by extrapolating from the neighboring boundary cell centroid using cell centroid value and gradient information. From this mix of user-provided functions and extrapolated boundary values for pressure, fluid temperature, and superficial velocity/momentum, the fluxes for mass, momentum, energy, and even passive scalars can be computed.

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
eqnThe equation you're solving.
C++ Type:MooseEnum
Options:mass, momentum, energy, scalar
Controllable:No
Description:The equation you're solving.
fpFluid properties userobject
C++ Type:UserObjectName
Controllable:No
Description:Fluid properties userobject
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

Required Parameters

T_fluidAn optional name of a function for the fluid temperature. If not provided then the fluid temperature will be treated implicitly (e.g. we will use the interior value
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:An optional name of a function for the fluid temperature. If not provided then the fluid temperature will be treated implicitly (e.g. we will use the interior value
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)
mfr_postprocessorA postprocessor used for outputting mass flow rates on the same boundary this object acts on
C++ Type:UserObjectName
Controllable:No
Description:A postprocessor used for outputting mass flow rates on the same boundary this object acts on
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.
pressureAn optional name of a function for the pressure. If not provided then the pressure will be treated implicitly (e.g. we will use the interior value
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:An optional name of a function for the pressure. If not provided then the pressure will be treated implicitly (e.g. we will use the interior value
scalarA function describing the value of the scalar at the boundary. If this function is not provided, then the interior value will be used.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:A function describing the value of the scalar at the boundary. If this function is not provided, then the interior value will be used.
superficial_velocityAn optional name of a vector function for the velocity. If not provided then the superficial velocity will be treated implicitly (e.g. we will use the interior value
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:An optional name of a vector function for the velocity. If not provided then the superficial velocity will be treated implicitly (e.g. we will use the interior value
velocity_function_includes_rhoFalseWhether the provided superficial velocity function actually includes multiplication by rho (e.g. the function is representative of momentum.
Default:False
C++ Type:bool
Controllable:No
Description:Whether the provided superficial velocity function actually includes multiplication by rho (e.g. the function is representative of momentum.

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
search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
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/cns/mms/1d-with-bcs/varying-eps-hllc.i)
(modules/navier_stokes/test/tests/finite_volume/cns/scalar_advection/mass-frac-advection.i)
(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/rotated-2d-bkt-function-porosity-mixed.i)
(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/rotated-2d-bkt-function-porosity.i)
(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/hllc.i)
(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/basic-conserved-pcnsfv-kt.i)
(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-basic-kt-mixed.i)
(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/basic-primitive-pcnsfv-kt.i)
(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/implicit-euler-basic-kt-primitive.i)
(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/dc.i)
(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-basic-kt-primitive.i)
(modules/navier_stokes/test/tests/finite_volume/cns/heated-channel/transient-porous-kt-primitive.i)

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-hllc.i)

[GlobalParams]
  fp = fp
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_mom_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_mom_x]
    type = FunctionIC
    variable = sup_mom_x
    function = 'exact_rho_ud'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVMassHLLC
    variable = pressure
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVMomentumHLLC
    variable = sup_mom_x
    momentum_component = x
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_mom_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_mom_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVFluidEnergyHLLC
    variable = T_fluid
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []
[]

[Materials]
  [var_mat]
    type = PorousMixedVarMaterial
    pressure = pressure
    superficial_rhou = sup_mom_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  expression = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  expression = '-3.83667087618017*sin(1.1*x)*cos(1.3*x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  expression = '3.48788261470924*cos(1.1*x)*cos(1.3*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  expression = '(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x))*cos(1.3*x) + 3.48788261470924*sin(x)*cos(1.1*x)^2*cos(1.3*x)/cos(x)^2 - 7.67334175236034*sin(1.1*x)*cos(1.1*x)*cos(1.3*x)/cos(x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)^2/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  expression = '26.7439413073546*cos(1.5*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  expression = '1.0*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(x)*cos(1.1*x)*cos(1.3*x)/cos(x)^2 - 1.1*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.1*x)*cos(1.3*x)/cos(x) - 1.3*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.3*x)*cos(1.1*x)/cos(x) + 1.0*(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x) - 40.1159119610319*sin(1.5*x))*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  expression = '0.0106975765229418*cos(1.5*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)*cos(1.3*x)'
[]
[exact_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  expression = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  expression = 'cos(1.3*x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  expression_x = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_mom_x]
    variable = sup_mom_x
    function = exact_rho_ud
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/scalar_advection/mass-frac-advection.i)

rho_initial=1.29
p_initial=1.01e5
T=273.15
gamma=1.4
e_initial=${fparse p_initial / (gamma - 1) / rho_initial}
et_initial=${e_initial}
rho_et_initial=${fparse rho_initial * et_initial}
v_in=1

[GlobalParams]
  fp = fp
  # retain behavior at time of test creation
  two_term_boundary_expansion = false
[]

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

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

[Variables]
  [rho]
    type = MooseVariableFVReal
    initial_condition = ${rho_initial}
  []
  [rho_u]
    type = MooseVariableFVReal
    initial_condition = 1e-15
  []
  [rho_v]
    type = MooseVariableFVReal
    initial_condition = 1e-15
  []
  [rho_et]
    type = MooseVariableFVReal
    initial_condition = ${rho_et_initial}
    scaling = 1e-5
  []
  [mass_frac]
    type = MooseVariableFVReal
    initial_condition = 1e-15
  []
[]

[AuxVariables]
  [U_x]
    type = MooseVariableFVReal
  []
  [U_y]
    type = MooseVariableFVReal
  []
  [pressure]
    type = MooseVariableFVReal
  []
  [temperature]
    type = MooseVariableFVReal
  []
  [courant]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [U_x]
    type = ADMaterialRealAux
    variable = U_x
    property = vel_x
    execute_on = 'timestep_end'
  []
  [U_y]
    type = ADMaterialRealAux
    variable = U_y
    property = vel_y
    execute_on = 'timestep_end'
  []
  [pressure]
    type = ADMaterialRealAux
    variable = pressure
    property = pressure
    execute_on = 'timestep_end'
  []
  [temperature]
    type = ADMaterialRealAux
    variable = temperature
    property = T_fluid
    execute_on = 'timestep_end'
  []
  [courant]
    type = Courant
    variable = courant
    u = U_x
    v = U_y
  []
[]

[FVKernels]
  [mass_time]
    type = FVPorosityTimeDerivative
    variable = rho
  []
  [mass_advection]
    type = PCNSFVKT
    variable = rho
    eqn = "mass"
  []

  [momentum_time_x]
    type = FVTimeKernel
    variable = rho_u
  []
  [momentum_advection_and_pressure_x]
    type = PCNSFVKT
    variable = rho_u
    eqn = "momentum"
    momentum_component = 'x'
  []

