LinearFVPressureCorrectionDiffusion

Adds the pressure correction diffusion term for the linear finite volume SIMPLE algorithm.

This kernel adds the pressure correction diffusion term used by the linear finite volume SIMPLE algorithm. The pressure correction equation uses Ainv, the inverse momentum matrix diagonal, as the diffusion tensor. The Ainv functor is computed by RhieChowMassFlux.

For direct syntax, add the kernel to the [LinearFVKernels] block and pass the same kernel name to the "p_diffusion_kernel" parameter of RhieChowMassFlux:

[UserObjects<<<{"href": "../../syntax/UserObjects/index.html"}>>>]
  [rc]
    type = RhieChowMassFlux<<<{"description": "Computes H/A and 1/A together with face mass fluxes for segregated momentum-pressure equations using linear systems.", "href": "../userobjects/RhieChowMassFlux.html"}>>>
    u<<<{"description": "The x-component of velocity"}>>> = vel_x
    v<<<{"description": "The y-component of velocity"}>>> = vel_y
    pressure<<<{"description": "The pressure variable."}>>> = pressure
    rho<<<{"description": "Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${rho}
    p_diffusion_kernel<<<{"description": "The LinearFVPressureCorrectionDiffusion kernel acting on the pressure."}>>> = p_diffusion
  []
[]

[LinearFVKernels<<<{"href": "../../syntax/LinearFVKernels/index.html"}>>>]
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion<<<{"description": "Adds the pressure correction diffusion term for the linear finite volume SIMPLE algorithm.", "href": "LinearFVPressureCorrectionDiffusion.html"}>>>
    variable<<<{"description": "The name of the variable whose linear system this object contributes to"}>>> = pressure
    diffusion_tensor<<<{"description": "Functor describing a diagonal diffusion tensor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = Ainv
    use_nonorthogonal_correction<<<{"description": "If the nonorthogonal correction should be used when computing the normal gradient."}>>> = false
  []
[]

Selecting Interpolation

Select average or harmonic interpolation for the Ainv face values with "pressure_diffusion_interpolation" on RhieChowMassFlux. When using the Physics syntax, set "pressure_diffusion_interpolation" instead:

      pressure_diffusion_interpolation = ${pressure_diffusion_ainv_interp_method}

      momentum_advection_interpolation = ${advected_interp_method}
      pressure_diffusion_interpolation = ${pressure_diffusion_ainv_interp_method}

Input Parameters

diffusion_tensorFunctor describing a diagonal diffusion tensor. 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:Functor describing a diagonal diffusion tensor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
variableThe name of the variable whose linear system this object contributes to
C++ Type:LinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable whose linear system this object contributes to

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
force_boundary_executionFalseWhether to force execution of this object on all external boundaries.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to force execution of this object on all external boundaries.
use_nonorthogonal_correctionTrueIf the nonorthogonal correction should be used when computing the normal gradient.
Default:True
C++ Type:bool
Controllable:No
Description:If the nonorthogonal correction should be used when computing the normal gradient.
use_nonorthogonal_correction_on_boundaryFalseIf the nonorthogonal correction should be used when computing the normal gradient.
Default:False
C++ Type:bool
Controllable:No
Description:If the nonorthogonal correction should be used when computing the normal gradient.

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_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)
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_tagsrhsThe tag for the vectors this Kernel should fill
Default:rhs
C++ Type:MultiMooseEnum
Options:rhs, 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
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
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

ghost_layers1The number of layers of elements to ghost.
Default:1
C++ Type:unsigned short
Controllable:No
Description:The number of layers of elements to ghost.
use_point_neighborsFalseWhether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/SIMPLEC/3d/3d-velocity-pressure.i)
(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/segregated/channel-drift-flux.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/lid-driven/linear-segregated/lid-driven-turb-std-wall.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/2d-boussinesq-transient.i)
(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/linear-segregated/lid-driven-segregated.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex-rz/2d-symmetric-vortex-rz.i)
(modules/navier_stokes/test/tests/finite_volume/ins/radiation_participating_media/p1_radiation_cht_SIMPLE.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-vortex/2d-vortex.i)
(modules/navier_stokes/test/tests/finite_volume/ins/cht/bulk_heat_transfer/flow-around-square-linear-fluidonly.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d-scalar/channel.i)
(modules/navier_stokes/test/tests/finite_volume/ins/natural_convection/linear_segregated/2d/diff_heated_cavity_linear_segregated.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated/channel_ERCOFTAC_symmetric.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated-transient/channel_ERCOFTAC.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex/2d-symmetric-vortex.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated/channel_ERCOFTAC.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/steady-transient-compare/common-blocks.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated/channel_ERCOFTAC_mu_eff.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/lid-driven/linear-segregated/lid-driven-turb-non-eq-wall.i)
(modules/navier_stokes/test/tests/postprocessors/flow_rates/conservation_LinearFV.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d-symmetric/channel.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/enthalpy_equation.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/bfs/linear-segregated/BFS_ERCOFTAC.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/rotated-channel.i)
(modules/navier_stokes/test/tests/finite_volume/ins/natural_convection/linear_segregated/2d/diff_heated_cavity_linear_buoyancy.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/pressure-drop-advection.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/SIMPLEC/2d/2d-velocity-pressure.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d-heated/fluid.i)
(modules/navier_stokes/test/tests/finite_volume/ins/cht/bulk_heat_transfer/flow-around-square-linear.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-vortex/spacedependent_mu/sl.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/3d/3d-velocity-pressure.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/2d-velocity-pressure.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/bfs/linear-segregated-transient/BFS_ERCOFTAC.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/segregated-comparison/segregated-linear.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex-rz/2d-symmetric-vortex-rz-spacedependent.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/2d-boussinesq.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/block-restricted/block-ke.i)
(modules/navier_stokes/test/tests/finite_volume/ins/cht/conjugate_heat_transfer/cht_rob-rob.i)
(modules/navier_stokes/test/tests/finite_volume/ins/cht/conjugate_heat_transfer/cht_neu-dir.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)
(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h_fp.i)

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/linear-segregated/lid-driven-segregated.i)

mu = .01
rho = 1
advected_interp_method = 'average'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 3
    ny = 3
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [top_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'top'
    functor = 1
  []
  [no_slip_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'left right bottom'
    functor = 0
  []
  [no_slip_y]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = 'left right top bottom'
    functor = 0
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left right top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 500
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.05 0.05 0.0'
[]

[Outputs]
  exodus = true
  csv = false
  perf_graph = false
  print_nonlinear_residuals = false
  print_linear_residuals = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/linear-segregated/lid-driven-segregated.i)

mu = .01
rho = 1
advected_interp_method = 'average'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 3
    ny = 3
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [top_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'top'
    functor = 1
  []
  [no_slip_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'left right bottom'
    functor = 0
  []
  [no_slip_y]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = 'left right top bottom'
    functor = 0
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left right top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 500
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.05 0.05 0.0'
[]

[Outputs]
  exodus = true
  csv = false
  perf_graph = false
  print_nonlinear_residuals = false
  print_linear_residuals = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/linear-segregated/lid-driven-segregated-physics.i)

mu = .01
rho = 1
advected_interp_method = 'average'
pressure_diffusion_ainv_interp_method = 'average'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 3
    ny = 3
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
[]


[Physics]
  [NavierStokes]
    [FlowSegregated/flow]
      velocity_variable = 'vel_x vel_y'
      pressure_variable = 'pressure'

      initial_velocity = '0 0 0'
      initial_pressure = '0.2'

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

      # use inlet for moving wall to match the reference input
      # we could also use a noslip BC with a velocity wall functor
      inlet_boundaries = 'top'
      momentum_inlet_types = 'fixed-velocity'
      momentum_inlet_functors = '1 0'

      wall_boundaries = 'left right bottom'
      momentum_wall_types = 'noslip noslip noslip'

      orthogonality_correction = false
      pressure_two_term_bc_expansion = true
      momentum_advection_interpolation = ${advected_interp_method}
      pressure_diffusion_interpolation = ${pressure_diffusion_ainv_interp_method}
    []
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 100
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.05 0.05 0.0'
[]

[Outputs]
  exodus = true
  csv = false
  perf_graph = false
  print_nonlinear_residuals = false
  print_linear_residuals = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/linear-segregated/lid-driven-segregated-physics.i)

mu = .01
rho = 1
advected_interp_method = 'average'
pressure_diffusion_ainv_interp_method = 'average'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 3
    ny = 3
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
[]


[Physics]
  [NavierStokes]
    [FlowSegregated/flow]
      velocity_variable = 'vel_x vel_y'
      pressure_variable = 'pressure'

      initial_velocity = '0 0 0'
      initial_pressure = '0.2'

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

      # use inlet for moving wall to match the reference input
      # we could also use a noslip BC with a velocity wall functor
      inlet_boundaries = 'top'
      momentum_inlet_types = 'fixed-velocity'
      momentum_inlet_functors = '1 0'

      wall_boundaries = 'left right bottom'
      momentum_wall_types = 'noslip noslip noslip'

      orthogonality_correction = false
      pressure_two_term_bc_expansion = true
      momentum_advection_interpolation = ${advected_interp_method}
      pressure_diffusion_interpolation = ${pressure_diffusion_ainv_interp_method}
    []
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 100
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.05 0.05 0.0'
[]

[Outputs]
  exodus = true
  csv = false
  perf_graph = false
  print_nonlinear_residuals = false
  print_linear_residuals = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/SIMPLEC/3d/3d-velocity-pressure.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 3
    dx = '1.0'
    dy = '0.3'
    dz = '0.3'
    ix = '10'
    iy = '3'
    iz = '3'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system w_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    w = vel_z
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    pressure_projection_method = consistent
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [vel_z]
    type = MooseLinearVariableFVReal
    solver_sys = w_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [w_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_z
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'z'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [w_pressure]
    type = LinearFVMomentumPressure
    variable = vel_z
    pressure = pressure
    momentum_component = 'z'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [inlet-w]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_z
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom back front'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom back front'
    variable = vel_y
    functor = 0.0
  []
  [walls-w]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom back front'
    variable = vel_z
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_w]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_z
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system w_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 1.0
  num_iterations = 100
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type -pc_hypre_boomeramg_agg_nl -pc_hypre_boomeramg_agg_num_paths -pc_hypre_boomeramg_truncfactor -pc_hypre_boomeramg_strong_threshold -pc_hypre_boomeramg_coarsen_type -pc_hypre_boomeramg_interp_type'
  momentum_petsc_options_value = 'hypre boomeramg 4 1 0.1 0.6 HMIS ext+i'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type -pc_hypre_boomeramg_agg_nl -pc_hypre_boomeramg_agg_num_paths -pc_hypre_boomeramg_truncfactor -pc_hypre_boomeramg_strong_threshold -pc_hypre_boomeramg_coarsen_type -pc_hypre_boomeramg_interp_type'
  pressure_petsc_options_value = 'hypre boomeramg 2 1 0.1 0.6 HMIS ext+i'
  print_fields = false
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/two_phase/mixture_model/segregated/channel-drift-flux.i)

mu = 1.0
rho = 10.0
mu_d = 0.1
rho_d = 1.0
l = 2
# 'average' leads to slight oscillations, upwind may be preferred
# This method is selected for consistency with the original nonlinear input
advected_interp_method = 'average'

# TODO remove need for those
cp = 1
k = 1
cp_d = 1
k_d = 1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = '${fparse l * 5}'
    ymin = '${fparse -l / 2}'
    ymax = '${fparse l / 2}'
    nx = 10
    ny = 4
  []
  uniform_refine = 0
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system phi_system'
  previous_nl_solution_required = true
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = 1
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
  []
  [phase_2]
    type = MooseLinearVariableFVReal
    solver_sys = phi_system
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [flow_p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
    variable = pressure
  []
  [flow_HbyA_divergence]
    type = LinearFVDivergence
    face_flux = HbyA
    force_boundary_execution = true
    variable = pressure
  []
  [flow_ins_momentum_flux_x]
    type = LinearWCNSFVMomentumFlux
    advected_interp_method_name = ${advected_interp_method}
    momentum_component = x
    mu = mu_mixture
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u = vel_x
    use_deviatoric_terms = false
    use_nonorthogonal_correction = false
    v = vel_y
    variable = vel_x
  []
  [flow_ins_momentum_flux_y]
    type = LinearWCNSFVMomentumFlux
    advected_interp_method_name = ${advected_interp_method}
    momentum_component = y
    mu = mu_mixture
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u = vel_x
    use_deviatoric_terms = false
    use_nonorthogonal_correction = false
    v = vel_y
    variable = vel_y
  []
  [mixture_drift_flux_x]
    type = LinearWCNSFV2PMomentumDriftFlux
    density_interp_method = average
    fraction_dispersed = phase_2
    momentum_component = x
    rhie_chow_user_object = ins_rhie_chow_interpolator
    rho_d = ${rho_d}
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = vel_x
  []
  [mixture_drift_flux_y]
    type = LinearWCNSFV2PMomentumDriftFlux
    density_interp_method = average
    fraction_dispersed = phase_2
    momentum_component = y
    rhie_chow_user_object = ins_rhie_chow_interpolator
    rho_d = ${rho_d}
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = vel_y
  []
  [flow_ins_momentum_pressure_x]
    type = LinearFVMomentumPressure
    momentum_component = x
    pressure = pressure
    variable = vel_x
  []
  [flow_ins_momentum_pressure_y]
    type = LinearFVMomentumPressure
    momentum_component = y
    pressure = pressure
    variable = vel_y
  []
  [flow_momentum_friction_0_x]
    type = LinearFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    momentum_component = x
    mu = mu_mixture
    variable = vel_x
  []
  [flow_momentum_friction_0_y]
    type = LinearFVMomentumFriction
    Darcy_name = Darcy_coefficient_vec
    momentum_component = y
    mu = mu_mixture
    variable = vel_y
  []

  # Mixture phase equation
  [mixture_ins_phase_2_advection]
    type = LinearFVScalarAdvection
    advected_interp_method_name = upwind
    rhie_chow_user_object = ins_rhie_chow_interpolator
    u_slip = vel_slip_x
    v_slip = vel_slip_y
    variable = phase_2
  []
  [mixture_phase_interface_reaction]
    type = LinearFVReaction
    coeff = 0.1
    variable = phase_2
  []
  [mixture_phase_interface_source]
    type = LinearFVSource
    scaling_factor = 0.1
    source_density = phase_1
    variable = phase_2
  []
[]

[LinearFVBCs]
  [vel_x_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 1
    variable = vel_x
  []
  [vel_y_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 0
    variable = vel_y
  []
  [pressure_extrapolation_inlet_left]
    type = LinearFVExtrapolatedPressureBC
    boundary = left
    use_two_term_expansion = true
    variable = pressure
  []
  [vel_x_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = vel_x
  []
  [vel_y_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = vel_y
  []
  [pressure_right]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = right
    functor = 0
    variable = pressure
  []
  [vel_x_bottom]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = bottom
    functor = 0
    variable = vel_x
  []
  [vel_y_bottom]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = bottom
    functor = 0
    variable = vel_y
  []
  [vel_x_top]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = top
    functor = 0
    variable = vel_x
  []
  [vel_y_top]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = top
    functor = 0
    variable = vel_y
  []
  [pressure_extrapolation_top_bottom]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top bottom'
    use_two_term_expansion = true
    variable = pressure
  []

  [phase_2_left]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = left
    functor = 0.1
    variable = phase_2
  []
  [phase_2_right]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = right
    use_two_term_expansion = true
    variable = phase_2
  []
[]

[FunctorMaterials]
  [flow_ins_speed_material]
    type = ADVectorMagnitudeFunctorMaterial
    execute_on = ALWAYS
    outputs = none
    vector_magnitude_name = speed
    x_functor = vel_x
    y_functor = vel_y
  []

  [mixture_phase_1_fraction]
    type = ParsedFunctorMaterial
    execute_on = ALWAYS
    expression = '1 - phase_2'
    functor_names = phase_2
    output_properties = phase_1
    outputs = all
    property_name = phase_1
  []
  [mixture_mixture_material]
    type = WCNSLinearFVMixtureFunctorMaterial
    execute_on = ALWAYS
    limit_phase_fraction = true
    outputs = all
    phase_1_fraction = phase_2
    phase_1_names = '${rho_d} ${mu_d} ${cp_d} ${k_d}'
    phase_2_names = '${rho}   ${mu}   ${cp}   ${k}'
    prop_names = 'rho_mixture mu_mixture cp_mixture k_mixture'
  []
  [mixture_slip_x]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    execute_on = ALWAYS
    gravity = '0 0 0'
    linear_coef_name = Darcy_coefficient
    momentum_component = x
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = ${rho}
    rho_d = ${rho_d}
    slip_velocity_name = vel_slip_x
    u = vel_x
    v = vel_y
  []
  [mixture_slip_y]
    type = WCNSFV2PSlipVelocityFunctorMaterial
    execute_on = ALWAYS
    gravity = '0 0 0'
    linear_coef_name = Darcy_coefficient
    momentum_component = y
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = ${rho}
    rho_d = ${rho_d}
    slip_velocity_name = vel_slip_y
    u = vel_x
    v = vel_y
  []
  [mixture_dispersed_drag]
    type = NSFVDispersePhaseDragFunctorMaterial
    drag_coef_name = Darcy_coefficient
    execute_on = ALWAYS
    mu = mu_mixture
    outputs = all
    particle_diameter = 0.01
    rho = rho_mixture
    u = vel_x
    v = vel_y
  []
[]

[UserObjects]
  [ins_rhie_chow_interpolator]
    type = RhieChowMassFlux
    p_diffusion_kernel = flow_p_diffusion
    pressure = pressure
    rho = rho_mixture
    u = vel_x
    v = vel_y
  []
[]

[Executioner]
  type = SIMPLE
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'

  # Systems
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  active_scalar_systems = 'phi_system'
  momentum_equation_relaxation = 0.8
  active_scalar_equation_relaxation = '0.7'
  pressure_variable_relaxation = 0.3

  # We need to converge the problem to show conservation
  num_iterations = 200
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  active_scalar_absolute_tolerance = '1e-10'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  active_scalar_petsc_options_iname = '-pc_type -pc_hypre_type'
  active_scalar_petsc_options_value = 'hypre boomeramg'
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  active_scalar_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  active_scalar_l_tol = 0
  # print_fields = true
  continue_on_max_its = true
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '10.0 * 2 * 1'
  []
  [average_phase2]
    type = ElementAverageValue
    variable = phase_2
  []
  [dp]
    type = PressureDrop
    boundary = 'left right'
    downstream_boundary = right
    pressure = pressure
    upstream_boundary = left
  []
  [max_phase2]
    type = ElementExtremeValue
    variable = phase_2
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/lid-driven/linear-segregated/lid-driven-turb-std-wall.i)

### Thermophysical Properties ###
mu = 1e-3
rho = 1.0

### Operation Conditions ###
lid_velocity = 1.0
side_length = 0.1

### Initial Conditions ###
intensity = 0.01
k_init = '${fparse 1.5*(intensity * lid_velocity)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / side_length}'

### k-epsilon Closure Parameters ###
sigma_k = 1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'left top right bottom'
wall_treatment = 'eq_newton' # Options: eq_newton, eq_incremental, eq_linearized, neq

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${side_length}
    ymin = 0
    ymax = ${side_length}
    nx = 12
    ny = 12
  []
  # Prevent test diffing on distributed parallel element numbering
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${lid_velocity}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = upwind
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = upwind
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = true
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = 'upwind'
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = true
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = 'upwind'
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = true
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [top_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'top'
    functor = 1
  []
  [no_slip_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'left right bottom'
    functor = 0
  []
  [no_slip_y]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = 'left right top bottom'
    functor = 0
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left right top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = ${walls}
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
  [yplus]
    type = MooseLinearVariableFVReal
  []
  [mu_eff]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
  [compute_mu_eff]
    type = ParsedAux
    variable = 'mu_eff'
    coupled_variables = 'mu_t'
    expression = 'mu_t + ${mu}'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = SIMPLE

  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  turbulence_systems = 'TKE_system TKED_system'

  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_tol = 1e-14
  pressure_l_tol = 1e-14
  turbulence_l_tol = 1e-14

  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  turbulence_equation_relaxation = '0.5 0.5'
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  turbulence_absolute_tolerance = '1e-12 1e-12'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  turbulence_petsc_options_iname = '-pc_type -pc_hypre_type'
  turbulence_petsc_options_value = 'hypre boomeramg'

  print_fields = false
  continue_on_max_its = true

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.01 0.099 0.0'
[]

[Outputs]
  csv = true
  perf_graph = false
  print_nonlinear_residuals = false
  print_linear_residuals = true
[]

[VectorPostprocessors]
  [side_bottom]
    type = SideValueSampler
    boundary = 'bottom'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [side_top]
    type = SideValueSampler
    boundary = 'top'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [side_left]
    type = SideValueSampler
    boundary = 'left'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'y'
    execute_on = 'timestep_end'
  []
  [side_right]
    type = SideValueSampler
    boundary = 'right'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'y'
    execute_on = 'timestep_end'
  []
  [horizontal_center]
    type = LineValueSampler
    start_point = '${fparse 0.01 * side_length} ${fparse 0.499 * side_length} 0'
    end_point = '${fparse 0.99 * side_length} ${fparse 0.499 * side_length} 0'
    num_points = ${Mesh/gen/nx}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [vertical_center]
    type = LineValueSampler
    start_point = '${fparse 0.499 * side_length} ${fparse 0.01 * side_length} 0'
    end_point = '${fparse 0.499 * side_length} ${fparse 0.99 * side_length} 0'
    num_points =  ${Mesh/gen/ny}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'y'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/2d-boussinesq-transient.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'
cp = 300
k = 10
alpha_b = 1e-4

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1.'
    dy = '0.2'
    ix = '10'
    iy = '5'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
  [T]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_time]
    type = LinearFVTimeDerivative
    variable = vel_x
    factor = ${rho}
  []
  [v_time]
    type = LinearFVTimeDerivative
    variable = vel_y
    factor = ${rho}
  []
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_boussinesq]
    type = LinearFVMomentumBoussinesq
    variable = vel_x
    rho = ${rho}
    gravity = '0 -9.81 0'
    alpha_name = ${alpha_b}
    ref_temperature = 300.0
    T_fluid = T
    momentum_component = 'x'
  []
  [v_boussinesq]
    type = LinearFVMomentumBoussinesq
    variable = vel_y
    rho = ${rho}
    gravity = '0 -9.81 0'
    alpha_name = ${alpha_b}
    ref_temperature = 300.0
    T_fluid = T
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_time]
    type = LinearFVTimeDerivative
    variable = T
    factor = ${fparse rho*cp}
  []
  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = false
  []
[]

[FunctorMaterials]
  [constant_functors]
    type = GenericFunctorMaterial
    prop_names = 'cp alpha_b'
    prop_values = '${cp} ${alpha_b}'
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_top_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    functor = 300.0
    boundary = 'left top'
  []
  [bottom_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    functor = wall-temperature
    boundary = bottom
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T
    use_two_term_expansion = false
    boundary = right
  []
[]

[Functions]
  [wall-temperature]
    type = ParsedFunction
    expression = '350 + 50 * sin(6.28*t)'
  []
[]

[Executioner]
  type = PIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 1e-12
  pressure_l_tol = 1e-12
  energy_l_tol = 1e-12
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.9
  num_iterations = 100
  pressure_absolute_tolerance = 1e-11
  momentum_absolute_tolerance = 1e-11
  energy_absolute_tolerance = 1e-11
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
  dt = 0.01
  num_steps = 6
  num_piso_iterations = 0
[]


[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/linear-segregated/lid-driven-segregated.i)

mu = .01
rho = 1
advected_interp_method = 'average'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = .1
    ymin = 0
    ymax = .1
    nx = 3
    ny = 3
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [top_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'top'
    functor = 1
  []
  [no_slip_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'left right bottom'
    functor = 0
  []
  [no_slip_y]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = 'left right top bottom'
    functor = 0
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left right top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 500
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.05 0.05 0.0'
[]

[Outputs]
  exodus = true
  csv = false
  perf_graph = false
  print_nonlinear_residuals = false
  print_linear_residuals = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex-rz/2d-symmetric-vortex-rz.i)

mu = 1.2
rho = 1.5
advected_interp_method = 'average'

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
  coord_type = 'RZ'
  rz_coord_axis = x
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    pressure_projection_method = consistent
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.0
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_forcing]
    type = LinearFVSource
    variable = vel_x
    source_density = forcing_u
  []
  [v_forcing]
    type = LinearFVSource
    variable = vel_y
    source_density = forcing_v
  []
  [v_viscous_forcing]
    type = LinearFVRZViscousSource
    variable = vel_y
    mu = ${mu}
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = 'Ainv'
    use_nonorthogonal_correction = false
    use_nonorthogonal_correction_on_boundary = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = 'HbyA'
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [no-slip-wall-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top'
    variable = vel_x
    functor = exact_u
  []
  [no-slip-wall-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top'
    variable = vel_y
    functor = exact_v
  []
  [symmetry-u]
    type = LinearFVVelocitySymmetryBC
    boundary = 'bottom'
    variable = vel_x
    u = vel_x
    v = vel_y
    momentum_component = x
  []
  [symmetry-v]
    type = LinearFVVelocitySymmetryBC
    boundary = 'bottom'
    variable = vel_y
    u = vel_x
    v = vel_y
    momentum_component = y
  []

  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top left right'
    variable = pressure
    use_two_term_expansion = true
  []
  [pressure-symmetry]
    type = LinearFVPressureSymmetryBC
    boundary = 'bottom'
    variable = pressure
    HbyA_flux = 'HbyA'
  []
[]

[AuxVariables]
  [vel_x_aux]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
  []
  [vel_y_aux]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
  []
  [pressure_aux]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
  []
[]

[AuxKernels]
  [vel_x_function_aux]
    type = FunctionAux
    variable = vel_x_aux
    function = exact_u
    execute_on = TIMESTEP_END
  []
  [vel_y_function_aux]
    type = FunctionAux
    variable = vel_y_aux
    function = exact_v
    execute_on = TIMESTEP_END
  []
  [pressure_function_aux]
    type = FunctionAux
    variable = pressure_aux
    function = exact_p
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    expression = '4*x^2*y^2 - 20*x^2*y^3 - 8*x^3*y^2 + 36*x^2*y^4 + 40*x^3*y^3 + 4*x^4*y^2 - 28*x^2*y^5 - 72*x^3*y^4 - 20*x^4*y^3 + 8*x^2*y^6 + 56*x^3*y^5 + 36*x^4*y^4 - 16*x^3*y^6 - 28*x^4*y^5 + 8*x^4*y^6'
  []
  [exact_v]
    type = ParsedFunction
    expression = '-2*x*y^3*(x-1)*(2*x-1)*(y-1)^4'
  []
  [exact_p]
    type = ParsedFunction
    expression = 'x*y^2'
  []
  [forcing_u]
    type = ParsedFunction
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
    expression = 'rho*(8*x^3*y^4*(x-1)^3*(2*x-1)*(y-1)^6*(4*y^2 - 5*y + 2)) - mu*(4*(y-1)*(72*x^4*y^3 - 103*x^4*y^2 + 41*x^4*y - 4*x^4 - 144*x^3*y^3 + 206*x^3*y^2 - 82*x^3*y + 8*x^3 + 24*x^2*y^5 - 60*x^2*y^4 + 120*x^2*y^3 - 115*x^2*y^2 + 41*x^2*y - 4*x^2 - 24*x*y^5 + 60*x*y^4 - 48*x*y^3 + 12*x*y^2 + 4*y^5 - 10*y^4 + 8*y^3 - 2*y^2)) + y^2'
  []
  [forcing_v]
    type = ParsedFunction
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
    expression = 'rho*4*x^2*y^5*(x-1)^2*(y-1)^7*(2*(2*x^2 - 2*x + y) + (2*x - 1)^2*(y - 1)) + mu * (4*y*(2*x-1)*(y-1)^2*(24*x^2*y^2 - 22*x^2*y + 4*x^2 - 24*x*y^2 + 22*x*y - 4*x + 3*y^4 - 6*y^3 + 3*y^2)) + 2*x*y'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  momentum_l_max_its = 500
  pressure_l_max_its = 500
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.85
  pressure_variable_relaxation = 1.0
  num_iterations = 10000
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true

  pin_pressure = true
  pressure_pin_value = 0.125
  pressure_pin_point = '0.5 0.5 0.0'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = TIMESTEP_END
  []
  [L2u]
    type = ElementL2FunctorError
    approximate = vel_x
    exact = exact_u
    execute_on = TIMESTEP_END
  []
  [L2v]
    type = ElementL2FunctorError
    approximate = vel_y
    exact = exact_v
    execute_on = TIMESTEP_END
  []
  [L2p]
    approximate = pressure
    exact = exact_p
    type = ElementL2FunctorError
    execute_on = TIMESTEP_END
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/radiation_participating_media/p1_radiation_cht_SIMPLE.i)

# Coupled conduction and radiative heat transfer test in the linear FV system using the SIMPLE executioner.
# A 1D P1 radiation model is solved in the fluid region. Energy is solved in the
# fluid and solid region using two different variables. The radiative and conductive flux
# is maintained at the fluid-solid interface using conjugate heat transfer, Robin BCs for
# the solid side and Dirichlet BCs for the fluid side. Fixed temperatures are set at the solid and
# fluid external boundaries.
### Benchmark sources:
### https://hal.science/hal-02070285/document

nx = 10
Tw_left = 1.0
Tw_right = 0.0
sigma = 5.670374419e-8

sigma_a = 1.0

N = 0.1 # Stark number N = k sigma_a / (4*sigma*pow(T_w,3))
k_salt = ${fparse N*4*sigma*pow(Tw_left,3)/sigma_a}
k_solid = ${fparse 4.0*k_salt}
diffusion_coef = ${fparse 1/(3*sigma_a)}
b_eps = 1.0

rho = 1.
mu = 5.
h_s = 0.0

advected_interp_method = 'upwind'

[Mesh]
  [salt_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = ${nx}
    xmin = 0
    xmax = 1
    subdomain_ids = 0
  []
  [solid_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = ${nx}
    xmin = 1
    xmax = 2
    subdomain_ids = 1
  []
  [give_name_solid]
    type = RenameBlockGenerator
    input = solid_mesh
    old_block = 1
    new_block = 'solid'
  []
  [give_name_salt]
    type = RenameBlockGenerator
    input = salt_mesh
    old_block = 0
    new_block = 'salt'
  []
  [stitch]
    type = StitchMeshGenerator
    inputs = 'give_name_salt give_name_solid'
    stitch_boundaries_pairs = 'right left'
  []
  [interface]
    input = stitch
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 'solid'
    paired_block = 'salt'
    new_boundary = interface
  []
  # Prevent test diffing on distributed parallel element numbering
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system pressure_system energy_system solid_energy_system radiation_system '
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = 'salt'
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-6
    solver_sys = 'u_system'
    block = 'salt'
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = 'pressure_system'
    initial_condition = 1e-6
    block = 'salt'
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = 'energy_system'
    initial_condition = ${fparse Tw_left/2}
    block = 'salt'
  []
  [G]
    type = MooseLinearVariableFVReal
    solver_sys = 'radiation_system'
    initial_condition = ${fparse 4*sigma*pow(Tw_left/2,4)}
    block = 'salt'
  []
  [T_solid]
    type = MooseLinearVariableFVReal
    solver_sys = 'solid_energy_system'
    initial_condition = ${fparse Tw_left/2}
    block = 'solid'
  []
[]

[Postprocessors]
  [T_fluid_iface]
    type = ElementalVariableValue
    variable = T_fluid
    elementid = ${fparse nx-1}
  []
  [T_solid_iface]
    type = ElementalVariableValue
    variable = T_solid
    elementid = ${fparse nx}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [fluid_conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k_salt}
    use_nonorthogonal_correction = false
    block = salt
  []
  [fluid_radiation]
    type = LinearFVP1TemperatureSourceSink
    variable = T_fluid
    G = 'G'
    absorption_coeff = ${sigma_a}
    block = salt
  []