  [momentum_time_y]
    type = FVTimeKernel
    variable = rho_v
  []
  [momentum_advection_and_pressure_y]
    type = PCNSFVKT
    variable = rho_v
    eqn = "momentum"
    momentum_component = 'y'
  []

  [energy_time]
    type = FVPorosityTimeDerivative
    variable = rho_et
  []
  [energy_advection]
    type = PCNSFVKT
    variable = rho_et
    eqn = "energy"
  []

  [mass_frac_time]
    type = PCNSFVDensityTimeDerivative
    variable = mass_frac
    rho = rho
  []
  [mass_frac_advection]
    type = PCNSFVKT
    variable = mass_frac
    eqn = "scalar"
  []
[]

[Functions]
  [ud_in]
    type = ParsedVectorFunction
    expression_x = '0'
    expression_y = '${v_in}'
  []
[]


[FVBCs]
  [rho_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = rho
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'mass'
  []
  [rho_u_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = rho_u
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_v_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = rho_v
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'y'
  []
  [rho_et_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = rho_et
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'energy'
  []
  [mass_frac_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = mass_frac
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    scalar = 1
    eqn = 'scalar'
  []

  [rho_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = rho
    pressure = ${p_initial}
    eqn = 'mass'
  []
  [rho_u_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = rho_u
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_v_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = rho_v
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'y'
  []
  [rho_et_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = rho_et
    pressure = ${p_initial}
    eqn = 'energy'
  []
  [mass_frac_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = mass_frac
    pressure = ${p_initial}
    eqn = 'scalar'
  []

  [momentum_x_walls]
    type = PCNSFVImplicitMomentumPressureBC
    variable = rho_u
    boundary = 'left right'
    momentum_component = 'x'
  []
  [momentum_y_walls]
    type = PCNSFVImplicitMomentumPressureBC
    variable = rho_v
    boundary = 'left right'
    momentum_component = 'y'
  []
[]

[Materials]
  [var_mat]
    type = PorousConservedVarMaterial
    rho = rho
    rho_et = rho_et
    superficial_rhou = rho_u
    superficial_rhov = rho_v
    fp = fp
    porosity = porosity
  []
  [porosity]
    type = GenericConstantMaterial
    prop_names = 'porosity'
    prop_values = '1'
  []
[]

[Executioner]
  type = Transient
  [TimeIntegrator]
    type = ActuallyExplicitEuler
  []
  steady_state_detection = true
  steady_state_tolerance = 1e-12
  abort_on_solve_fail = true
  dt = 5e-4
  num_steps = 25
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'initial timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/rotated-2d-bkt-function-porosity-mixed.i)

p_initial=1.01e5
T=273.15
# u refers to the superficial velocity
u_in=1
rho_in=1.30524
sup_mom_y_in=${fparse u_in * rho_in}
user_limiter='upwind'
friction_coeff=10

[GlobalParams]
  fp = fp
  two_term_boundary_expansion = true
  limiter = ${user_limiter}
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    nx = 3
    ymin = 0
    ymax = 18
    ny = 90
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
    initial_condition = ${p_initial}
  []
  [sup_mom_x]
    type = MooseVariableFVReal
    initial_condition = 1e-15
    scaling = 1e-2
  []
  [sup_mom_y]
    type = MooseVariableFVReal
    initial_condition = 1e-15
    scaling = 1e-2
  []
  [T_fluid]
    type = MooseVariableFVReal
    initial_condition = ${T}
    scaling = 1e-5
  []
[]

[AuxVariables]
  [vel_y]
    type = MooseVariableFVReal
  []
  [rho]
    type = MooseVariableFVReal
  []
  [eps]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [vel_y]
    type = ADMaterialRealAux
    variable = vel_y
    property = vel_y
    execute_on = 'timestep_end'
  []
  [rho]
    type = ADMaterialRealAux
    variable = rho
    property = rho
    execute_on = 'timestep_end'
  []
  [eps]
    type = MaterialRealAux
    variable = eps
    property = porosity
    execute_on = 'timestep_end'
  []
[]

[FVKernels]
  [mass_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_dt'
    variable = pressure
  []
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []

  [momentum_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhou_dt'
    variable = sup_mom_x
  []
  [momentum_advection]
    type = PCNSFVKT
    variable = sup_mom_x
    eqn = "momentum"
    momentum_component = 'x'
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_mom_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [drag]
    type = PCNSFVMomentumFriction
    variable = sup_mom_x
    momentum_component = 'x'
    Darcy_name = 'cl'
    momentum_name = superficial_rhou
  []

  [momentum_time_y]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhov_dt'
    variable = sup_mom_y
  []
  [momentum_advection_y]
    type = PCNSFVKT
    variable = sup_mom_y
    eqn = "momentum"
    momentum_component = 'y'
  []
  [eps_grad_y]
    type = PNSFVPGradEpsilon
    variable = sup_mom_y
    momentum_component = 'y'
    epsilon_function = 'eps'
  []
  [drag_y]
    type = PCNSFVMomentumFriction
    variable = sup_mom_y
    momentum_component = 'y'
    Darcy_name = 'cl'
    momentum_name = superficial_rhov
  []

  [energy_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_et_dt'
    variable = T_fluid
  []
  [energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
[]

[FVBCs]
  [rho_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = pressure
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'mass'
    velocity_function_includes_rho = true
  []
  [rhou_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = sup_mom_x
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'x'
    velocity_function_includes_rho = true
  []
  [rhov_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = sup_mom_y
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'y'
    velocity_function_includes_rho = true
  []
  [rho_et_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = T_fluid
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'energy'
    velocity_function_includes_rho = true
  []
  [rho_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = pressure
    pressure = ${p_initial}
    eqn = 'mass'
  []
  [rhou_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = sup_mom_x
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rhov_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = sup_mom_y
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'y'
  []
  [rho_et_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = T_fluid
    pressure = ${p_initial}
    eqn = 'energy'
  []

  [wall_pressure_x]
    type = PCNSFVImplicitMomentumPressureBC
    momentum_component = 'x'
    boundary = 'left right'
    variable = sup_mom_x
  []
  [wall_pressure_y]
    type = PCNSFVImplicitMomentumPressureBC
    momentum_component = 'y'
    boundary = 'left right'
    variable = sup_mom_y
  []