  [G_diffusion]
    type = LinearFVDiffusion
    variable = G
    diffusion_coeff = ${diffusion_coef}
    block = salt
  []
  [G_source_and_sink]
    type = LinearFVP1RadiationSourceSink
    variable = G
    temperature_radiation = 'T_fluid'
    absorption_coeff = ${sigma_a}
    block = salt
  []

  [solid_conduction]
    type = LinearFVDiffusion
    variable = T_solid
    diffusion_coeff = ${k_solid}
    use_nonorthogonal_correction = false
    block = solid
  []
[]

[LinearFVBCs]
  # velocity BCs
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left interface'
    variable = vel_x
    functor = 0.0
  []

  # temperature BCs
  [left_bc_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    boundary = 'left'
    functor = ${Tw_left}
  []
  [right_bc_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_solid
    boundary = 'right'
    functor = ${Tw_right}
  []

  # G
  [right_bc_G]
    type = LinearFVP1RadiationMarshakBC
    boundary = 'interface'
    variable = G
    temperature_radiation = 'T_fluid'
    coeff_diffusion = ${diffusion_coef}
    boundary_emissivity = ${b_eps}
  []
  [left_bc_G]
    type = LinearFVP1RadiationMarshakBC
    boundary = 'left'
    variable = G
    temperature_radiation = ${Tw_left}
    coeff_diffusion = ${diffusion_coef}
    boundary_emissivity = ${b_eps}
  []

  # cht
  [fluid_solid]
    type = LinearFVDirichletCHTBC
    variable = T_fluid
    boundary = interface
    functor = interface_temperature_solid_interface
  []
  [solid_fluid]
    type = LinearFVRobinCHTBC
    variable = T_solid
    boundary = interface
    h = ${h_s}
    thermal_conductivity = ${k_solid}
    incoming_flux = heat_flux_to_solid_interface
    surface_temperature = interface_temperature_fluid_interface
  []
[]

[Executioner]
  type = SIMPLE

  num_iterations = 2000

  momentum_systems = 'u_system '
  pressure_system = 'pressure_system'
  rhie_chow_user_object = 'rc'
  momentum_l_abs_tol = 1e-8
  pressure_l_abs_tol = 1e-7
  momentum_l_tol = 0
  pressure_l_tol = 0
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  momentum_absolute_tolerance = 1e-5
  pressure_absolute_tolerance = 1e-5
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  #active_scalar_systems = 'radiation_system'
  pm_radiation_systems = 'radiation_system'
  energy_system = 'energy_system'
  solid_energy_system = 'solid_energy_system'
  #active_scalar_l_abs_tol = 1e-14
  pm_radiation_l_abs_tol = 1e-11
  energy_l_abs_tol = 1e-11
  solid_energy_l_abs_tol = 1e-11
  #active_scalar_l_tol = 0
  pm_radiation_l_tol = 0
  energy_l_tol = 0
  solid_energy_l_tol = 0
  #active_scalar_equation_relaxation = 0.95
  pm_radiation_equation_relaxation = 1.0
  energy_equation_relaxation = 0.9
  energy_absolute_tolerance = 1e-10
  solid_energy_absolute_tolerance = 1e-10
  #active_scalar_absolute_tolerance = 1e-14
  #active_scalar_petsc_options_iname = '-pc_type -pc_hypre_type'
  #active_scalar_petsc_options_value = 'hypre boomeramg'
  pm_radiation_absolute_tolerance = 1e-10
  pm_radiation_petsc_options_iname = '-pc_type -pc_hypre_type'
  pm_radiation_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  solid_energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  solid_energy_petsc_options_value = 'hypre boomeramg'

  cht_interfaces = 'interface'
  cht_solid_flux_relaxation = 0.3
  cht_fluid_flux_relaxation = 0.3
  cht_solid_temperature_relaxation = 0.3
  cht_fluid_temperature_relaxation = 0.3
  cht_heat_flux_tolerance = 1e-4
  max_cht_fpi = 10

  print_fields = false
  continue_on_max_its = true

[]

[Outputs]
  csv = true
  execute_on = timestep_end
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-vortex/2d-vortex.i)

mu = 1
rho = 1000
advected_interp_method = 'average'

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    pressure_projection_method = CONSISTENT
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
  [upwind]
    type = FVAdvectedUpwind
  []
  [min_mod]
    type = FVAdvectedMinmodWeightBased
  []
  [vanLeer]
    type = FVAdvectedVanLeerWeightBased
  []
  [venkatakrishnan]
    type = FVAdvectedVenkatakrishnanDeferredCorrection
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_forcing]
    type = LinearFVSource
    variable = vel_x
    source_density = forcing_u
  []
  [v_forcing]
    type = LinearFVSource
    variable = vel_y
    source_density = forcing_v
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
    use_nonorthogonal_correction_on_boundary = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [no-slip-wall-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top bottom'
    variable = vel_x
    functor = '0'
  []
  [no-slip-wall-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top bottom'
    variable = vel_y
    functor = '0'
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left right top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    expression = 'x^2*(1-x)^2*(2*y-6*y^2+4*y^3)'
  []
  [exact_v]
    type = ParsedFunction
    expression = '-y^2*(1-y)^2*(2*x-6*x^2+4*x^3)'
  []
  [exact_p]
    type = ParsedFunction
    expression = 'x*(1-x)'
  []
  [forcing_u]
    type = ParsedFunction
    expression = '-4*mu*(-1+2*y)*(y^2-6*x*y^2+6*x^2*y^2-y+6*x*y-6*x^2*y+3*x^2-6*x^3+3*x^4)+1-2*x+rho*4*x^3*y^2*(2*y^2-2*y+1)*(y-1)^2*(-1+2*x)*(x-1)^3'
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
  []
  [forcing_v]
    type = ParsedFunction
    expression = '4*mu*(-1+2*x)*(x^2-6*y*x^2+6*x^2*y^2-x+6*x*y-6*x*y^2+3*y^2-6*y^3+3*y^4)+rho*4*y^3*x^2*(2*x^2-2*x+1)*(x-1)^2*(-1+2*y)*(y-1)^3'
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-8
  pressure_l_abs_tol = 1e-8
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 1.0
  num_iterations = 2000
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false

  pin_pressure = true
  pressure_pin_value = 0.25
  pressure_pin_point = '0.5 0.5 0.0'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = FINAL
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'csv'
    execute_on = FINAL
  []
  [L2u]
    type = ElementL2FunctorError
    approximate = vel_x
    exact = exact_u
    outputs = 'csv'
    execute_on = FINAL
  []
  [L2v]
    type = ElementL2FunctorError
    approximate = vel_y
    exact = exact_v
    outputs = 'csv'
    execute_on = FINAL
  []
  [L2p]
    approximate = pressure
    exact = exact_p
    type = ElementL2FunctorError
    outputs = 'csv'
    execute_on = FINAL
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/cht/bulk_heat_transfer/flow-around-square-linear-fluidonly.i)

mu = 0.01
rho = 1.1
k = 0.0005
cp = 10
h_conv = 5

advected_interp_method = 'upwind'

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    ymin = 0
    ymax = 0.1
    xmax = 0.1
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    input = generated_mesh
    block_name = subdomain1
    bottom_left = '0.04 0.04 0'
    block_id = 1
    top_right = '0.06 0.06 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = subdomain1
    primary_block = 0
    paired_block = 1
    new_boundary = interface
  []
  [delete]
    type = BlockDeletionGenerator
    input = interface
    block = 1
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = 0
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.1
    solver_sys = u_system
    block = 0
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.01
    block = 0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
    block = 0
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
    block = 0
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = true
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '0.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []

  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    functor = 300
    boundary = 'left'
  []
  [walls_T]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_fluid
    functor = 0.0
    boundary = 'top bottom'
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T_fluid
    use_two_term_expansion = false
    boundary = right
  []

  [fluid_solid]
    type = LinearFVConvectiveHeatTransferBC
    variable = T_fluid
    T_solid = boundary_value
    T_fluid = T_fluid
    boundary = interface
    h = ${h_conv}
  []
[]

[FunctorMaterials]
  [rhocpT]
    property_name = 'rhocpT'
    type = ParsedFunctorMaterial
    functor_names = 'T_fluid'
    expression = '${rho}*${cp}*T_fluid'
  []
[]

[Functions]
  [boundary_value]
    type = ConstantFunction
    value = 350
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  energy_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.8
  energy_equation_relaxation = 1.0
  pressure_variable_relaxation = 0.3
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
[]

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

mu = 2.6
rho = 1.0
advected_interp_method = 'upwind'
scalar_advected_interp_method = ${advected_interp_method}
k1 = 0.1
k2 = 0.2

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.25 0.25'
    dy = '0.2'
    ix = '5 5'
    iy = '5'
    subdomain_id = '0 1'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system s1_system s2_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
  [scalar1]
    type = MooseLinearVariableFVReal
    solver_sys = s1_system
    initial_condition = 1.1
  []
  [scalar2]
    type = MooseLinearVariableFVReal
    solver_sys = s2_system
    initial_condition = 3
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
  [vanLeer]
    type = FVAdvectedVanLeerWeightBased
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [s1_advection]
    type = LinearFVScalarAdvection
    variable = scalar1
    advected_interp_method_name = ${scalar_advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [s1_diffusion]
    type = LinearFVDiffusion
    variable = scalar1
    diffusion_coeff = ${k1}
    use_nonorthogonal_correction = false
  []
  [s2_diffusion]
    type = LinearFVScalarAdvection
    variable = scalar2
    advected_interp_method_name = ${scalar_advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [s2_conduction]
    type = LinearFVDiffusion
    variable = scalar2
    diffusion_coeff = ${k2}
    use_nonorthogonal_correction = false
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_wall_scalar1]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = scalar1
    functor = 1
    boundary = 'left'
  []
  [outlet_scalar1]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = scalar1
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_wall_scalar2]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = scalar2
    functor = 2
    boundary = 'left'
  []
  [outlet_scalar2]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = scalar2
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  passive_scalar_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  passive_scalar_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  passive_scalar_systems = 's1_system s2_system'
  momentum_equation_relaxation = 0.8
  passive_scalar_equation_relaxation = '0.9 0.9'
  pressure_variable_relaxation = 0.3
  # We need to converge the problem to show conservation
  num_iterations = 200
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  # The solution being flat, the normalization factor based on fluxes goes to
  # 0. The convergence criteria being multiplied by said factor, we won't do any
  # better than this. For a non-flat solution, use tighter tolerances
  passive_scalar_absolute_tolerance = '1e-2 1e-2'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  passive_scalar_petsc_options_iname = '-pc_type -pc_hypre_type'
  passive_scalar_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  hide = 'pressure vel_x vel_y'
[]

(modules/navier_stokes/test/tests/finite_volume/ins/natural_convection/linear_segregated/2d/diff_heated_cavity_linear_segregated.i)

################################################################################
# MATERIAL PROPERTIES
################################################################################
rho = 3279.
T_0 = 875.0
mu = 1.
k_cond = 38.0
cp = 640.
alpha = 3.26e-5

walls = 'right left top bottom'

[GlobalParams]
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'
  advected_interp_method = 'upwind'
  u = vel_x
  v = vel_y
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

################################################################################
# GEOMETRY
################################################################################

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 15
    ny = 15
  []
[]

################################################################################
# EQUATIONS: VARIABLES, KERNELS & BCS
################################################################################

[UserObjects]
  [ins_rhie_chow_interpolator]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    body_force_kernel_names = "u_buoyancy; v_buoyancy"
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = pressure_system
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 875
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = upwind
    mu = ${mu}
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [u_buoyancy]
    type = LinearFVMomentumBoussinesq
    variable = vel_x
    T_fluid = T_fluid
    gravity = '0 -9.8 0'
    rho = ${rho}
    ref_temperature = ${T_0}
    alpha_name = ${alpha}
    momentum_component = 'x'
  []

  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = upwind
    mu = ${mu}
    momentum_component = 'y'
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [v_buoyancy]
    type = LinearFVMomentumBoussinesq
    variable = vel_y
    T_fluid = T_fluid
    gravity = '0 -9.81 0'
    rho = ${rho}
    ref_temperature = ${T_0}
    alpha_name = ${alpha}
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = false
  []

   ####### FUEL ENERGY EQUATION #######

  [heat_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${fparse k_cond}
  []
[]


[LinearFVBCs]
  [no-slip-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = ${walls}
    functor = 0
  []
  [no-slip-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = ${walls}
    functor = 0
  []
  [T_cold]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    boundary = 'right'
    functor = 870.0
  []
  [T_hot]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    boundary = 'left'
    functor = 880.0
  []
  [T_all]
    type = LinearFVAdvectionDiffusionExtrapolatedBC
    variable = T_fluid
    boundary = 'top bottom'
    use_two_term_expansion = false
  []
  [pressure]
    type = LinearFVPressureFluxBC
    boundary = 'top bottom left right'
    variable = pressure
    HbyA_flux = HbyA
    Ainv = Ainv
  []
[]

[FunctorMaterials]
  [constant_functors]
    type = GenericFunctorMaterial
    prop_names = 'cp alpha_b'
    prop_values = '${cp} ${alpha}'
  []
[]

################################################################################
# EXECUTION / SOLVE
################################################################################

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-11
  pressure_l_abs_tol = 1e-11
  energy_l_abs_tol = 1e-11
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.9
  num_iterations = 1500
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-8
  print_fields = false
  momentum_l_max_its = 300

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.5 0.0 0.0'

  # momentum_petsc_options = '-ksp_monitor'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'

  continue_on_max_its = true
[]

################################################################################
# SIMULATION OUTPUTS
################################################################################

[Outputs]
  #exodus = true
  [out]
    type = Exodus
    file_base = 'diff_heated_cavity_linear_segregated_out'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated/channel_ERCOFTAC_symmetric.i)

H = 1 #halfwidth of the channel
L = 100

Re = 13700

rho = 1
bulk_u = 1
mu = '${fparse rho * bulk_u * 2 * H / Re}'

advected_interp_method = 'upwind'

### k-epsilon Closure Parameters ###
sigma_k = 1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Initial and Boundary Conditions ###
intensity = '${fparse 0.16*Re^(-1./8.)}'
k_init = '${fparse 1.5*(intensity * bulk_u)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / (2*H)}'

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'top'
wall_treatment = 'eq_newton' # Options: eq_newton, eq_incremental, eq_linearized, neq

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${L}
    ymin = 0
    ymax = ${H}
    nx = 4
    ny = 4
    bias_y = 0.7
  []
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${bulk_u}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = ${advected_interp_method}
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = ${advected_interp_method}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = ${walls}
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = ${walls}
    variable = vel_y
    functor = 0.0
  []
  [symmetry-u]
    type = LinearFVVelocitySymmetryBC
    variable = vel_x
    boundary = 'bottom'
    momentum_component = 'x'
    u = 'vel_x'
    v = 'vel_y'
  []
  [symmetry-v]
    type = LinearFVVelocitySymmetryBC
    variable = vel_y
    boundary = 'bottom'
    momentum_component = 'y'
    u = 'vel_x'
    v = 'vel_y'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [symmetry-p]
    type = LinearFVPressureSymmetryBC
    variable = pressure
    boundary = 'bottom'
    HbyA_flux = 'HbyA' # Functor created in the RhieChowMassFlux UO
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []

  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKE
    functor = '${k_init}'
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKE
    use_two_term_expansion = false
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKED
    functor = '${eps_init}'
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKED
    use_two_term_expansion = false
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = ${walls}
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
  [yplus]
    type = MooseLinearVariableFVReal
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = SIMPLE

  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  turbulence_systems = 'TKE_system TKED_system'

  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_tol = 1e-14
  pressure_l_tol = 1e-14
  turbulence_l_tol = 1e-14

  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  turbulence_equation_relaxation = '0.2 0.2'
  turbulence_field_relaxation = '0.2 0.2'
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  turbulence_absolute_tolerance = '1e-12 1e-12'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  turbulence_petsc_options_iname = '-pc_type -pc_hypre_type'
  turbulence_petsc_options_value = 'hypre boomeramg'

  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  csv = true
  execute_on = 'TIMESTEP_END'
[]

[AuxVariables]
  [pressure_over_density]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
[]

[AuxKernels]
  [compute_pressure_over_density]
    type = ParsedAux
    variable = pressure_over_density
    coupled_variables = 'pressure'
    expression = 'pressure/${rho}'
  []
[]

[VectorPostprocessors]
  [side_top]
    type = SideValueSampler
    boundary = 'top'
    variable = 'vel_x vel_y pressure_over_density TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_center_channel]
    type = LineValueSampler
    start_point = '${fparse 0.125 * L} ${fparse 0.0001} 0'
    end_point = '${fparse 0.875 * L} ${fparse 0.0001} 0'
    num_points = ${Mesh/gmg/nx}
    variable = 'vel_x vel_y pressure_over_density TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_quarter_radius_channel]
    type = LineValueSampler
    start_point = '${fparse 0.125 * L} ${fparse 0.5 * H} 0'
    end_point = '${fparse 0.875 * L} ${fparse 0.5 * H} 0'
    num_points = ${Mesh/gmg/nx}
    variable = 'vel_x vel_y pressure_over_density TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated-transient/channel_ERCOFTAC.i)

H = 1 #halfwidth of the channel
L = 100

Re = 13700

rho = 1
bulk_u = 1
mu = '${fparse rho * bulk_u * 2 * H / Re}'

advected_interp_method = 'upwind'

### k-epsilon Closure Parameters ###
sigma_k =1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Initial and Boundary Conditions ###
intensity = 0.01
k_init = '${fparse 1.5*(intensity * bulk_u)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / (2*H)}'

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'top bottom'
wall_treatment = 'eq_newton'  # Options: eq_newton, eq_incremental, eq_linearized, neq

[Mesh]
  [block_1]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${L}
    ymin = 0
    ymax = ${H}
    nx = 4
    ny = 3
    bias_y = 0.7
  []
  [block_2]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${L}
    ymin = ${fparse -H}
    ymax = 0
    nx = 4
    ny = 3
    bias_y = ${fparse 1/0.7}
  []
  [smg]
    type = StitchedMeshGenerator
    inputs = 'block_1 block_2'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'bottom top'
    merge_boundaries_with_same_name = true
  []
  # Prevent test diffing on distributed parallel element numbering
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${bulk_u}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_time]
    type = LinearFVTimeDerivative
    variable = vel_x
    factor = ${rho}
  []
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_time]
    type = LinearFVTimeDerivative
    variable = vel_y
    factor = ${rho}
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_time]
    type = LinearFVTimeDerivative
    variable = TKE
    factor = ${rho}
  []
  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = ${advected_interp_method}
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_time]
    type = LinearFVTimeDerivative
    variable = TKED
    factor = ${rho}
  []
  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = ${advected_interp_method}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []

  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKE
    functor = '${k_init}'
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKE
    use_two_term_expansion = false
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKED
    functor = '${eps_init}'
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKED
    use_two_term_expansion = false
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = 'bottom top'
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
  [yplus]
    type = MooseLinearVariableFVReal
  []
  [mu_eff]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
  [compute_mu_eff]
    type = ParsedAux
    variable = 'mu_eff'
    coupled_variables = 'mu_t'
    expression = 'mu_t + ${mu}'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = PIMPLE

  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  turbulence_systems = 'TKE_system TKED_system'

  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_tol = 1e-14
  pressure_l_tol = 1e-14
  turbulence_l_tol = 1e-14

  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  turbulence_equation_relaxation = '0.25 0.25'
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  turbulence_absolute_tolerance = '1e-12 1e-12'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  turbulence_petsc_options_iname = '-pc_type -pc_hypre_type'
  turbulence_petsc_options_value = 'hypre boomeramg'

  print_fields = false
  continue_on_max_its = true
  dt = 1.0
  num_steps = 2
[]

[Outputs]
  csv = true
[]

[VectorPostprocessors]
  [side_bottom]
    type = SideValueSampler
    boundary = 'bottom'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [side_top]
    type = SideValueSampler
    boundary = 'top'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_center_channel]
    type = LineValueSampler
    start_point = '${fparse 0.125 * L} ${fparse 0.0001} 0'
    end_point = '${fparse 0.875 * L} ${fparse 0.0001} 0'
    num_points = ${Mesh/block_1/nx}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_quarter_radius_channel]
    type = LineValueSampler
    start_point = '${fparse 0.125 * L} ${fparse 0.5 * H} 0'
    end_point = '${fparse 0.875 * L} ${fparse 0.5 * H} 0'
    num_points =  ${Mesh/block_1/nx}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex/2d-symmetric-vortex.i)

mu = 1.2
rho = 1.5
advected_interp_method = 'average'

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    body_force_kernel_names = "u_forcing; v_forcing"
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.0
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_forcing]
    type = LinearFVSource
    variable = vel_x
    source_density = forcing_u
  []
  [v_forcing]
    type = LinearFVSource
    variable = vel_y
    source_density = forcing_v
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = 'Ainv' # Functor created in the RhieChowMassFlux UO
    use_nonorthogonal_correction = false
    use_nonorthogonal_correction_on_boundary = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = 'HbyA' # Functor created in the RhieChowMassFlux UO
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [no-slip-wall-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top'
    variable = vel_x
    functor = exact_u
  []
  [no-slip-wall-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top'
    variable = vel_y
    functor = exact_v
  []
  [symmetry-u]
    type = LinearFVVelocitySymmetryBC
    boundary = 'bottom'
    variable = vel_x
    u = vel_x
    v = vel_y
    momentum_component = x
  []
  [symmetry-v]
    type = LinearFVVelocitySymmetryBC
    boundary = 'bottom'
    variable = vel_y
    u = vel_x
    v = vel_y
    momentum_component = y
  []
  [pressure-extrapolation]
    type = LinearFVPressureFluxBC
    boundary = 'top left right'
    variable = pressure
    HbyA_flux = HbyA
    Ainv = Ainv
  []
  [pressure-symmetry]
    type = LinearFVPressureSymmetryBC
    boundary = 'bottom'
    variable = pressure
    HbyA_flux = 'HbyA' # Functor created in the RhieChowMassFlux UO
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    expression = 'x^2*(1-x)^2*(8*y^3 - 9*y^2 + 1)'
  []
  [exact_v]
    type = ParsedFunction
    expression = '-(2*x - 6*x^2 + 4*x^3)*y*(1-y)^2*(2*y+1)'
  []
  [exact_p]
    type = ParsedFunction
    expression = 'y^2'
  []
  [forcing_u]
    type = ParsedFunction
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
    expression = 'rho*( (x^2*(1-x)^2)*(2*x - 6*x^2 + 4*x^3)*
                        ( (8*y^3 - 9*y^2 + 1)^2
                          - (2*y^4 - 3*y^3 + y)*(24*y^2 - 18*y) ) )
                  - mu*( (2 - 12*x + 12*x^2)*(8*y^3 - 9*y^2 + 1)
                         + (x^2*(1-x)^2)*(48*y - 18) )'
  []
  [forcing_v]
    type = ParsedFunction
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
    expression = 'rho*( (8*y^3 - 9*y^2 + 1)*(2*y^4 - 3*y^3 + y)*
                        ( (2*x - 6*x^2 + 4*x^3)^2
                          - (x^2*(1-x)^2)*(2 - 12*x + 12*x^2) ) )
                  + mu*( (24*x - 12)*(2*y^4 - 3*y^3 + y)
                         + (2*x - 6*x^2 + 4*x^3)*(24*y^2 - 18*y) )
                  + 2*y'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-8
  pressure_l_abs_tol = 1e-8
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 10000
  pressure_absolute_tolerance = 1e-7
  momentum_absolute_tolerance = 1e-7
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true

  pin_pressure = true
  pressure_pin_value = 0.25
  pressure_pin_point = '0.5 0.5 0.0'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = TIMESTEP_END
  []
  [L2u]
    type = ElementL2FunctorError
    approximate = vel_x
    exact = exact_u
    execute_on = TIMESTEP_END
  []
  [L2v]
    type = ElementL2FunctorError
    approximate = vel_y
    exact = exact_v
    execute_on = TIMESTEP_END
  []
  [L2p]
    approximate = pressure
    exact = exact_p
    type = ElementL2FunctorError
    execute_on = TIMESTEP_END
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated/channel_ERCOFTAC.i)


!include header_and_mesh.i

turbulence_advected_interp_method = ${advected_interp_method}

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${bulk_u}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
  [vanLeer]
    type = FVAdvectedVanLeerWeightBased
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    # we use mu_eff directly here to be able to have deviatoric term for both mu and mu_t
    mu = 'mu_eff'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_eff'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = ${turbulence_advected_interp_method}
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = ${turbulence_advected_interp_method}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []

  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKE
    functor = '${k_init}'
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKE
    use_two_term_expansion = false
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKED
    functor = '${eps_init}'
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKED
    use_two_term_expansion = false
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = 'bottom top'
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
[]

[FunctorMaterials]
  [compute_mu_eff]
    type = FunctorEffectiveDynamicViscosity
    property_name = mu_eff
    mu = ${mu}
    mu_t = mu_t
    mu_t_inverse_factor = 1
    execute_on = 'ALWAYS'
  []
[]

!include executioner_regular_channel.i

variables_to_sample = 'vel_x vel_y pressure_over_density TKE TKED'
!include postprocessing.i

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/steady-transient-compare/common-blocks.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'
cp = 300
k = 20
alpha_b = 1e-4

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1.'
    dy = '0.2'
    ix = '10'
    iy = '5'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
  [T]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_boussinesq]
    type = LinearFVMomentumBoussinesq
    variable = vel_x
    rho = ${rho}
    gravity = '0 -9.81 0'
    alpha_name = ${alpha_b}
    ref_temperature = 300.0
    T_fluid = T
    momentum_component = 'x'
  []
  [v_boussinesq]
    type = LinearFVMomentumBoussinesq
    variable = vel_y
    rho = ${rho}
    gravity = '0 -9.81 0'
    alpha_name = ${alpha_b}
    ref_temperature = 300.0
    T_fluid = T
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = false
  []
[]

[FunctorMaterials]
  [constant_functors]
    type = GenericFunctorMaterial
    prop_names = 'cp alpha_b'
    prop_values = '${cp} ${alpha_b}'
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_top_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    functor = ${fparse 300.0}
    boundary = 'left top'
  []
  [bottom_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    functor = ${fparse 350.0}
    boundary = bottom
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T
    use_two_term_expansion = false
    boundary = right
  []
[]

[Outputs]
  exodus = true
  execute_on = FINAL
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated/channel_ERCOFTAC_mu_eff.i)

!include header_and_mesh.i

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${bulk_u}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_eff'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_eff'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = ${advected_interp_method}
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_eff_k'
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = ${advected_interp_method}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_eff_eps'
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []

  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKE
    functor = '${k_init}'
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKE
    use_two_term_expansion = false
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKED
    functor = '${eps_init}'
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKED
    use_two_term_expansion = false
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = 'bottom top'
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
[]

[FunctorMaterials]
  [compute_mu_eff]
    type = FunctorEffectiveDynamicViscosity
    property_name = mu_eff
    mu = ${mu}
    mu_t = mu_t
    mu_t_inverse_factor = 1
    execute_on = 'ALWAYS'
  []
  [compute_mu_eff_k]
    type = FunctorEffectiveDynamicViscosity
    property_name = mu_eff_k
    mu = ${mu}
    mu_t = mu_t
    mu_t_inverse_factor = ${sigma_k}
    execute_on = 'ALWAYS'
  []
  [compute_mu_eff_eps]
    type = FunctorEffectiveDynamicViscosity
    property_name = mu_eff_eps
    mu = ${mu}
    mu_t = mu_t
    mu_t_inverse_factor = ${sigma_eps}
    execute_on = 'ALWAYS'
  []
[]

!include executioner_regular_channel.i

variables_to_sample = 'vel_x vel_y pressure_over_density TKE TKED'
!include postprocessing.i

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/lid-driven/linear-segregated/lid-driven-turb-non-eq-wall.i)

### Thermophysical Properties ###
mu = 1e-3
rho = 1.0

### Operation Conditions ###
lid_velocity = 1.0
side_length = 0.1

### Initial Conditions ###
intensity = 0.01
k_init = '${fparse 1.5*(intensity * lid_velocity)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / side_length}'

### k-epsilon Closure Parameters ###
sigma_k = 1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'left top right bottom'
wall_treatment = 'neq' # Options: eq_newton, eq_incremental, eq_linearized, neq

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${side_length}
    ymin = 0
    ymax = ${side_length}
    nx = 12
    ny = 12
  []
  # Prevent test diffing on distributed parallel element numbering
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${lid_velocity}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = upwind
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = upwind
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = 'upwind'
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = 'upwind'
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [top_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'top'
    functor = 1
  []
  [no_slip_x]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'left right bottom'
    functor = 0
  []
  [no_slip_y]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = 'left right top bottom'
    functor = 0
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left right top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = 'bottom top'
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
  [yplus]
    type = MooseLinearVariableFVReal
  []
  [mu_eff]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
  [compute_mu_eff]
    type = ParsedAux
    variable = 'mu_eff'
    coupled_variables = 'mu_t'
    expression = 'mu_t + ${mu}'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = SIMPLE

  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  turbulence_systems = 'TKE_system TKED_system'

  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_tol = 1e-14
  pressure_l_tol = 1e-14
  turbulence_l_tol = 1e-14

  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  turbulence_equation_relaxation = '0.5 0.5'
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  turbulence_absolute_tolerance = '1e-12 1e-12'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  turbulence_petsc_options_iname = '-pc_type -pc_hypre_type'
  turbulence_petsc_options_value = 'hypre boomeramg'

  print_fields = false
  continue_on_max_its = true

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '0.01 0.099 0.0'
[]

[Outputs]
  csv = true
  perf_graph = false
  print_nonlinear_residuals = false
  print_linear_residuals = true
[]

[VectorPostprocessors]
  [side_bottom]
    type = SideValueSampler
    boundary = 'bottom'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [side_top]
    type = SideValueSampler
    boundary = 'top'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [side_left]
    type = SideValueSampler
    boundary = 'left'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'y'
    execute_on = 'timestep_end'
  []
  [side_right]
    type = SideValueSampler
    boundary = 'right'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'y'
    execute_on = 'timestep_end'
  []
  [horizontal_center]
    type = LineValueSampler
    start_point = '${fparse 0.01 * side_length} ${fparse 0.499 * side_length} 0'
    end_point = '${fparse 0.99 * side_length} ${fparse 0.499 * side_length} 0'
    num_points = ${Mesh/gen/nx}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [vertical_center]
    type = LineValueSampler
    start_point = '${fparse 0.499 * side_length} ${fparse 0.01 * side_length} 0'
    end_point = '${fparse 0.499 * side_length} ${fparse 0.99 * side_length} 0'
    num_points =  ${Mesh/gen/ny}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'y'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/postprocessors/flow_rates/conservation_LinearFV.i)

mu = 2.6
rho = 1.1
advected_interp_method='average'

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.3'
    dy = '0.3'
    ix = '3'
    iy = '3'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 100
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
[]

[Postprocessors]
  [inlet_mass]
    type = VolumetricFlowRate
    boundary = left
    rhie_chow_user_object = rc
    advected_quantity = ${rho}
    vel_x = vel_x
    vel_y = vel_y
    subtract_mesh_velocity = false
  []
  [outlet_mass]
    type = VolumetricFlowRate
    boundary = right
    rhie_chow_user_object = rc
    advected_quantity = ${rho}
    vel_x = vel_x
    vel_y = vel_y
    subtract_mesh_velocity = false
  []
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d-symmetric/channel.i)

mu = 2.6
rho = 1.2
advected_interp_method = 'upwind'
u_inlet = 1.1
half_width = 0.2