  # Use these to help create more accurate cell centered gradients for cells adjacent to boundaries
  [T_bottom]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T}
    boundary = 'bottom'
  []
  [sup_mom_x_bottom_and_walls]
    type = FVDirichletBC
    variable = sup_mom_x
    value = 0
    boundary = 'bottom left right'
  []
  [sup_mom_y_walls]
    type = FVDirichletBC
    variable = sup_mom_y
    value = 0
    boundary = 'left right'
  []
  [sup_mom_y_bottom]
    type = FVDirichletBC
    variable = sup_mom_y
    value = ${sup_mom_y_in}
    boundary = 'bottom'
  []
  [p_top]
    type = FVDirichletBC
    variable = pressure
    value = ${p_initial}
    boundary = 'top'
  []
[]

[Functions]
  [ud_in]
    type = ParsedVectorFunction
    expression_x = '0'
    expression_y = '${sup_mom_y_in}'
  []
  [eps]
    type = ParsedFunction
    expression = 'if(y < 2.8, 1,
             if(y < 3.2, 1 - .5 / .4 * (y - 2.8),
             if(y < 6.8, .5,
             if(y < 7.2, .5 - .25 / .4 * (y - 6.8),
             if(y < 10.8, .25,
             if(y < 11.2, .25 + .25 / .4 * (y - 10.8),
             if(y < 14.8, .5,
             if(y < 15.2, .5 + .5 / .4 * (y - 14.8),
                1))))))))'
  []
[]

[Materials]
  [var_mat]
    type = PorousMixedVarMaterial
    pressure = pressure
    T_fluid = T_fluid
    superficial_rhou = sup_mom_x
    superficial_rhov = sup_mom_y
    fp = fp
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
  [ad_generic]
    type = ADGenericConstantVectorMaterial
    prop_names = 'cl'
    prop_values = '${friction_coeff} ${friction_coeff} ${friction_coeff}'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  solve_type = NEWTON
  line_search = 'bt'

  type = Transient
  nl_max_its = 20
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e-5
    optimal_iterations = 6
    growth_factor = 1.2
  []
  num_steps = 10000
  end_time = 500
  nl_abs_tol = 1e-7

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       mumps'
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
  checkpoint = true
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/rotated-2d-bkt-function-porosity.i)

p_initial=1.01e5
T=273.15
# u refers to the superficial velocity
u_in=1
user_limiter='upwind'
friction_coeff=10

[GlobalParams]
  fp = fp
  two_term_boundary_expansion = true
  limiter = ${user_limiter}
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    nx = 3
    ymin = 0
    ymax = 18
    ny = 90
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
    initial_condition = ${p_initial}
  []
  [sup_vel_x]
    type = MooseVariableFVReal
    initial_condition = 1e-15
    scaling = 1e-2
  []
  [sup_vel_y]
    type = MooseVariableFVReal
    initial_condition = 1e-15
    scaling = 1e-2
  []
  [T_fluid]
    type = MooseVariableFVReal
    initial_condition = ${T}
    scaling = 1e-5
  []
[]

[AuxVariables]
  [vel_y]
    type = MooseVariableFVReal
  []
  [sup_mom_y]
    type = MooseVariableFVReal
  []
  [rho]
    type = MooseVariableFVReal
  []
  [eps]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [vel_y]
    type = ADMaterialRealAux
    variable = vel_y
    property = vel_y
    execute_on = 'timestep_end'
  []
  [sup_mom_y]
    type = ADMaterialRealAux
    variable = sup_mom_y
    property = superficial_rhov
    execute_on = 'timestep_end'
  []
  [rho]
    type = ADMaterialRealAux
    variable = rho
    property = rho
    execute_on = 'timestep_end'
  []
  [eps]
    type = MaterialRealAux
    variable = eps
    property = porosity
    execute_on = 'timestep_end'
  []
[]

[FVKernels]
  [mass_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_dt'
    variable = pressure
  []
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []

  [momentum_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhou_dt'
    variable = sup_vel_x
  []
  [momentum_advection]
    type = PCNSFVKT
    variable = sup_vel_x
    eqn = "momentum"
    momentum_component = 'x'
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_vel_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [drag]
    type = PCNSFVMomentumFriction
    variable = sup_vel_x
    momentum_component = 'x'
    Darcy_name = 'cl'
    momentum_name = superficial_rhou
  []

  [momentum_time_y]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhov_dt'
    variable = sup_vel_y
  []
  [momentum_advection_y]
    type = PCNSFVKT
    variable = sup_vel_y
    eqn = "momentum"
    momentum_component = 'y'
  []
  [eps_grad_y]
    type = PNSFVPGradEpsilon
    variable = sup_vel_y
    momentum_component = 'y'
    epsilon_function = 'eps'
  []
  [drag_y]
    type = PCNSFVMomentumFriction
    variable = sup_vel_y
    momentum_component = 'y'
    Darcy_name = 'cl'
    momentum_name = superficial_rhov
  []

  [energy_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_et_dt'
    variable = T_fluid
  []
  [energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
[]

[FVBCs]
  [rho_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = pressure
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'mass'
  []
  [rhou_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = sup_vel_x
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rhov_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = sup_vel_y
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'y'
  []
  [rho_et_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = T_fluid
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'energy'
  []
  [rho_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = pressure
    pressure = ${p_initial}
    eqn = 'mass'
  []
  [rhou_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = sup_vel_x
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rhov_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = sup_vel_y
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'y'
  []
  [rho_et_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = T_fluid
    pressure = ${p_initial}
    eqn = 'energy'
  []

  [wall_pressure_x]
    type = PCNSFVImplicitMomentumPressureBC
    momentum_component = 'x'
    boundary = 'left right'
    variable = sup_vel_x
  []
  [wall_pressure_y]
    type = PCNSFVImplicitMomentumPressureBC
    momentum_component = 'y'
    boundary = 'left right'
    variable = sup_vel_y
  []

  # Use these to help create more accurate cell centered gradients for cells adjacent to boundaries
  [T_bottom]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T}
    boundary = 'bottom'
  []
  [sup_vel_x_bottom_and_walls]
    type = FVDirichletBC
    variable = sup_vel_x
    value = 0
    boundary = 'bottom left right'
  []
  [sup_vel_y_walls]
    type = FVDirichletBC
    variable = sup_vel_y
    value = 0
    boundary = 'left right'
  []
  [sup_vel_y_bottom]
    type = FVDirichletBC
    variable = sup_vel_y
    value = ${u_in}
    boundary = 'bottom'
  []
  [p_top]
    type = FVDirichletBC
    variable = pressure
    value = ${p_initial}
    boundary = 'top'
  []
[]

[Functions]
  [ud_in]
    type = ParsedVectorFunction
    expression_x = '0'
    expression_y = '${u_in}'
  []
  [eps]
    type = ParsedFunction
    expression = 'if(y < 2.8, 1,
             if(y < 3.2, 1 - .5 / .4 * (y - 2.8),
             if(y < 6.8, .5,
             if(y < 7.2, .5 - .25 / .4 * (y - 6.8),
             if(y < 10.8, .25,
             if(y < 11.2, .25 + .25 / .4 * (y - 10.8),
             if(y < 14.8, .5,
             if(y < 15.2, .5 + .5 / .4 * (y - 14.8),
                1))))))))'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    T_fluid = T_fluid
    superficial_vel_x = sup_vel_x
    superficial_vel_y = sup_vel_y
    fp = fp
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
  [ad_generic]
    type = ADGenericConstantVectorMaterial
    prop_names = 'cl'
    prop_values = '${friction_coeff} ${friction_coeff} ${friction_coeff}'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  solve_type = NEWTON
  line_search = 'bt'

  type = Transient
  nl_max_its = 20
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e-5
    optimal_iterations = 6
    growth_factor = 1.2
  []
  num_steps = 10000
  end_time = 500
  nl_abs_tol = 1e-7

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       mumps'
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
  checkpoint = true
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/hllc.i)

p_initial=1.01e5
T=273.15
# u refers to the superficial velocity
u_in=1

[GlobalParams]
  fp = fp
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 18
    nx = 180
  []
  [to_pt5]
    input = cartesian
    type = SubdomainBoundingBoxGenerator
    bottom_left = '2 0 0'
    top_right = '4 1 0'
    block_id = 1
  []
  [pt5]
    input = to_pt5
    type = SubdomainBoundingBoxGenerator
    bottom_left = '4 0 0'
    top_right = '6 1 0'
    block_id = 2
  []
  [to_pt25]
    input = pt5
    type = SubdomainBoundingBoxGenerator
    bottom_left = '6 0 0'
    top_right = '8 1 0'
    block_id = 3
  []
  [pt25]
    input = to_pt25
    type = SubdomainBoundingBoxGenerator
    bottom_left = '8 0 0'
    top_right = '10 1 0'
    block_id = 4
  []
  [to_pt5_again]
    input = pt25
    type = SubdomainBoundingBoxGenerator
    bottom_left = '10 0 0'
    top_right = '12 1 0'
    block_id = 5
  []
  [pt5_again]
    input = to_pt5_again
    type = SubdomainBoundingBoxGenerator
    bottom_left = '12 0 0'
    top_right = '14 1 0'
    block_id = 6
  []
  [to_one]
    input = pt5_again
    type = SubdomainBoundingBoxGenerator
    bottom_left = '14 0 0'
    top_right = '16 1 0'
    block_id = 7
  []
  [one]
    input = to_one
    type = SubdomainBoundingBoxGenerator
    bottom_left = '16 0 0'
    top_right = '18 1 0'
    block_id = 8
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
    initial_condition = ${p_initial}
  []
  [sup_vel_x]
    type = MooseVariableFVReal
    initial_condition = 1
    scaling = 1e-2
  []
  [T_fluid]
    type = MooseVariableFVReal
    initial_condition = ${T}
    scaling = 1e-5
  []
[]

[AuxVariables]
  [vel_x]
    type = MooseVariableFVReal
  []
  [sup_mom_x]
    type = MooseVariableFVReal
  []
  [rho]
    type = MooseVariableFVReal
  []
  [worst_courant]
    type = MooseVariableFVReal
  []
  [porosity]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [vel_x]
    type = ADMaterialRealAux
    variable = vel_x
    property = vel_x
    execute_on = 'timestep_end'
  []
  [sup_mom_x]
    type = ADMaterialRealAux
    variable = sup_mom_x
    property = superficial_rhou
    execute_on = 'timestep_end'
  []
  [rho]
    type = ADMaterialRealAux
    variable = rho
    property = rho
    execute_on = 'timestep_end'
  []
  [worst_courant]
    type = Courant
    variable = worst_courant
    u = sup_vel_x
    execute_on = 'timestep_end'
  []
  [porosity]
    type = MaterialRealAux
    variable = porosity
    property = porosity
    execute_on = 'timestep_end'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVMassHLLC
    variable = pressure
  []

  [momentum_advection]
    type = PCNSFVMomentumHLLC
    variable = sup_vel_x
    momentum_component = 'x'
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_vel_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []

  [energy_advection]
    type = PCNSFVFluidEnergyHLLC
    variable = T_fluid
  []
[]

[FVBCs]
  [rho_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = pressure
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'mass'
  []
  [rhou_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = sup_vel_x
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_et_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = T_fluid
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'energy'
  []
  [rho_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = pressure
    pressure = ${p_initial}
    eqn = 'mass'
  []
  [rhou_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = sup_vel_x
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_et_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = T_fluid
    pressure = ${p_initial}
    eqn = 'energy'
  []

  # Use these to help create more accurate cell centered gradients for cells adjacent to boundaries
  [T_left]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T}
    boundary = 'left'
  []
  [sup_vel_left]
    type = FVDirichletBC
    variable = sup_vel_x
    value = ${u_in}
    boundary = 'left'
  []
  [p_right]
    type = FVDirichletBC
    variable = pressure
    value = ${p_initial}
    boundary = 'right'
  []
[]