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1.0'
    dy = '${half_width}'
    ix = '30'
    iy = '15'
    subdomain_id = '0'
  []
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  inactive = v_viscous_forcing
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [v_viscous_forcing]
    type = LinearFVRZViscousSource
    variable = vel_y
    mu = ${mu}
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${u_inlet}
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = vel_y
    functor = 0.0
  []
  [symmetry-u]
    type = LinearFVVelocitySymmetryBC
    variable = vel_x
    momentum_component = x
    u = vel_x
    v = vel_y
    boundary = 'bottom'
  []
  [symmetry-v]
    type = LinearFVVelocitySymmetryBC
    variable = vel_y
    momentum_component = y
    u = vel_x
    v = vel_y
    boundary = 'bottom'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top left'
    variable = pressure
    use_two_term_expansion = true
  []
  [symmetry-p]
    type = LinearFVPressureSymmetryBC
    variable = pressure
    boundary = 'bottom'
    HbyA_flux = 'HbyA' # Functor created in the RhieChowMassFlux UO
  []
[]

[Functions]
  [u_parabolic_profile]
    type = ParsedFunction
    expression = '3/2*${u_inlet}*(1 - pow(y/${half_width}, 2))' # Poiseuille profile
  []
  [u_parabolic_profile_rz]
    type = ParsedFunction
    expression = '2*${u_inlet}*(1 - pow(y/${half_width}, 2))' # Cylindrical profile
  []
[]

[AuxVariables]
  [vel_exact]
    type = MooseLinearVariableFVReal
  []
[]

[AuxKernels]
  [assign_vel_exact]
    type = FunctionAux
    variable = vel_exact
    function = u_parabolic_profile
    execute_on = TIMESTEP_END
  []
[]

[VectorPostprocessors]
  [outlet_velocity_profile]
    type = SideValueSampler
    variable = 'vel_x vel_exact'
    boundary = 'right'
    sort_by = 'y'
    execute_on = TIMESTEP_END
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.5
  pressure_variable_relaxation = 0.3
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/enthalpy_equation.i)

H = 0.015 #halfwidth of the channel, 10 cm of channel height
L = 1
bulk_u = 0.01
p_ref = 101325.0

advected_interp_method = 'upwind'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${L}
    ymin = -${H}
    ymax = ${H}
    nx = 30
    ny = 15
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 44000 # 1900 is an approx of cp(T)
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 777.
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
    advected_interp_method_name = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
    u = vel_x
    v = vel_y
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    mu = 'mu'
    momentum_component = 'y'
    use_nonorthogonal_correction = false
    advected_interp_method_name = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
    u = vel_x
    v = vel_y
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [temp_conduction]
    type = LinearFVDiffusion
    diffusion_coeff = 'alpha'
    variable = h
  []
  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = 0
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = h_from_p_T # ${fparse 1900.*860.}
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = 860.
  []

  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = 'top bottom'
    functor = 0.
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = 'top bottom'
    functor = 0.
  []
  [walls_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'top bottom'
    functor = h_from_p_T # ${fparse 1900. * 950}
  []
  [walls_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'top bottom'
    functor = 950.
  []
  [walls_p]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top bottom'
    variable = pressure
    use_two_term_expansion = false
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[FluidProperties]
  [lead]
    type = LeadFluidProperties
  []
[]

[FunctorMaterials]
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = lead
    pressure = ${p_ref}
    T_fluid = 'T'
    speed = 1
    porosity = 1
    characteristic_length = 1
  []
  [alpha]
    type = ADParsedFunctorMaterial
    property_name = 'alpha'
    functor_names = 'k cp'
    expression = 'k/cp'
  []
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    fp = lead
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-6
  pressure_l_abs_tol = 1e-6
  energy_l_abs_tol = 1e-8
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.9
  num_iterations = 200
  pressure_absolute_tolerance = 1e-6
  momentum_absolute_tolerance = 1e-6
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 1000

  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = 'TIMESTEP_BEGIN FINAL'
  [out]
    type = Checkpoint
    execute_on = 'TIMESTEP_END'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/bfs/linear-segregated/BFS_ERCOFTAC.i)

Re = 5100

rho = 1.0
bulk_u = 1.0
H = 1.0
mu = '${fparse rho * bulk_u * H / Re}'

advected_interp_method = 'upwind'

### k-epsilon Closure Parameters ###
sigma_k = 1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Initial and Boundary Conditions ###
intensity = 0.01
k_init = '${fparse 1.5*(intensity * bulk_u)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / H}'

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'bottom wall-side top'
wall_treatment = 'eq_incremental' # Options: eq_newton, eq_incremental, eq_linearized, neq

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${fparse 10.0*H} ${fparse 20.0*H}'
    dy = '${H} ${fparse 5*H}'
    ix = '8 16'
    iy = '2 8'
    subdomain_id = '
                    2 1
                    1 1
                  '
  []
  [corner_walls]
    type = SideSetsBetweenSubdomainsGenerator
    input = gen
    primary_block = '1'
    paired_block = '2'
    new_boundary = 'wall-side'
  []
  [delete_bottom]
    type = BlockDeletionGenerator
    input = corner_walls
    block = '2'
  []
  # Prevent test diffing on distributed parallel element numbering
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${bulk_u}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = ${advected_interp_method}
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = ${advected_interp_method}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKE
    functor = '${k_init}'
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKED
    functor = '${eps_init}'
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKE
    use_two_term_expansion = false
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKED
    use_two_term_expansion = false
  []

  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = ${walls}
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = ${walls}
    variable = vel_y
    functor = 0.0
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = ${walls}
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
  [yplus]
    type = MooseLinearVariableFVReal
  []
  [mu_eff]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init + mu}'
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
  [compute_mu_eff]
    type = ParsedAux
    variable = 'mu_eff'
    coupled_variables = 'mu_t'
    expression = 'mu_t + ${mu}'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = SIMPLE

  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  turbulence_systems = 'TKE_system TKED_system'

  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_tol = 1e-14
  pressure_l_tol = 1e-14
  turbulence_l_tol = 1e-14

  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  turbulence_equation_relaxation = '0.5 0.5'
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  turbulence_absolute_tolerance = '1e-12 1e-12'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  turbulence_petsc_options_iname = '-pc_type -pc_hypre_type'
  turbulence_petsc_options_value = 'hypre boomeramg'

  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  csv = true
  [console]
    type = Console
    outlier_variable_norms = false
  []
[]


[VectorPostprocessors]
  [side_bottom]
    type = SideValueSampler
    boundary = 'bottom'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [side_top]
    type = SideValueSampler
    boundary = 'top'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_entry_channel_wall]
    type = LineValueSampler
    start_point = '${fparse 0.5 * H} ${fparse 1.00001 * H} 0'
    end_point = '${fparse 29.5 * H} ${fparse 1.00001 * H} 0'
    num_points = 24
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_quarter_entry_channel]
    type = LineValueSampler
    start_point = '${fparse 0.5 * H} ${fparse 2.25001 * H} 0'
    end_point = '${fparse 29.5 * H} ${fparse 2.25001 * H} 0'
    num_points = 24
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/rotated-channel.i)

mu = 1
rho = 1
advected_interp_method = 'average'

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 5
    nx = 20
    ny = 4
  []
  [transform]
    type = TransformGenerator
    transform = rotate
    vector_value = '45 0 0'
    input = mesh
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVNormalVelocityFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    normal_velocity = '-1'
    component = 'x'
  []
  [inlet-v]
    type = LinearFVNormalVelocityFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    normal_velocity = '-1'
    component = 'y'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 100
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/natural_convection/linear_segregated/2d/diff_heated_cavity_linear_buoyancy.i)

################################################################################
# MATERIAL PROPERTIES
################################################################################
rho_0 = 3279.
mu = 1.0
k_cond = 38.0
cp = ${fparse 640}
alpha_b = 3.26e-5
T_0 = 875.0

walls = 'right left top bottom'

[GlobalParams]
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'
  advected_interp_method = 'upwind'
  u = vel_x
  v = vel_y
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

################################################################################
# GEOMETRY
################################################################################

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 1
    xmax = 2.0
    ymin = 1.0
    ymax = 2.0
    nx = 15
    ny = 15
  []
[]

################################################################################
# EQUATIONS: VARIABLES, KERNELS & BCS
################################################################################

[UserObjects]
  [ins_rhie_chow_interpolator]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
    body_force_kernel_names = 'u_buoyancy; v_buoyancy'
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = pressure_system
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 875
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = upwind
    mu = ${mu}
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [u_buoyancy]
    type = LinearFVMomentumBuoyancy
    variable = vel_x
    rho = 'rho'
    reference_rho = ${rho_0}
    gravity = '0 -9.81 0'
    momentum_component = 'x'
  []

  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = upwind
    mu = ${mu}
    momentum_component = 'y'
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [v_buoyancy]
    type = LinearFVMomentumBuoyancy
    variable = vel_y
    rho = 'rho'
    reference_rho = ${rho_0}
    gravity = '0 -9.81 0'
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = false
  []

   ####### FUEL ENERGY EQUATION #######

  [heat_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k_cond}
  []
[]

[LinearFVBCs]
  [no-slip-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_x
    boundary = ${walls}
    functor = 0
  []
  [no-slip-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = vel_y
    boundary = ${walls}
    functor = 0
  []
  [T_cold]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    boundary = 'right'
    functor = 870.0
  []
  [T_hot]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    boundary = 'left'
    functor = 880.0
  []
  [T_all]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_fluid
    boundary = 'top bottom'
    functor = 0.0
  []
  [pressure]
    type = LinearFVPressureFluxBC
    boundary = 'top bottom left right'
    variable = pressure
    HbyA_flux = HbyA
    Ainv = Ainv
  []
[]

[FunctorMaterials]
  [rho_function]
    type = ParsedFunctorMaterial
    property_name = 'rho'
    functor_names = 'T_fluid'
    expression = '${rho_0}*(1-${alpha_b}*(T_fluid-${T_0})) '
  []
[]

################################################################################
# EXECUTION / SOLVE
################################################################################

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-11
  pressure_l_abs_tol = 1e-11
  energy_l_abs_tol = 1e-11
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'ins_rhie_chow_interpolator'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.9
  num_iterations = 1500
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-8
  print_fields = false
  momentum_l_max_its = 300

  pin_pressure = true
  pressure_pin_value = 0.0
  pressure_pin_point = '1.5 1.5 0.0'

  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'

  continue_on_max_its = true
[]

################################################################################
# SIMULATION OUTPUTS
################################################################################

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/pressure-drop-advection.i)

rho = 1
u_inlet = 1
height = 1
mu = 0.02
nx = 12
ny = 3
advected_interp_method = 'average'
momentum_relaxation = 0.5
pressure_relaxation = 1.0

# Reference pressure drop computed from this input with advected_interp_method = average,
# nx = 192, ny = 48, use_two_term_expansion = true on the velocity outflow and
# pressure extrapolation BCs, and pressure/momentum absolute tolerances of 1e-10. The
# convergence test compares the absolute pressure-drop deviation from this stored
# refined value.
reference_pressure_drop = 0.8386252

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

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    pressure_projection_method = CONSISTENT
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${u_inlet}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = pressure_system
  []
[]

[Functions]
  [inlet_u]
    type = ParsedFunction
    expression = '30 * ${u_inlet} * y^2 * (${height} - y)^2 / ${height}^4'
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
  [upwind]
    type = FVAdvectedUpwind
  []
  [vanLeer]
    type = FVAdvectedVanLeerWeightBased
  []
  [min_mod]
    type = FVAdvectedMinmodWeightBased
  []
  [venkatakrishnan]
    type = FVAdvectedVenkatakrishnanDeferredCorrection
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = inlet_u
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = 0
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0
  []
  [inlet_p]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left'
    variable = pressure
    use_two_term_expansion = true
  []
  [walls_p]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = true
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = true
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'

  momentum_equation_relaxation = ${momentum_relaxation}
  pressure_variable_relaxation = ${pressure_relaxation}
  num_iterations = 2000
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = 'timestep_end'
  []
  [pressure_drop]
    type = PressureDrop
    pressure = pressure
    upstream_boundary = 'left'
    downstream_boundary = 'right'
    boundary = 'left right'
  []
  [pressure_drop_deviation]
    type = ParsedPostprocessor
    expression = 'abs(pressure_drop - ${reference_pressure_drop})'
    pp_names = 'pressure_drop'
  []
[]

[Outputs]
  exodus = false
  csv = true
  print_linear_residuals = false
  print_nonlinear_residuals = false
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/SIMPLEC/2d/2d-velocity-pressure.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1.0'
    dy = '0.1'
    ix = '20'
    iy = '3'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    pressure_projection_method = consistent
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 1.0
  num_iterations = 100
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d-heated/fluid.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'upwind'
cp = 1000
k = 1

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.25 0.25'
    dy = '0.2'
    ix = '5 5'
    iy = '5'
    subdomain_id = '0 1'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = false
  []
  [heat_exchange]
    type = LinearFVVolumetricHeatTransfer
    variable = T_fluid
    h_solid_fluid = 100
    T_fluid = T_fluid
    T_solid = T_solid
    is_solid = false
    block = 1
  []
[]

[FunctorMaterials]
  [constant_functors]
    type = GenericFunctorMaterial
    prop_names = 'cp'
    prop_values = '${cp}'
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_wall_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    functor = 300
    boundary = 'left top bottom'
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T_fluid
    use_two_term_expansion = false
    boundary = right
  []
[]

[AuxVariables]
  [T_solid]
    type = MooseLinearVariableFVReal
    initial_condition = 300
    block = 1
  []
[]

[MultiApps]
  inactive = 'solid'
  [solid]
    type = FullSolveMultiApp
    input_files = solid.i
    execute_on = timestep_begin
    no_restore = true
  []
[]

[Transfers]
  inactive = 'from_solid to_solid'
  [from_solid]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    from_multi_app = solid
    source_variable = 'T_solid'
    variable = 'T_solid'
    execute_on = timestep_begin
    from_blocks = 1
  []
  [to_solid]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    to_multi_app = solid
    source_variable = 'T_fluid'
    variable = 'T_fluid'
    execute_on = timestep_begin
    to_blocks = 1
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  energy_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.8
  energy_equation_relaxation = 0.9
  pressure_variable_relaxation = 0.3
  num_iterations = 20
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/ins/cht/bulk_heat_transfer/flow-around-square-linear.i)

mu = 0.01
rho = 1.1
k = 0.0005
cp = 10
k_s = 3.0
h_conv = 5

power_density = 10000

advected_interp_method = 'upwind'

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    ymin = 0
    ymax = 0.1
    xmax = 0.1
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    input = generated_mesh
    block_name = subdomain1
    bottom_left = '0.04 0.04 0'
    block_id = 1
    top_right = '0.06 0.06 0'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = subdomain1
    primary_block = 0
    paired_block = 1
    new_boundary = interface
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system solid_energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = 0
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.1
    solver_sys = u_system
    block = 0
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.01
    block = 0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
    block = 0
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
    block = 0
  []
  [T_solid]
    type = MooseLinearVariableFVReal
    solver_sys = solid_energy_system
    initial_condition = 500
    block = 1
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = true
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = true
  []

  [solid-conduction]
    type = LinearFVDiffusion
    variable = T_solid
    diffusion_coeff = ${k_s}
    use_nonorthogonal_correction = true
  []
  [solid-source]
    type = LinearFVSource
    variable = T_solid
    source_density = ${power_density}
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '0.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom interface'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []

  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    functor = 300
    boundary = 'left'
  []
  [walls_T]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_fluid
    functor = 0.0
    boundary = 'top bottom'
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T_fluid
    use_two_term_expansion = false
    boundary = right
  []

  [fluid_solid]
    type = LinearFVConvectiveHeatTransferBC
    variable = T_fluid
    T_solid = T_solid
    T_fluid = T_fluid
    boundary = interface
    h = ${h_conv}
  []
  [solid_fluid]
    type = LinearFVConvectiveHeatTransferBC
    variable = T_solid
    T_solid = T_solid
    T_fluid = T_fluid
    boundary = interface
    h = ${h_conv}
  []
[]

[FunctorMaterials]
  [rhocpT]
    property_name = 'rhocpT'
    type = ParsedFunctorMaterial
    functor_names = 'T_fluid'
    expression = '${rho}*${cp}*T_fluid'
  []
[]

[Postprocessors]
  [h_in]
    type = VolumetricFlowRate
    boundary = left
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    subtract_mesh_velocity = false
  []
  [h_out]
    type = VolumetricFlowRate
    boundary = right
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    advected_interp_method = upwind
    subtract_mesh_velocity = false
  []
  [power]
    type = ElementIntegralFunctorPostprocessor
    functor = ${power_density}
    block = 1
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-13
  pressure_l_abs_tol = 1e-13
  energy_l_abs_tol = 1e-13
  solid_energy_l_abs_tol = 1e-13
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  solid_energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  solid_energy_system = 'solid_energy_system'
  momentum_equation_relaxation = 0.8
  energy_equation_relaxation = 1.0
  pressure_variable_relaxation = 0.3
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  solid_energy_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  solid_energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  solid_energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-vortex/spacedependent_mu/sl.i)

rho = 1
advected_interp_method = 'average'

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_forcing]
    type = LinearFVSource
    variable = vel_x
    source_density = forcing_u
  []
  [v_forcing]
    type = LinearFVSource
    variable = vel_y
    source_density = forcing_v
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
    use_nonorthogonal_correction_on_boundary = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [no-slip-wall-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top bottom'
    variable = vel_x
    functor = '0'
  []
  [no-slip-wall-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top bottom'
    variable = vel_y
    functor = '0'
  []
  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'left right top bottom'
    variable = pressure
    use_two_term_expansion = true
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    expression = 'x^2*(1-x)^2*(2*y-6*y^2+4*y^3)'
  []
  [exact_v]
    type = ParsedFunction
    expression = '-y^2*(1-y)^2*(2*x-6*x^2+4*x^3)'
  []
  [exact_p]
    type = ParsedFunction
    expression = 'x*(1-x)'
  []
  [mu]
    type = ParsedFunction
    expression = '1+(x-1)*x*(y-1)*y'
  []
  [forcing_u]
    type = ParsedFunction
    expression = '-(2*x-1)*y*(y-1)*(2*x-6*x^2+4*x^3)*(2*y-6*y^2+4*y^3)'
                 '-(1+x*(x-1)*y*(y-1))*(2*y-6*y^2+4*y^3)*(2-12*x+12*x^2)'
                 '-(2*y-1)*x*(x-1)*(x^2*(1-x)^2*(2-12*y+12*y^2))'
                 '-(1+x*(x-1)*y*(y-1))*(x^2*(1-x)^2*(-12+24*y))'
                 '+1-2*x+rho*4*x^3*y^2*(2*y^2-2*y+1)*(y-1)^2*(-1+2*x)*(x-1)^3'
    symbol_names = 'rho'
    symbol_values = '${rho}'
  []
  [forcing_v]
    type = ParsedFunction
    expression = '(2*y-1)*x*(x-1)*(2*y-6*y^2+4*y^3)*(2*x-6*x^2+4*x^3)'
                 '+(1+x*(x-1)*y*(y-1))*(2-12*y+12*y^2)*(2*x-6*x^2+4*x^3)'
                 '+(2*x-1)*y*(y-1)*(y^2*(1-y)^2*(2-12*x+12*x^2))'
                 '+(1+x*(x-1)*y*(y-1))*(y^2*(1-y)^2*(-12+24*x))'
                 '+rho*4*y^3*x^2*(2*x^2-2*x+1)*(x-1)^2*(-1+2*y)*(y-1)^3'
    symbol_names = 'rho'
    symbol_values = '${rho}'
  []
  [forcing_u_deviatoric]
    type = ParsedFunction
    expression = '-2*(2*x-1)*y*(y-1)*(2*x-6*x^2+4*x^3)*(2*y-6*y^2+4*y^3)'
                 '-2*(1+x*(x-1)*y*(y-1))*(2*y-6*y^2+4*y^3)*(2-12*x+12*x^2)'
                 '-(2*y-1)*x*(x-1)*(x^2*(1-x)^2*(2-12*y+12*y^2)-y^2*(1-y)^2*(2-12*x+12*x^2))'
                 '-(1+x*(x-1)*y*(y-1))*(x^2*(1-x)^2*(-12+24*y)-(2*y-6*y^2+4*y^3)*(2-12*x+12*x^2))'
                 '+1-2*x+rho*4*x^3*y^2*(2*y^2-2*y+1)*(y-1)^2*(-1+2*x)*(x-1)^3'
    symbol_names = 'rho'
    symbol_values = '${rho}'
  []
  [forcing_v_deviatoric]
    type = ParsedFunction
    expression = '2*(2*y-1)*x*(x-1)*(2*y-6*y^2+4*y^3)*(2*x-6*x^2+4*x^3)'
                 '+2*(1+x*(x-1)*y*(y-1))*(2-12*y+12*y^2)*(2*x-6*x^2+4*x^3)'
                 '-(2*x-1)*y*(y-1)*(x^2*(1-x)^2*(2-12*y+12*y^2)-y^2*(1-y)^2*(2-12*x+12*x^2))'
                 '-(1+x*(x-1)*y*(y-1))*(-y^2*(1-y)^2*(-12+24*x)+(2*x-6*x^2+4*x^3)*(2-12*y+12*y^2))'
                 '+rho*4*y^3*x^2*(2*x^2-2*x+1)*(x-1)^2*(-1+2*y)*(y-1)^3'
    symbol_names = 'rho'
    symbol_values = '${rho}'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_max_its = 30
  pressure_l_max_its = 30
  momentum_l_tol = 0.0
  pressure_l_tol = 0.0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 2000
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false

  pin_pressure = true
  pressure_pin_value = 0.25
  pressure_pin_point = '0.5 0.5 0.0'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = FINAL
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'csv'
    execute_on = FINAL
  []
  [L2u]
    type = ElementL2FunctorError
    approximate = vel_x
    exact = exact_u
    outputs = 'csv'
    execute_on = FINAL
  []
  [L2v]
    type = ElementL2FunctorError
    approximate = vel_y
    exact = exact_v
    outputs = 'csv'
    execute_on = FINAL
  []
  [L2p]
    approximate = pressure
    exact = exact_p
    type = ElementL2FunctorError
    outputs = 'csv'
    execute_on = FINAL
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/3d/3d-velocity-pressure.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 3
    dx = '0.3'
    dy = '0.3'
    dz = '0.3'
    ix = '3'
    iy = '3'
    iz = '3'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system w_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    w = vel_z
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [vel_z]
    type = MooseLinearVariableFVReal
    solver_sys = w_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [w_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_z
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'z'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [w_pressure]
    type = LinearFVMomentumPressure
    variable = vel_z
    pressure = pressure
    momentum_component = 'z'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [inlet-w]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_z
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom back front'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom back front'
    variable = vel_y
    functor = 0.0
  []
  [walls-w]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom back front'
    variable = vel_z
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_w]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_z
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system w_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 100
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type -pc_hypre_boomeramg_agg_nl -pc_hypre_boomeramg_agg_num_paths -pc_hypre_boomeramg_truncfactor -pc_hypre_boomeramg_strong_threshold -pc_hypre_boomeramg_coarsen_type -pc_hypre_boomeramg_interp_type'
  momentum_petsc_options_value = 'hypre boomeramg 4 1 0.1 0.6 HMIS ext+i'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type -pc_hypre_boomeramg_agg_nl -pc_hypre_boomeramg_agg_num_paths -pc_hypre_boomeramg_truncfactor -pc_hypre_boomeramg_strong_threshold -pc_hypre_boomeramg_coarsen_type -pc_hypre_boomeramg_interp_type'
  pressure_petsc_options_value = 'hypre boomeramg 2 1 0.1 0.6 HMIS ext+i'
  print_fields = false
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/2d-velocity-pressure.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.3'
    dy = '0.3'
    ix = '3'
    iy = '3'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 100
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/bfs/linear-segregated-transient/BFS_ERCOFTAC.i)

Re = 5100

rho = 1.0
bulk_u = 1.0
H = 1.0
mu = '${fparse rho * bulk_u * H / Re}'

advected_interp_method = 'upwind'

### k-epsilon Closure Parameters ###
sigma_k = 1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Initial and Boundary Conditions ###
intensity = 0.01
k_init = '${fparse 1.5*(intensity * bulk_u)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / H}'

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'bottom wall-side top'
wall_treatment = 'neq' # Options: eq_newton, eq_incremental, eq_linearized, neq

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${fparse 10.0*H} ${fparse 20.0*H}'
    dy = '${H} ${fparse 5*H}'
    ix = '8 16'
    iy = '2 8'
    subdomain_id = '
                    2 1
                    1 1
                  '
  []
  [corner_walls]
    type = SideSetsBetweenSubdomainsGenerator
    input = gen
    primary_block ='1'
    paired_block ='2'
    new_boundary = 'wall-side'
  []
  [delete_bottom]
    type = BlockDeletionGenerator
    input = corner_walls
    block ='2'
  []
  # Prevent test diffing on distributed parallel element numbering
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${bulk_u}
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 0
    solver_sys = v_system
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_time]
    type = LinearFVTimeDerivative
    variable = vel_x
    factor = ${rho}
  []
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_time]
    type = LinearFVTimeDerivative
    variable = vel_y
    factor = ${rho}
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_time]
    type = LinearFVTimeDerivative
    variable = TKE
    factor = ${rho}
  []
  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = ${advected_interp_method}
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_time]
    type = LinearFVTimeDerivative
    variable = TKED
    factor = ${rho}
  []
  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = ${advected_interp_method}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKE
    functor = '${k_init}'
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKED
    functor = '${eps_init}'
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKE
    use_two_term_expansion = false
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKED
    use_two_term_expansion = false
  []

  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = ${walls}
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = ${walls}
    variable = vel_y
    functor = 0.0
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = ${walls}
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
  []
  [yplus]
    type = MooseLinearVariableFVReal
  []
  [mu_eff]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init + mu}'
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
  [compute_mu_eff]
    type = ParsedAux
    variable = 'mu_eff'
    coupled_variables = 'mu_t'
    expression = 'mu_t + ${mu}'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = PIMPLE

  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  turbulence_systems = 'TKE_system TKED_system'

  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_tol = 1e-14
  pressure_l_tol = 1e-14
  turbulence_l_tol = 1e-14

  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  turbulence_equation_relaxation = '0.5 0.5'
  num_iterations = 20
  pressure_absolute_tolerance = 1e-6
  momentum_absolute_tolerance = 1e-6
  turbulence_absolute_tolerance = '1e-6 1e-6'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  turbulence_petsc_options_iname = '-pc_type -pc_hypre_type'
  turbulence_petsc_options_value = 'hypre boomeramg'

  print_fields = false
  continue_on_max_its = true
  dt = 10.0
  num_steps = 10
  num_piso_iterations = 2
[]

[Outputs]
  csv = true
[]

[VectorPostprocessors]
  [side_bottom]
    type = SideValueSampler
    boundary = 'bottom'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [side_top]
    type = SideValueSampler
    boundary = 'top'
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_entry_channel_wall]
    type = LineValueSampler
    start_point = '${fparse 0.5 * H} ${fparse 1.00001 * H} 0'
    end_point = '${fparse 29.5 * H} ${fparse 1.00001 * H} 0'
    num_points = 24
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_quarter_entry_channel]
    type = LineValueSampler
    start_point = '${fparse 0.5 * H} ${fparse 2.25001 * H} 0'
    end_point = '${fparse 29.5 * H} ${fparse 2.25001 * H} 0'
    num_points = 24
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/segregated-comparison/segregated-linear.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.3'
    dy = '0.3'
    ix = '3'
    iy = '3'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  num_iterations = 2
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
[]

[Outputs]
  exodus = true
  execute_on = TIMESTEP_END
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex-rz/2d-symmetric-vortex-rz-spacedependent.i)

mu_ref = 1.2
mu_r = 0.1
mu_x = 0.2
rho_ref = 1.4
rho_r = 0.15
rho_x = 0.25

use_dev = true

advected_interp_method = 'average'

[Problem]
  linear_sys_names = 'u_system v_system pressure_system'
  previous_nl_solution_required = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
  coord_type = 'RZ'
  rz_coord_axis = x
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = rho_fun
    p_diffusion_kernel = p_diffusion
    pressure_projection_method = consistent
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.0
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = mu_fun
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = ${use_dev}
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = mu_fun
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = ${use_dev}
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_forcing]
    type = LinearFVSource
    variable = vel_x
    source_density = forcing_u
  []
  [v_forcing]
    type = LinearFVSource
    variable = vel_y
    source_density = forcing_v
  []
  [v_viscous_forcing]
    type = LinearFVRZViscousSource
    variable = vel_y
    mu = mu_fun
    momentum_component = 'y'
    u = vel_x
    v = vel_y
    use_deviatoric_terms = ${use_dev}
  []
  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = 'Ainv'
    use_nonorthogonal_correction = false
    use_nonorthogonal_correction_on_boundary = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = 'HbyA'
    force_boundary_execution = true
  []
[]

[LinearFVBCs]
  [no-slip-wall-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top'
    variable = vel_x
    functor = exact_u
  []
  [no-slip-wall-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left right top'
    variable = vel_y
    functor = exact_v
  []
  [symmetry-u]
    type = LinearFVVelocitySymmetryBC
    boundary = 'bottom'
    variable = vel_x
    u = vel_x
    v = vel_y
    momentum_component = x
  []
  [symmetry-v]
    type = LinearFVVelocitySymmetryBC
    boundary = 'bottom'
    variable = vel_y
    u = vel_x
    v = vel_y
    momentum_component = y
  []

  [pressure-extrapolation]
    type = LinearFVExtrapolatedPressureBC
    boundary = 'top left right'
    variable = pressure
    use_two_term_expansion = true
  []
  [pressure-symmetry]
    type = LinearFVPressureSymmetryBC
    boundary = 'bottom'
    variable = pressure
    HbyA_flux = 'HbyA'
  []
[]

[AuxVariables]
  [vel_x_aux]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
  []
  [vel_y_aux]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
  []
  [pressure_aux]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
  []
[]