[Functions]
  [ud_in]
    type = ParsedVectorFunction
    expression_x = '${u_in}'
  []
  [eps]
    type = ParsedFunction
    expression = 'if(x < 2, 1,
             if(x < 4, 1 - .5 / 2 * (x - 2),
             if(x < 6, .5,
             if(x < 8, .5 - .25 / 2 * (x - 6),
             if(x < 10, .25,
             if(x < 12, .25 + .25 / 2 * (x - 10),
             if(x < 14, .5,
             if(x < 16, .5 + .5 / 2 * (x - 14),
                1))))))))'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    T_fluid = T_fluid
    superficial_vel_x = sup_vel_x
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Executioner]
  solve_type = NEWTON
  line_search = 'bt'
  type = Steady
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
  checkpoint = true
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/basic-conserved-pcnsfv-kt.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [rho]
    type = MooseVariableFVReal
  []
  [rho_ud]
    type = MooseVariableFVReal
  []
  [rho_et]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = rho
    function = 'exact_rho'
  []
  [sup_vel_x]
    type = FunctionIC
    variable = rho_ud
    function = 'exact_rho_ud'
  []
  [T_fluid]
    type = FunctionIC
    variable = rho_et
    function = 'exact_rho_et'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = rho
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = rho
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = rho_ud
    momentum_component = x
    eqn = "momentum"
  []
  [momentum_fn]
    type = FVBodyForce
    variable = rho_ud
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = rho_et
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = rho_et
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = rho
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = rho_ud
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = rho_et
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = rho
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = rho_ud
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = rho_et
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [rho_right]
    type = FVFunctionDirichletBC
    variable = rho
    function = exact_rho
    boundary = 'right'
  []
  [rho_ud_left]
    type = FVFunctionDirichletBC
    variable = rho_ud
    function = exact_rho_ud
    boundary = 'left'
  []
  [rho_et_left]
    type = FVFunctionDirichletBC
    variable = rho_et
    function = exact_rho_et
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousConservedVarMaterial
    rho = rho
    superficial_rhou = rho_ud
    rho_et = rho_et
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  expression = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  expression = '-3.45300378856215*sin(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  expression = '3.13909435323832*cos(1.1*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  expression = '-0.9*(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + 0.9*(10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) + 3.13909435323832*sin(x)*cos(1.1*x)^2/cos(x)^2 - 6.9060075771243*sin(1.1*x)*cos(1.1*x)/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  expression = '26.7439413073546*cos(1.2*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  expression = '0.9*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(x)*cos(1.1*x)/cos(x)^2 - 0.99*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(1.1*x)/cos(x) + 0.9*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) - 32.0927295688256*sin(1.2*x))*cos(1.1*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  expression = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  expression = '3.13909435323832*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  expression = '0.9*cos(1.1*x)/cos(x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  expression_x = '0.9*cos(1.1*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  expression = '0.9'
[]
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options = '-snes_linesearch_monitor'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho]
    type = ElementL2Error
    variable = rho
    function = exact_rho
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_ud]
    variable = rho_ud
    function = exact_rho_ud
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2rho_et]
    variable = rho_et
    function = exact_rho_et
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-basic-kt-mixed.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_mom_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_mom_x]
    type = FunctionIC
    variable = sup_mom_x
    function = 'exact_rho_ud'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = sup_mom_x
    momentum_component = x
    eqn = "momentum"
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_mom_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_mom_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_mom_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [pressure_right]
    type = FVFunctionDirichletBC
    variable = pressure
    function = exact_p
    boundary = 'right'
  []
  [sup_mom_x_left]
    type = FVFunctionDirichletBC
    variable = sup_mom_x
    function = exact_rho_ud
    boundary = 'left'
  []
  [T_fluid_left]
    type = FVFunctionDirichletBC
    variable = T_fluid
    function = exact_T
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousMixedVarMaterial
    pressure = pressure
    superficial_rhou = sup_mom_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  expression = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  expression = '-3.83667087618017*sin(1.1*x)*cos(1.3*x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  expression = '3.48788261470924*cos(1.1*x)*cos(1.3*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  expression = '(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x))*cos(1.3*x) + 3.48788261470924*sin(x)*cos(1.1*x)^2*cos(1.3*x)/cos(x)^2 - 7.67334175236034*sin(1.1*x)*cos(1.1*x)*cos(1.3*x)/cos(x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)^2/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  expression = '26.7439413073546*cos(1.5*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  expression = '1.0*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(x)*cos(1.1*x)*cos(1.3*x)/cos(x)^2 - 1.1*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.1*x)*cos(1.3*x)/cos(x) - 1.3*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.3*x)*cos(1.1*x)/cos(x) + 1.0*(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x) - 40.1159119610319*sin(1.5*x))*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  expression = '0.0106975765229418*cos(1.5*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)*cos(1.3*x)'
[]
[exact_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  expression = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  expression = 'cos(1.3*x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  expression_x = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_mom_x]
    variable = sup_mom_x
    function = exact_rho_ud
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/basic-primitive-pcnsfv-kt.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_vel_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_vel_x]
    type = FunctionIC
    variable = sup_vel_x
    function = 'exact_sup_vel_x'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = sup_vel_x
    momentum_component = x
    eqn = "momentum"
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_vel_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [pressure_right]
    type = FVFunctionDirichletBC
    variable = pressure
    function = exact_p
    boundary = 'right'
  []
  [sup_vel_x_left]
    type = FVFunctionDirichletBC
    variable = sup_vel_x
    function = exact_sup_vel_x
    boundary = 'left'
  []
  [T_fluid_left]
    type = FVFunctionDirichletBC
    variable = T_fluid
    function = exact_T
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    superficial_vel_x = sup_vel_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  expression = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  expression = '-3.45300378856215*sin(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  expression = '3.13909435323832*cos(1.1*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  expression = '-0.9*(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + 0.9*(10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) + 3.13909435323832*sin(x)*cos(1.1*x)^2/cos(x)^2 - 6.9060075771243*sin(1.1*x)*cos(1.1*x)/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  expression = '26.7439413073546*cos(1.2*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  expression = '0.9*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(x)*cos(1.1*x)/cos(x)^2 - 0.99*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(1.1*x)/cos(x) + 0.9*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) - 32.0927295688256*sin(1.2*x))*cos(1.1*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  expression = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  expression = '3.13909435323832*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  expression = '0.9*cos(1.1*x)/cos(x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  expression_x = '0.9*cos(1.1*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  expression = '0.9'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_vel_x]
    variable = sup_vel_x
    function = exact_sup_vel_x
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/implicit-euler-basic-kt-primitive.i)

p_initial=1.01e5
T=273.15
# u refers to the superficial velocity
u_in=1
user_limiter='upwind'

[GlobalParams]
  fp = fp
  two_term_boundary_expansion = true
  limiter = ${user_limiter}
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 18
    nx = 180
  []
  [to_pt5]
    input = cartesian
    type = SubdomainBoundingBoxGenerator
    bottom_left = '2 0 0'
    top_right = '4 1 0'
    block_id = 1
  []
  [pt5]
    input = to_pt5
    type = SubdomainBoundingBoxGenerator
    bottom_left = '4 0 0'
    top_right = '6 1 0'
    block_id = 2
  []
  [to_pt25]
    input = pt5
    type = SubdomainBoundingBoxGenerator
    bottom_left = '6 0 0'
    top_right = '8 1 0'
    block_id = 3
  []
  [pt25]
    input = to_pt25
    type = SubdomainBoundingBoxGenerator
    bottom_left = '8 0 0'
    top_right = '10 1 0'
    block_id = 4
  []
  [to_pt5_again]
    input = pt25
    type = SubdomainBoundingBoxGenerator
    bottom_left = '10 0 0'
    top_right = '12 1 0'
    block_id = 5
  []
  [pt5_again]
    input = to_pt5_again
    type = SubdomainBoundingBoxGenerator
    bottom_left = '12 0 0'
    top_right = '14 1 0'
    block_id = 6
  []
  [to_one]
    input = pt5_again
    type = SubdomainBoundingBoxGenerator
    bottom_left = '14 0 0'
    top_right = '16 1 0'
    block_id = 7
  []
  [one]
    input = to_one
    type = SubdomainBoundingBoxGenerator
    bottom_left = '16 0 0'
    top_right = '18 1 0'
    block_id = 8
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
    initial_condition = ${p_initial}
  []
  [sup_vel_x]
    type = MooseVariableFVReal
    initial_condition = 1e-15
    scaling = 1e-2
  []
  [T_fluid]
    type = MooseVariableFVReal
    initial_condition = ${T}
    scaling = 1e-5
  []
[]

[AuxVariables]
  [vel_x]
    type = MooseVariableFVReal
  []
  [sup_mom_x]
    type = MooseVariableFVReal
  []
  [rho]
    type = MooseVariableFVReal
  []
  [worst_courant]
    type = MooseVariableFVReal
  []
  [porosity]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [vel_x]
    type = ADMaterialRealAux
    variable = vel_x
    property = vel_x
    execute_on = 'timestep_end'
  []
  [sup_mom_x]
    type = ADMaterialRealAux
    variable = sup_mom_x
    property = superficial_rhou
    execute_on = 'timestep_end'
  []
  [rho]
    type = ADMaterialRealAux
    variable = rho
    property = rho
    execute_on = 'timestep_end'
  []
  [worst_courant]
    type = Courant
    variable = worst_courant
    u = sup_vel_x
    execute_on = 'timestep_end'
  []
  [porosity]
    type = MaterialRealAux
    variable = porosity
    property = porosity
    execute_on = 'timestep_end'
  []
[]

[FVKernels]
  [mass_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_dt'
    variable = pressure
  []
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []

  [momentum_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhou_dt'
    variable = sup_vel_x
  []
  [momentum_advection]
    type = PCNSFVKT
    variable = sup_vel_x
    eqn = "momentum"
    momentum_component = 'x'
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_vel_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []

  [energy_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_et_dt'
    variable = T_fluid
  []
  [energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
[]

[FVBCs]
  [rho_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = pressure
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'mass'
  []
  [rhou_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = sup_vel_x
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_et_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = T_fluid
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'energy'
  []
  [rho_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = pressure
    pressure = ${p_initial}
    eqn = 'mass'
  []
  [rhou_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = sup_vel_x
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_et_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = T_fluid
    pressure = ${p_initial}
    eqn = 'energy'
  []

  # Use these to help create more accurate cell centered gradients for cells adjacent to boundaries
  [T_left]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T}
    boundary = 'left'
  []
  [sup_vel_left]
    type = FVDirichletBC
    variable = sup_vel_x
    value = ${u_in}
    boundary = 'left'
  []
  [p_right]
    type = FVDirichletBC
    variable = pressure
    value = ${p_initial}
    boundary = 'right'
  []
[]

[Functions]
  [ud_in]
    type = ParsedVectorFunction
    expression_x = '${u_in}'
  []
  [eps]
    type = ParsedFunction
    expression = 'if(x < 2, 1,
             if(x < 4, 1 - .5 / 2 * (x - 2),
             if(x < 6, .5,
             if(x < 8, .5 - .25 / 2 * (x - 6),
             if(x < 10, .25,
             if(x < 12, .25 + .25 / 2 * (x - 10),
             if(x < 14, .5,
             if(x < 16, .5 + .5 / 2 * (x - 14),
                1))))))))'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    T_fluid = T_fluid
    superficial_vel_x = sup_vel_x
    fp = fp
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Executioner]
  solve_type = NEWTON
  line_search = 'bt'

  type = Transient
  nl_max_its = 20
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e-5
    optimal_iterations = 6
    growth_factor = 1.2
  []
  num_steps = 10000
  end_time = 500
  nl_abs_tol = 1e-8
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
  checkpoint = true
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/navier_stokes/test/tests/finite_volume/cns/straight_channel_porosity_step/dc.i)

p_initial=1.01e5
T=273.15
# u refers to the superficial velocity
u_in=1
rho_in=1.30524
sup_mom_y_in=${fparse u_in * rho_in}
user_limiter='min_mod'
friction_coeff=10

[GlobalParams]
  fp = fp
  two_term_boundary_expansion = true
  limiter = ${user_limiter}
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    nx = 3
    ymin = 0
    ymax = 18
    ny = 90
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
    initial_condition = ${p_initial}
  []
  [sup_mom_x]
    type = MooseVariableFVReal
    initial_condition = 1e-15
  []
  [sup_mom_y]
    type = MooseVariableFVReal
    initial_condition = 1e-15
  []
  [T_fluid]
    type = MooseVariableFVReal
    initial_condition = ${T}
  []
[]

[AuxVariables]
  [vel_y]
    type = MooseVariableFVReal
  []
  [rho]
    type = MooseVariableFVReal
  []
  [eps]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [vel_y]
    type = ADMaterialRealAux
    variable = vel_y
    property = vel_y
    execute_on = 'timestep_end'
  []
  [rho]
    type = ADMaterialRealAux
    variable = rho
    property = rho
    execute_on = 'timestep_end'
  []
  [eps]
    type = MaterialRealAux
    variable = eps
    property = porosity
    execute_on = 'timestep_end'
  []
[]

[FVKernels]
  [mass_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_dt'
    variable = pressure
  []
  [mass_advection]
    type = PCNSFVKTDC
    variable = pressure
    eqn = "mass"
  []

  [momentum_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhou_dt'
    variable = sup_mom_x
  []
  [momentum_advection]
    type = PCNSFVKTDC
    variable = sup_mom_x
    eqn = "momentum"
    momentum_component = 'x'
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_mom_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [drag]
    type = PCNSFVMomentumFriction
    variable = sup_mom_x
    momentum_component = 'x'
    Darcy_name = 'cl'
    momentum_name = superficial_rhou
  []

  [momentum_time_y]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhov_dt'
    variable = sup_mom_y
  []
  [momentum_advection_y]
    type = PCNSFVKTDC
    variable = sup_mom_y
    eqn = "momentum"
    momentum_component = 'y'
  []
  [eps_grad_y]
    type = PNSFVPGradEpsilon
    variable = sup_mom_y
    momentum_component = 'y'
    epsilon_function = 'eps'
  []
  [drag_y]
    type = PCNSFVMomentumFriction
    variable = sup_mom_y
    momentum_component = 'y'
    Darcy_name = 'cl'
    momentum_name = superficial_rhov
  []

  [energy_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_et_dt'
    variable = T_fluid
  []
  [energy_advection]
    type = PCNSFVKTDC
    variable = T_fluid
    eqn = "energy"
  []
[]

[FVBCs]
  [rho_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = pressure
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'mass'
    velocity_function_includes_rho = true
  []
  [rhou_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = sup_mom_x
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'x'
    velocity_function_includes_rho = true
  []
  [rhov_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = sup_mom_y
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'y'
    velocity_function_includes_rho = true
  []
  [rho_et_bottom]
    type = PCNSFVStrongBC
    boundary = 'bottom'
    variable = T_fluid
    superficial_velocity = 'ud_in'
    T_fluid = ${T}
    eqn = 'energy'
    velocity_function_includes_rho = true
  []
  [rho_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = pressure
    pressure = ${p_initial}
    eqn = 'mass'
  []
  [rhou_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = sup_mom_x
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rhov_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = sup_mom_y
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'y'
  []
  [rho_et_top]
    type = PCNSFVStrongBC
    boundary = 'top'
    variable = T_fluid
    pressure = ${p_initial}
    eqn = 'energy'
  []

  [wall_pressure_x]
    type = PCNSFVImplicitMomentumPressureBC
    momentum_component = 'x'
    boundary = 'left right'
    variable = sup_mom_x
  []
  [wall_pressure_y]
    type = PCNSFVImplicitMomentumPressureBC
    momentum_component = 'y'
    boundary = 'left right'
    variable = sup_mom_y
  []

  # Use these to help create more accurate cell centered gradients for cells adjacent to boundaries
  [T_bottom]
    type = FVDirichletBC
    variable = T_fluid
    value = ${T}
    boundary = 'bottom'
  []
  [sup_mom_x_bottom_and_walls]
    type = FVDirichletBC
    variable = sup_mom_x
    value = 0
    boundary = 'bottom left right'
  []
  [sup_mom_y_walls]
    type = FVDirichletBC
    variable = sup_mom_y
    value = 0
    boundary = 'left right'
  []
  [sup_mom_y_bottom]
    type = FVDirichletBC
    variable = sup_mom_y
    value = ${sup_mom_y_in}
    boundary = 'bottom'
  []
  [p_top]
    type = FVDirichletBC
    variable = pressure
    value = ${p_initial}
    boundary = 'top'
  []
[]

[Functions]
  [ud_in]
    type = ParsedVectorFunction
    expression_x = '0'
    expression_y = '${sup_mom_y_in}'
  []
  [eps]
    type = ParsedFunction
    expression = 'if(y < 2.8, 1,
             if(y < 3.2, 1 - .5 / .4 * (y - 2.8),
             if(y < 6.8, .5,
             if(y < 7.2, .5 - .25 / .4 * (y - 6.8),
             if(y < 10.8, .25,
             if(y < 11.2, .25 + .25 / .4 * (y - 10.8),
             if(y < 14.8, .5,
             if(y < 15.2, .5 + .5 / .4 * (y - 14.8),
                1))))))))'
  []
[]

[Materials]
  [var_mat]
    type = PorousMixedVarMaterial
    pressure = pressure
    T_fluid = T_fluid
    superficial_rhou = sup_mom_x
    superficial_rhov = sup_mom_y
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
  [ad_generic]
    type = ADGenericConstantVectorMaterial
    prop_names = 'cl'
    prop_values = '${friction_coeff} ${friction_coeff} ${friction_coeff}'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  solve_type = NEWTON
  line_search = 'bt'

  type = Transient
  nl_max_its = 20
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e-5
    optimal_iterations = 6
    growth_factor = 1.2
  []
  num_steps = 10
  nl_abs_tol = 1e-8

  automatic_scaling = true
  compute_scaling_once = false
  resid_vs_jac_scaling_param = 0.5
  verbose = true
  steady_state_detection = true
  steady_state_tolerance = 1e-8
  normalize_solution_diff_norm_by_dt = false

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

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

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  active = ''
  [num_nl]
    type = NumNonlinearIterations
  []
  [total_nl]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/varying-eps-basic-kt-primitive.i)

[GlobalParams]
  fp = fp
  limiter = 'central_difference'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = .1
    xmax = .6
    nx = 2
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
  []
  [sup_vel_x]
    type = MooseVariableFVReal
  []
  [T_fluid]
    type = MooseVariableFVReal
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    variable = pressure
    function = 'exact_p'
  []
  [sup_vel_x]
    type = FunctionIC
    variable = sup_vel_x
    function = 'exact_sup_vel_x'
  []
  [T_fluid]
    type = FunctionIC
    variable = T_fluid
    function = 'exact_T'
  []
[]

[FVKernels]
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []
  [mass_fn]
    type = FVBodyForce
    variable = pressure
    function = 'forcing_rho'
  []

  [momentum_x_advection]
    type = PCNSFVKT
    variable = sup_vel_x
    momentum_component = x
    eqn = "momentum"
  []
  [eps_grad]
    type = PNSFVPGradEpsilon
    variable = sup_vel_x
    momentum_component = 'x'
    epsilon_function = 'eps'
  []
  [momentum_fn]
    type = FVBodyForce
    variable = sup_vel_x
    function = 'forcing_rho_ud'
  []

  [fluid_energy_advection]
    type = PCNSFVKT
    variable = T_fluid
    eqn = "energy"
  []
  [energy_fn]
    type = FVBodyForce
    variable = T_fluid
    function = 'forcing_rho_et'
  []
[]

[FVBCs]
  [mass_left]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'mass'
  []
  [momentum_left]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [energy_left]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = left
    T_fluid = 'exact_T'
    superficial_velocity = 'exact_superficial_velocity'
    eqn = 'energy'
  []
  [mass_right]
    variable = pressure
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'mass'
    pressure = 'exact_p'
  []
  [momentum_right]
    variable = sup_vel_x
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'momentum'
    momentum_component = 'x'
    pressure = 'exact_p'
  []
  [energy_right]
    variable = T_fluid
    type = PCNSFVStrongBC
    boundary = right
    eqn = 'energy'
    pressure = 'exact_p'
  []

  # help gradient reconstruction
  [pressure_right]
    type = FVFunctionDirichletBC
    variable = pressure
    function = exact_p
    boundary = 'right'
  []
  [sup_vel_x_left]
    type = FVFunctionDirichletBC
    variable = sup_vel_x
    function = exact_sup_vel_x
    boundary = 'left'
  []
  [T_fluid_left]
    type = FVFunctionDirichletBC
    variable = T_fluid
    function = exact_T
    boundary = 'left'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    superficial_vel_x = sup_vel_x
    T_fluid = T_fluid
    porosity = porosity
  []
  [porosity]
    type = GenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'eps'
  []
[]

[Functions]
[exact_rho]
  type = ParsedFunction
  expression = '3.48788261470924*cos(x)'
[]
[forcing_rho]
  type = ParsedFunction
  expression = '-3.83667087618017*sin(1.1*x)*cos(1.3*x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)'
[]
[exact_rho_ud]
  type = ParsedFunction
  expression = '3.48788261470924*cos(1.1*x)*cos(1.3*x)'
[]
[forcing_rho_ud]
  type = ParsedFunction
  expression = '(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x))*cos(1.3*x) + 3.48788261470924*sin(x)*cos(1.1*x)^2*cos(1.3*x)/cos(x)^2 - 7.67334175236034*sin(1.1*x)*cos(1.1*x)*cos(1.3*x)/cos(x) - 4.53424739912202*sin(1.3*x)*cos(1.1*x)^2/cos(x)'
[]
[exact_rho_et]
  type = ParsedFunction
  expression = '26.7439413073546*cos(1.5*x)'
[]
[forcing_rho_et]
  type = ParsedFunction
  expression = '1.0*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(x)*cos(1.1*x)*cos(1.3*x)/cos(x)^2 - 1.1*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.1*x)*cos(1.3*x)/cos(x) - 1.3*(3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.5*x))*sin(1.3*x)*cos(1.1*x)/cos(x) + 1.0*(-(10.6975765229419*cos(1.5*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.5*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 16.0463647844128*sin(1.5*x)/cos(x))*cos(x) - 40.1159119610319*sin(1.5*x))*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[exact_T]
  type = ParsedFunction
  expression = '0.0106975765229418*cos(1.5*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
[]
[exact_eps_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)*cos(1.3*x)'
[]
[exact_p]
  type = ParsedFunction
  expression = '3.48788261470924*(3.06706896551724*cos(1.5*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
[]
[exact_sup_vel_x]
  type = ParsedFunction
  expression = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[eps]
  type = ParsedFunction
  expression = 'cos(1.3*x)'
[]
[exact_superficial_velocity]
  type = ParsedVectorFunction
  expression_x = '1.0*cos(1.1*x)*cos(1.3*x)/cos(x)'
[]
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  num_steps = 1
  dtmin = 1
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_max_its = 50
  line_search = bt
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2pressure]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2sup_vel_x]
    variable = sup_vel_x
    function = exact_sup_vel_x
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T_fluid]
    variable = T_fluid
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/cns/heated-channel/transient-porous-kt-primitive.i)

p_initial=1.01e5
T=273.15
u_in=10
eps=1
superficial_vel_in=${fparse u_in * eps}

[GlobalParams]
  fp = fp
  limiter = 'vanLeer'
  two_term_boundary_expansion = true
[]

[Mesh]
  [cartesian]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 10
    nx = 100
  []
[]

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

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [pressure]
    type = MooseVariableFVReal
    initial_condition = ${p_initial}
  []
  [superficial_vel_x]
    type = MooseVariableFVReal
    initial_condition = ${superficial_vel_in}
  []
  [temperature]
    type = MooseVariableFVReal
    initial_condition = ${T}
  []
[]

[AuxVariables]
  [rho]
    type = MooseVariableFVReal
  []
  [superficial_rhou]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [rho]
    type = ADMaterialRealAux
    variable = rho
    property = rho
    execute_on = 'timestep_end'
  []
  [superficial_rhou]
    type = ADMaterialRealAux
    variable = superficial_rhou
    property = superficial_rhou
    execute_on = 'timestep_end'
  []
[]

[FVKernels]
  [mass_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_dt'
    variable = pressure
  []
  [mass_advection]
    type = PCNSFVKT
    variable = pressure
    eqn = "mass"
  []

  [momentum_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rhou_dt'
    variable = superficial_vel_x
  []
  [momentum_advection]
    type = PCNSFVKT
    variable = superficial_vel_x
    eqn = "momentum"
    momentum_component = 'x'
  []

  [energy_time]
    type = FVMatPropTimeKernel
    mat_prop_time_derivative = 'dsuperficial_rho_et_dt'
    variable = temperature
  []
  [energy_advection]
    type = PCNSFVKT
    variable = temperature
    eqn = "energy"
  []
  [heat]
    type = FVBodyForce
    variable = temperature
    value = 1e6
  []
[]

[FVBCs]
  [rho_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = pressure
    superficial_velocity = 'superficial_vel_in'
    T_fluid = ${T}
    eqn = 'mass'
  []
  [rhou_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = superficial_vel_x
    superficial_velocity = 'superficial_vel_in'
    T_fluid = ${T}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_et_left]
    type = PCNSFVStrongBC
    boundary = 'left'
    variable = temperature
    superficial_velocity = 'superficial_vel_in'
    T_fluid = ${T}
    eqn = 'energy'
  []
  [rho_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = pressure
    pressure = ${p_initial}
    eqn = 'mass'
  []
  [rhou_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = superficial_vel_x
    pressure = ${p_initial}
    eqn = 'momentum'
    momentum_component = 'x'
  []
  [rho_et_right]
    type = PCNSFVStrongBC
    boundary = 'right'
    variable = temperature
    pressure = ${p_initial}
    eqn = 'energy'
  []

  # Use these to help create more accurate cell centered gradients for cells adjacent to boundaries
  [T_left]
    type = FVDirichletBC
    variable = temperature
    value = ${T}
    boundary = 'left'
  []
  [sup_vel_left]
    type = FVDirichletBC
    variable = superficial_vel_x
    value = ${superficial_vel_in}
    boundary = 'left'
  []
  [p_right]
    type = FVDirichletBC
    variable = pressure
    value = ${p_initial}
    boundary = 'right'
  []
[]

[Functions]
  [superficial_vel_in]
    type = ParsedVectorFunction
    expression_x = '${superficial_vel_in}'
  []
[]

[Materials]
  [var_mat]
    type = PorousPrimitiveVarMaterial
    pressure = pressure
    T_fluid = temperature
    superficial_vel_x = superficial_vel_x
    fp = fp
    porosity = porosity
  []
  [fluid_only]
    type = GenericConstantMaterial
    prop_names = 'porosity'
    prop_values = '${eps}'
  []
[]

[Executioner]
  solve_type = NEWTON
  type = Transient
  nl_max_its = 20
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e-5
    optimal_iterations = 10
  []
  steady_state_detection = false
  steady_state_tolerance = 1e-12
  abort_on_solve_fail = false
  end_time = 100
  nl_abs_tol = 1e-8
  dtmin = 5e-5
  automatic_scaling = true
  compute_scaling_once = false
  verbose = true

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -pc_factor_shift_type -snes_linesearch_minlambda'
  petsc_options_value = 'lu       mumps                      NONZERO               1e-3 '
[]

[Outputs]
  [exo]
    type = Exodus
    execute_on = 'final'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
  checkpoint = true
[]

[Debug]
  show_var_residual_norms = true
[]

Overview
Input Parameters
Input Files