[AuxKernels]
  [vel_x_function_aux]
    type = FunctionAux
    variable = vel_x_aux
    function = exact_u
    execute_on = TIMESTEP_END
  []
  [vel_y_function_aux]
    type = FunctionAux
    variable = vel_y_aux
    function = exact_v
    execute_on = TIMESTEP_END
  []
  [pressure_function_aux]
    type = FunctionAux
    variable = pressure_aux
    function = exact_p
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  # --------------------------------------------------
  # Material property functions
  # --------------------------------------------------
  [rho_fun]
    type = ParsedFunction
    symbol_names = 'rho_ref rho_r rho_x'
    symbol_values = '${rho_ref} ${rho_r} ${rho_x}'
    expression = 'rho_ref + rho_x*x + rho_r*y'
  []
  [mu_fun]
    type = ParsedFunction
    symbol_names = 'mu_ref mu_r mu_x'
    symbol_values = '${mu_ref} ${mu_r} ${mu_x}'
    expression = 'mu_ref + mu_x*x + mu_r*y'
  []
  # --------------------------------------------------
  # Convenience reciprocals
  # --------------------------------------------------
  [S]
    type=ParsedFunction
    symbol_names = 'rho_fun'
    symbol_values = 'rho_fun'
    expression='1.0/rho_fun'
  []
  [S2]
    type=ParsedFunction
    symbol_names = 'rho_fun'
    symbol_values = 'rho_fun'
    expression='(1.0/rho_fun)^2'
  []
  [S3]
    type=ParsedFunction
    symbol_names = 'rho_fun'
    symbol_values = 'rho_fun'
    expression='(1.0/rho_fun)^3'
  []
  # --------------------------------------------------
  # Building blocks
  # --------------------------------------------------
  [A]
    type=ParsedFunction
    expression='x^2*(1-x)^2'
  []
  [Ap]
    type=ParsedFunction
    expression='2*x - 6*x^2 + 4*x^3'
  []
  [App]
    type=ParsedFunction
    expression='2 - 12*x + 12*x^2'
  []
  [Appp]
    type=ParsedFunction
    expression='-12 + 24*x'
  []
  [Q]
    type=ParsedFunction
    expression='4*y^2 - 10*y^3 + 6*y^4'
  []
  [Qp]
    type=ParsedFunction
    expression='8*y - 30*y^2 + 24*y^3'
  []
  [Qpp]
    type=ParsedFunction
    expression='8 - 60*y + 72*y^2'
  []
  [R]
    type=ParsedFunction
    expression='y^3 - 2*y^4 + y^5'
  []
  [Rp]
    type=ParsedFunction
    expression='3*y^2 - 8*y^3 + 5*y^4'
  []
  [Rpp]
    type=ParsedFunction
    expression='6*y - 24*y^2 + 20*y^3'
  []
  # --------------------------------------------------
  # Exact solutions
  # --------------------------------------------------
  [exact_u]
    type=ParsedFunction
    symbol_names = 'A Q rho_fun'
    symbol_values = 'A Q rho_fun'
    expression='A*Q / rho_fun'
  []
  [exact_v]
    type=ParsedFunction
    symbol_names = 'Ap R rho_fun'
    symbol_values = 'Ap R rho_fun'
    expression='-Ap*R / rho_fun'
  []
  [exact_p]
    type=ParsedFunction
    expression='x*y^2'
  []
  # --------------------------------------------------
  # First derivatives
  # --------------------------------------------------
  [ux]
    type=ParsedFunction
    symbol_names = 'A Ap Q rho_fun rho_x'
    symbol_values = 'A Ap Q rho_fun ${rho_x}'
    expression='(Ap*Q)/rho_fun - (A*Q*rho_x)/rho_fun^2'
  []
  [ur]
    type=ParsedFunction
    symbol_names = 'A Q Qp rho_fun rho_r'
    symbol_values = 'A Q Qp rho_fun ${rho_r}'
    expression='(A*Qp)/rho_fun - (A*Q*rho_r)/rho_fun^2'
  []
  [vx]
    type=ParsedFunction
    symbol_names = 'App Ap R rho_fun rho_x'
    symbol_values = 'App Ap R rho_fun ${rho_x}'
    expression='-(App*R)/rho_fun + (Ap*R*rho_x)/rho_fun^2'
  []
  [vr]
    type=ParsedFunction
    symbol_names = 'Ap Rp R rho_fun rho_r'
    symbol_values = 'Ap Rp R rho_fun ${rho_r}'
    expression='-(Ap*Rp)/rho_fun + (Ap*R*rho_r)/rho_fun^2'
  []
  # --------------------------------------------------
  # Second derivatives
  # --------------------------------------------------
  [uxx]
    type = ParsedFunction
    symbol_names  = 'rho_x App Q S Ap S2 A S3'
    symbol_values = '${rho_x} App Q S Ap S2 A S3'
    expression = 'App*Q*S - 2*Ap*Q*rho_x*S2 + 2*A*Q*(rho_x^2)*S3'
  []
  [uxr]
    type = ParsedFunction
    symbol_names  = 'rho_x rho_r Ap Qp S Q S2 A S3'
    symbol_values = '${rho_x} ${rho_r} Ap Qp S Q S2 A S3'
    expression = 'Ap*Qp*S - Ap*Q*rho_r*S2 - A*Qp*rho_x*S2 + 2*A*Q*(rho_x*rho_r)*S3'
  []
  [urr]
    type = ParsedFunction
    symbol_names  = 'rho_r A Qpp S Qp S2 Q S3'
    symbol_values = '${rho_r} A Qpp S Qp S2 Q S3'
    expression = 'A*Qpp*S - 2*A*Qp*rho_r*S2 + 2*A*Q*(rho_r^2)*S3'
  []
  [vxx]
    type = ParsedFunction
    symbol_names  = 'rho_x Appp R S App S2 Ap S3'
    symbol_values = '${rho_x} Appp R S App S2 Ap S3'
    expression = '-Appp*R*S + 2*App*R*rho_x*S2 - 2*Ap*R*(rho_x^2)*S3'
  []
  [vxr]
    type = ParsedFunction
    symbol_names  = 'rho_x rho_r App Rp S R Ap S2 S3'
    symbol_values = '${rho_x} ${rho_r} App Rp S R Ap S2 S3'
    expression = '-App*Rp*S + (App*R*rho_r + Ap*Rp*rho_x)*S2 - 2*Ap*R*(rho_x*rho_r)*S3'
  []
  [vrr]
    type = ParsedFunction
    symbol_names  = 'rho_r Ap Rpp S Rp S2 R S3'
    symbol_values = '${rho_r} Ap Rpp S Rp S2 R S3'
    expression = '-Ap*Rpp*S + 2*Ap*Rp*rho_r*S2 - 2*Ap*R*(rho_r^2)*S3'
  []
  # --------------------------------------------------
  # Derivatives of theta
  # --------------------------------------------------
  [theta]
    type = ParsedFunction
    symbol_names = 'ux vr exact_v'
    symbol_values = 'ux vr exact_v'
    expression = 'ux + vr + (exact_v/y)'
  []
  [thetax]
    type = ParsedFunction
    symbol_names = 'uxx vxr vx'
    symbol_values = 'uxx vxr vx'
    expression = 'uxx + vxr + (vx/y)'
  []
  [thetar]
    type = ParsedFunction
    symbol_names = 'uxr vrr vr exact_v'
    symbol_values = 'uxr vrr vr exact_v'
    expression = 'uxr + vrr + (vr/y) - (exact_v/(y^2))'
  []
  # --------------------------------------------------
  # Stress components
  # --------------------------------------------------
  [tau_xx]
    type=ParsedFunction
    symbol_names = 'ux theta mu_fun'
    symbol_values = 'ux theta mu_fun'
    expression='2*mu_fun*ux - (2.0/3.0)*mu_fun*theta'
  []
  [tau_rr]
    type=ParsedFunction
    symbol_names = 'vr theta mu_fun'
    symbol_values = 'vr theta mu_fun'
    expression='2*mu_fun*vr - (2.0/3.0)*mu_fun*theta'
  []
  [tau_xr]
    type=ParsedFunction
    symbol_names = 'ur vx mu_fun'
    symbol_values = 'ur vx mu_fun'
    expression='mu_fun*(ur + vx)'
  []
  [tau_tt]
    type=ParsedFunction
    symbol_names = 'exact_v theta mu_fun'
    symbol_values = 'exact_v theta mu_fun'
    expression='2*mu_fun*(exact_v/y) - (2.0/3.0)*mu_fun*theta'
  []
  # --------------------------------------------------
  # Convective fluxes
  # --------------------------------------------------
  [Fxx]
    type=ParsedFunction
    symbol_names = 'exact_u rho_fun'
    symbol_values = 'exact_u rho_fun'
    expression='rho_fun*exact_u*exact_u'
  []
  [Fxr]
    type=ParsedFunction
    symbol_names = 'exact_u exact_v rho_fun'
    symbol_values = 'exact_u exact_v rho_fun'
    expression='rho_fun*exact_u*exact_v'
  []
  [Frx]
    type=ParsedFunction
    symbol_names = 'exact_u exact_v rho_fun'
    symbol_values = 'exact_u exact_v rho_fun'
    expression='rho_fun*exact_v*exact_u'
  []
  [Frr]
    type=ParsedFunction
    symbol_names = 'exact_v rho_fun'
    symbol_values = 'exact_v rho_fun'
    expression='rho_fun*exact_v*exact_v'
  []
  # --------------------------------------------------
  # Stress derivatives
  # --------------------------------------------------
  [tau_xx_x]
    type = ParsedFunction
    symbol_names  = 'mu_x ux mu_fun uxx theta thetax'
    symbol_values = '${mu_x} ux mu_fun uxx theta thetax'
    expression = '2*mu_x*ux + 2*mu_fun*uxx - (2.0/3.0)*(mu_x*theta + mu_fun*thetax)'
  []
  [tau_xr_x]
    type = ParsedFunction
    symbol_names  = 'mu_x ur vx mu_fun uxr vxx'
    symbol_values = '${mu_x} ur vx mu_fun uxr vxx'
    expression = 'mu_x*(ur + vx) + mu_fun*(uxr + vxx)'
  []
  [tau_xr_r]
    type = ParsedFunction
    symbol_names  = 'mu_r ur vx mu_fun urr vxr'
    symbol_values = '${mu_r} ur vx mu_fun urr vxr'
    expression = 'mu_r*(ur + vx) + mu_fun*(urr + vxr)'
  []
  [tau_rr_r]
    type = ParsedFunction
    symbol_names  = 'mu_r vr mu_fun vrr theta thetar'
    symbol_values = '${mu_r} vr mu_fun vrr theta thetar'
    expression = '2*mu_r*vr + 2*mu_fun*vrr - (2.0/3.0)*(mu_r*theta + mu_fun*thetar)'
  []
  # --------------------------------------------------
  # Conservative flux derivatives
  # --------------------------------------------------
  [Fxx_x]
    type = ParsedFunction
    symbol_names  = 'rho_x A Ap Q S S2'
    symbol_values = '${rho_x} A Ap Q S S2'
    expression = '2*A*Ap*Q^2*S - A^2*Q^2*rho_x*S2'
  []
  [Frx_r]
    type = ParsedFunction
    symbol_names  = 'rho_r A Ap Qp R Q Rp S S2'
    symbol_values = '${rho_r} A Ap Qp R Q Rp S S2'
    expression = '-A*Ap*((Qp*R + Q*Rp)*S - Q*R*rho_r*S2)'
  []
  [Fxr_x]
    type = ParsedFunction
    symbol_names  = 'rho_x Ap A App Q R S S2'
    symbol_values = '${rho_x} Ap A App Q R S S2'
    expression = '-((Ap^2 + A*App)*Q*R*S - A*Ap*Q*R*rho_x*S2)'
  []
  [Frr_r]
    type = ParsedFunction
    symbol_names  = 'rho_r Ap R Rp S S2'
    symbol_values = '${rho_r} Ap R Rp S S2'
    expression = 'Ap^2*(2*R*Rp*S - R^2*rho_r*S2)'
  []
  # --------------------------------------------------
  # Pressure gradients
  # --------------------------------------------------
  [px]
    type=ParsedFunction
    expression='y^2'
  []
  [pr]
    type=ParsedFunction
    expression='2*x*y'
  []
  # --------------------------------------------------
  # Forcing terms
  # --------------------------------------------------
  [forcing_u]
    type = ParsedFunction
    symbol_names  = 'Fxx_x Frx Frx_r px tau_xx_x tau_xr tau_xr_r'
    symbol_values = 'Fxx_x Frx Frx_r px tau_xx_x tau_xr tau_xr_r'
    expression = 'Fxx_x + (Frx/y) + Frx_r + px - ( tau_xx_x + (tau_xr/y) + tau_xr_r )'
  []
  [forcing_v]
    type = ParsedFunction
    symbol_names  = 'Fxr_x Frr Frr_r pr tau_xr_x tau_rr tau_rr_r tau_tt'
    symbol_values = 'Fxr_x Frr Frr_r pr tau_xr_x tau_rr tau_rr_r tau_tt'
    expression = 'Fxr_x + (Frr/y) + Frr_r + pr - ( tau_xr_x + (tau_rr/y) + tau_rr_r - (tau_tt)/y )'
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  momentum_l_max_its = 500
  pressure_l_max_its = 500
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  momentum_equation_relaxation = 0.85
  pressure_variable_relaxation = 1.0
  num_iterations = 10000
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  print_fields = false
  continue_on_max_its = true

  pin_pressure = true
  pressure_pin_value = 0.125
  pressure_pin_point = '0.5 0.5 0.0'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = TIMESTEP_END
  []
  [L2u]
    type = ElementL2FunctorError
    approximate = vel_x
    exact = exact_u
    execute_on = TIMESTEP_END
  []
  [L2v]
    type = ElementL2FunctorError
    approximate = vel_y
    exact = exact_v
    execute_on = TIMESTEP_END
  []
  [L2p]
    approximate = pressure
    exact = exact_p
    type = ElementL2FunctorError
    execute_on = TIMESTEP_END
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/2d-boussinesq.i)

mu = 2.6
rho = 1.0
advected_interp_method = 'average'
cp = 300
k = 20
alpha_b = 1e-4

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1.'
    dy = '0.2'
    ix = '10'
    iy = '5'
  []
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.5
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = 0.2
  []
  [T]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = 300
  []
[]

[FVInterpolationMethods]
  [average]
    type = FVGeometricAverage
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [u_boussinesq]
    type = LinearFVMomentumBoussinesq
    variable = vel_x
    rho = ${rho}
    gravity = '0 -9.81 0'
    alpha_name = ${alpha_b}
    ref_temperature = 300.0
    T_fluid = T
    momentum_component = 'x'
  []
  [v_boussinesq]
    type = LinearFVMomentumBoussinesq
    variable = vel_y
    rho = ${rho}
    gravity = '0 -9.81 0'
    alpha_name = ${alpha_b}
    ref_temperature = 300.0
    T_fluid = T
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = false
  []
[]

[FunctorMaterials]
  [constant_functors]
    type = GenericFunctorMaterial
    prop_names = 'cp alpha_b'
    prop_values = '${cp} ${alpha_b}'
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
  [inlet_top_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    functor = ${fparse 300.0}
    boundary = 'left top'
  []
  [bottom_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    functor = ${fparse 350.0}
    boundary = bottom
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T
    use_two_term_expansion = false
    boundary = right
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  energy_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.8
  energy_equation_relaxation = 0.9
  pressure_variable_relaxation = 0.3
  num_iterations = 200
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  energy_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  print_fields = false
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/block-restricted/block-ke.i)

H = 1 #halfwidth of the channel
L = 100

Re = 13700

rho = 1
bulk_u = 1
mu = '${fparse rho * bulk_u * 2 * H / Re}'

advected_interp_method = 'upwind'

### k-epsilon Closure Parameters ###
sigma_k = 1.0
sigma_eps = 1.3
C1_eps = 1.44
C2_eps = 1.92
C_mu = 0.09

### Initial and Boundary Conditions ###
intensity = '${fparse 0.16*Re^(-1./8.)}'
k_init = '${fparse 1.5*(intensity * bulk_u)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / (2*H)}'

### Modeling parameters ###
bulk_wall_treatment = false
walls = 'walls'
wall_treatment = 'eq_newton' # Options: eq_newton, eq_incremental, eq_linearized, neq

[Mesh]
  [block_left]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = '${fparse -2*H}'
    xmax = '${fparse -H}'
    ymin = 0
    ymax = ${L}
    nx = 3
    ny = 4
  []
  [block_1]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = '${fparse -H}'
    xmax = 0
    ymin = 0
    ymax = ${L}
    nx = 4
    ny = 4
    bias_x = '${fparse 1/0.7}'
  []
  [block_2]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${H}
    ymin = 0
    ymax = ${L}
    nx = 4
    ny = 4
    bias_x = 0.7
  []
  [block_right]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = ${H}
    xmax = '${fparse 2*H}'
    ymin = 0
    ymax = ${L}
    nx = 3
    ny = 4
  []
  [smg]
    type = StitchedMeshGenerator
    inputs = 'block_left block_1 block_2 block_right'
    stitch_boundaries_pairs = 'right left; right left; right left'
  []
  [middle]
    input = smg
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '${fparse -H} 0 0'
    top_right = '${H} ${L} 50'
  []
  [walls]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 0
    new_boundary = walls
    input = middle
  []
  # Prevent test diffing on distributed parallel element numbering
  allow_renumbering = false
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system TKE_system TKED_system'
  previous_nl_solution_required = true
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = 1
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 0.0
    solver_sys = u_system
    block = 1
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = ${bulk_u}
    solver_sys = v_system
    block = 1
  []
  [pressure]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = pressure_system
    block = 1
  []
  [TKE]
    type = MooseLinearVariableFVReal
    solver_sys = TKE_system
    initial_condition = ${k_init}
    block = 1
  []
  [TKED]
    type = MooseLinearVariableFVReal
    solver_sys = TKED_system
    initial_condition = ${eps_init}
    block = 1
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
    advected_interp_method_name = ${advected_interp_method}
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = false
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []

  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    advected_interp_method_name = ${advected_interp_method}
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = false
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    tke = TKE
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    C1_eps = ${C1_eps}
    C2_eps = ${C2_eps}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'bottom'
    variable = vel_x
    functor = 0
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'bottom'
    variable = vel_y
    functor = '${bulk_u}'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'walls'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'walls'
    variable = vel_y
    functor = 0.0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'top'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'top'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = pressure
    functor = 0.0
  []

  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'bottom'
    variable = TKE
    functor = '${k_init}'
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'top'
    variable = TKE
    use_two_term_expansion = false
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'bottom'
    variable = TKED
    functor = '${eps_init}'
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'top'
    variable = TKED
    use_two_term_expansion = false
  []
  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = 'walls'
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

[AuxVariables]
  [mu_t]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
    block = 1
  []
  [yplus]
    type = MooseLinearVariableFVReal
    block = 1
  []
  [mu_eff]
    type = MooseLinearVariableFVReal
    initial_condition = '${fparse rho * C_mu * ${k_init}^2 / eps_init}'
    block = 1
  []
[]

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 1e20
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
  [compute_mu_eff]
    type = ParsedAux
    variable = 'mu_eff'
    coupled_variables = 'mu_t'
    expression = 'mu_t + ${mu}'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = SIMPLE

  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  turbulence_systems = 'TKE_system TKED_system'

  momentum_l_abs_tol = 1e-14
  pressure_l_abs_tol = 1e-14
  turbulence_l_abs_tol = 1e-14
  momentum_l_tol = 1e-14
  pressure_l_tol = 1e-14
  turbulence_l_tol = 1e-14

  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  turbulence_equation_relaxation = '0.2 0.2'
  turbulence_field_relaxation = '0.2 0.2'
  num_iterations = 1000
  pressure_absolute_tolerance = 1e-12
  momentum_absolute_tolerance = 1e-12
  turbulence_absolute_tolerance = '1e-12 1e-12'
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'
  turbulence_petsc_options_iname = '-pc_type -pc_hypre_type'
  turbulence_petsc_options_value = 'hypre boomeramg'

  print_fields = false
  continue_on_max_its = true
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  csv = true
[]

[VectorPostprocessors]
  [line_wall]
    type = LineValueSampler
    start_point = '${fparse 0.99 * H} ${fparse 0.125 * L} 0'
    end_point = '${fparse 0.99 * H} ${fparse 0.875 * L} 0'
    num_points = ${Mesh/block_1/nx}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_center_channel]
    type = LineValueSampler
    start_point = ' ${fparse 0.0001 * H} ${fparse 0.125 * L} 0'
    end_point = '${fparse 0.0001 * H} ${fparse 0.875 * L} 0'
    num_points = ${Mesh/block_1/nx}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
  [line_quarter_radius_channel]
    type = LineValueSampler
    start_point = '${fparse 0.51 * H} ${fparse 0.125 * L} 0'
    end_point = '${fparse 0.51 * H} ${fparse 0.875 * L} 0'
    num_points =  ${Mesh/block_1/nx}
    variable = 'vel_x vel_y pressure TKE TKED'
    sort_by = 'x'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/cht/conjugate_heat_transfer/cht_rob-rob.i)

### benchmark sources:
### https://doi.org/10.1016/j.compfluid.2018.06.016
### https://doi.org/10.1016/0017-9310(74)90087-8

b = 0.01 # plate thickness
l = 0.2 # plate length

nxi = 24 # nx in the inlet/entrance region
nyf = 18 # ny in fluid
nxf = 24 # nx in the main fluid region
nys = 8 # ny in the solid domain

fx1_bias = 1.00 # bdry layer bias - fluid
fx2_bias = '${fparse 1.0/1.00}' # bdry layer bias - solid
fy_bias = 1.20 # bdry layer bias - fluid
sy_bias = '${fparse 1.0/1.05}' # bdry layer bias - solid

k_s = 0.2876
rho = 0.3525
mu = 3.95e-5
k = 0.06808
cp = 1142.6

vin = 12.0
Tin = 1000.0
T_s_bottom = 600.0
P_out = 1.03e5

h_s = 1.0
h_f = 1.0

advected_interp_method = 'upwind'

[Mesh]
  [fluid_channel]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${nxf}
    ny = ${nyf}
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = '${fparse 10.0*b}'
    subdomain_ids = '1'
    subdomain_name = 'fluid'
    bias_x = '${fx1_bias}'
    bias_y = '${fparse fy_bias}'
    boundary_name_prefix = 'fluid'
  []
  [solid_base]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${nxf}
    ny = ${nys}
    xmin = 0
    xmax = ${l}
    ymin = '${fparse -b}'
    ymax = 0
    subdomain_ids = '2'
    subdomain_name = 'solid'
    bias_x = ${fx1_bias}
    bias_y = '${fparse sy_bias}'
    boundary_id_offset = 10
    boundary_name_prefix = 'solid'
  []
  [entrance]
    type = GeneratedMeshGenerator
    dim = 2
    nx = '${fparse 2.0*nxi}'
    ny = ${nyf}
    xmin = '${fparse -2.0*l}'
    xmax = 0
    ymin = 0
    ymax = '${fparse 10.0*b}'
    subdomain_ids = '0'
    subdomain_name = 'entrance'
    bias_x = ${fx2_bias}
    bias_y = '${fparse fy_bias}'
    boundary_id_offset = 20
    boundary_name_prefix = 'ent'
  []
  [smg]
    type = StitchedMeshGenerator
    inputs = 'entrance fluid_channel solid_base'
    stitch_boundaries_pairs = 'ent_right fluid_left;
                              fluid_bottom solid_top'
    prevent_boundary_ids_overlap = false
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = 'smg'
    primary_block = 'fluid'
    paired_block = 'solid'
    new_boundary = interface
  []
  [symmetry_transform]
    type = SymmetryTransformGenerator
    input = interface
    mirror_point = '0 0 0'
    mirror_normal_vector = '0 1 0'
  []
  inactive = 'symmetry_transform'
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system solid_energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = '0 1'
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${vin}
    solver_sys = u_system
    block = '0 1'
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
    block = '0 1'
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${P_out}
    block = '0 1'
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${Tin}
    block = '0 1'
  []
  [T_solid]
    type = MooseLinearVariableFVReal
    solver_sys = solid_energy_system
    initial_condition = ${T_s_bottom}
    block = 2
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = false
  []

  [solid-conduction]
    type = LinearFVDiffusion
    variable = T_solid
    diffusion_coeff = ${k_s}
    use_nonorthogonal_correction = false
  []
[]

[LinearFVBCs]
  # velocity BCs
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_left'
    variable = vel_x
    functor = ${vin}
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_left'
    variable = vel_y
    functor = '0.000'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_bottom interface'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_bottom interface'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'fluid_right'
    variable = pressure
    functor = ${P_out}
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_right'
    variable = vel_y
    use_two_term_expansion = false
  []

  # freestream BCs for top of fluid domain
  [freestream_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_top ent_top'
    variable = vel_x
    use_two_term_expansion = false
  []
  [freestream_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_top ent_top'
    variable = vel_y
    use_two_term_expansion = false
  []
  [freestream_p]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'fluid_top ent_top'
    variable = pressure
    functor = 0
  []

  # temperature BCs
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    functor = ${Tin}
    boundary = 'ent_left'
  []
  [heated_wall_solid]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_solid
    functor = ${T_s_bottom}
    boundary = 'solid_bottom'
  []
  [insulated_fluid]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_fluid
    functor = 0
    boundary = 'ent_top ent_bottom fluid_top'
  []
  [insulated_solid]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_solid
    functor = 0
    boundary = 'solid_left solid_right'
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T_fluid
    use_two_term_expansion = false
    boundary = 'fluid_right'
  []

  [fluid_solid]
    type = LinearFVRobinCHTBC
    variable = T_fluid
    boundary = interface
    h = ${h_f}
    incoming_flux = heat_flux_to_fluid_interface
    surface_temperature = interface_temperature_solid_interface
    thermal_conductivity = ${k}
  []
  [solid_fluid]
    type = LinearFVRobinCHTBC
    variable = T_solid
    boundary = interface
    h = ${h_s}
    incoming_flux = heat_flux_to_solid_interface
    surface_temperature = interface_temperature_fluid_interface
    thermal_conductivity = ${k_s}
  []
[]

[FunctorMaterials]
  [rhocpT]
    property_name = 'rhocpT'
    type = ParsedFunctorMaterial
    functor_names = 'T_fluid'
    expression = '${rho}*${cp}*T_fluid'
  []
[]

[Postprocessors]
  [h_in]
    type = VolumetricFlowRate
    boundary = 'ent_left'
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    subtract_mesh_velocity = false
  []
  [h_out]
    type = VolumetricFlowRate
    boundary = 'fluid_right fluid_top ent_top interface'
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    advected_interp_method = upwind
    subtract_mesh_velocity = false
  []
[]

[VectorPostprocessors]
  [y_vs_ts]
    type = LineValueSampler
    variable = 'T_solid'
    start_point = '0.05 -1e-9 0' # making sure we are always in the domain
    end_point = '0.05 ${fparse -b+1e-9} 0'
    num_points = 8
    sort_by = id
    warn_discontinuous_face_values = false
  []
  [y_vs_tf]
    type = LineValueSampler
    variable = 'T_fluid'
    start_point = '0.05 1e-9 0' # making sure we are always in the domain
    end_point = '0.05 ${fparse b-1e-9} 0'
    num_points = 12
    sort_by = id
    warn_discontinuous_face_values = false
  []
[]

[Executioner]
  type = SIMPLE

  num_iterations = 1000

  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  rhie_chow_user_object = 'rc'
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  momentum_equation_relaxation = 0.9
  pressure_variable_relaxation = 0.3
  momentum_absolute_tolerance = 1e-7
  pressure_absolute_tolerance = 1e-7
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_system = 'energy_system'
  solid_energy_system = 'solid_energy_system'

  energy_l_abs_tol = 1e-10
  solid_energy_l_abs_tol = 1e-10
  energy_l_tol = 0
  solid_energy_l_tol = 0
  energy_equation_relaxation = 1.0
  energy_absolute_tolerance = 1e-7
  solid_energy_absolute_tolerance = 1e-7
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  solid_energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  solid_energy_petsc_options_value = 'hypre boomeramg'

  cht_interfaces = 'interface'
  cht_solid_flux_relaxation = 1.0
  cht_fluid_flux_relaxation = 1.0
  cht_solid_temperature_relaxation = 1.0
  cht_fluid_temperature_relaxation = 1.0
  max_cht_fpi = 2

  print_fields = false
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/ins/cht/conjugate_heat_transfer/cht_neu-dir.i)

### benchmark sources:
### https://doi.org/10.1016/j.compfluid.2018.06.016
### https://doi.org/10.1016/0017-9310(74)90087-8

b = 0.01 # plate thickness
l = 0.2 # plate length

nxi = 24 # nx in the inlet/entrance region
nyf = 18 # ny in fluid
nxf = 24 # nx in the main fluid region
nys = 8 # ny in the solid domain

fx1_bias = 1.00 # bdry layer bias - fluid
fx2_bias = '${fparse 1.0/1.00}' # bdry layer bias - solid
fy_bias = 1.20 # bdry layer bias - fluid
sy_bias = '${fparse 1.0/1.05}' # bdry layer bias - solid

k_s = 0.2876
rho = 0.3525
mu = 3.95e-5
k = 0.06808
cp = 1142.6

vin = 12.0
Tin = 1000.0
T_s_bottom = 600.0
P_out = 1.03e5

h_s = 0.0

advected_interp_method = 'upwind'

[Mesh]
  [fluid_channel]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${nxf}
    ny = ${nyf}
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = '${fparse 10.0*b}'
    subdomain_ids = '1'
    subdomain_name = 'fluid'
    bias_x = '${fx1_bias}'
    bias_y = '${fparse fy_bias}'
    boundary_name_prefix = 'fluid'
  []
  [solid_base]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${nxf}
    ny = ${nys}
    xmin = 0
    xmax = ${l}
    ymin = '${fparse -b}'
    ymax = 0
    subdomain_ids = '2'
    subdomain_name = 'solid'
    bias_x = ${fx1_bias}
    bias_y = '${fparse sy_bias}'
    boundary_id_offset = 10
    boundary_name_prefix = 'solid'
  []
  [entrance]
    type = GeneratedMeshGenerator
    dim = 2
    nx = '${fparse 2.0*nxi}'
    ny = ${nyf}
    xmin = '${fparse -2.0*l}'
    xmax = 0
    ymin = 0
    ymax = '${fparse 10.0*b}'
    subdomain_ids = '0'
    subdomain_name = 'entrance'
    bias_x = ${fx2_bias}
    bias_y = '${fparse fy_bias}'
    boundary_id_offset = 20
    boundary_name_prefix = 'ent'
  []
  [smg]
    type = StitchedMeshGenerator
    inputs = 'entrance fluid_channel solid_base'
    stitch_boundaries_pairs = 'ent_right fluid_left;
                              fluid_bottom solid_top'
    prevent_boundary_ids_overlap = false
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = 'smg'
    primary_block = 'fluid'
    paired_block = 'solid'
    new_boundary = interface
  []
  [symmetry_transform]
    type = SymmetryTransformGenerator
    input = interface
    mirror_point = '0 0 0'
    mirror_normal_vector = '0 1 0'
  []
  inactive = 'symmetry_transform'
[]

[Problem]
  linear_sys_names = 'u_system v_system pressure_system energy_system solid_energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    v = vel_y
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
    block = '0 1'
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${vin}
    solver_sys = u_system
    block = '0 1'
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    initial_condition = 0.0
    block = '0 1'
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${P_out}
    block = '0 1'
  []
  [T_fluid]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${Tin}
    block = '0 1'
  []
  [T_solid]
    type = MooseLinearVariableFVReal
    solver_sys = solid_energy_system
    initial_condition = ${T_s_bottom}
    block = 2
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method_name = ${advected_interp_method}
    mu = ${mu}
    u = vel_x
    v = vel_y
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [h_advection]
    type = LinearFVEnergyAdvection
    variable = T_fluid
    advected_quantity = temperature
    cp = ${cp}
    advected_interp_method = ${advected_interp_method}
    rhie_chow_user_object = 'rc'
  []
  [conduction]
    type = LinearFVDiffusion
    variable = T_fluid
    diffusion_coeff = ${k}
    use_nonorthogonal_correction = false
  []
  [solid-conduction]
    type = LinearFVDiffusion
    variable = T_solid
    diffusion_coeff = ${k_s}
    use_nonorthogonal_correction = false
  []
[]

[LinearFVBCs]
  # velocity BCs
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_left'
    variable = vel_x
    functor = ${vin}
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_left'
    variable = vel_y
    functor = '0.000'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_bottom interface'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'ent_bottom interface'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'fluid_right'
    variable = pressure
    functor = ${P_out}
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_right'
    variable = vel_y
    use_two_term_expansion = false
  []

  # freestream BCs for top of fluid domain
  [freestream_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_top ent_top'
    variable = vel_x
    use_two_term_expansion = false
  []
  [freestream_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'fluid_top ent_top'
    variable = vel_y
    use_two_term_expansion = false
  []
  [freestream_p]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'fluid_top ent_top'
    variable = pressure
    functor = 0
  []

  # temperature BCs
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_fluid
    functor = ${Tin}
    boundary = 'ent_left'
  []
  [heated_wall_solid]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T_solid
    functor = ${T_s_bottom}
    boundary = 'solid_bottom'
  []
  [insulated_fluid]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_fluid
    functor = 0
    boundary = 'ent_bottom ent_top fluid_top'
  []
  [insulated_solid]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    variable = T_solid
    functor = 0
    boundary = 'solid_left solid_right'
  []
  [outlet_T]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = T_fluid
    use_two_term_expansion = false
    boundary = 'fluid_right'
  []

  [fluid_solid]
    type = LinearFVDirichletCHTBC
    variable = T_fluid
    boundary = interface
    functor = interface_temperature_solid_interface
  []
  [solid_fluid]
    type = LinearFVRobinCHTBC
    variable = T_solid
    boundary = interface
    h = ${h_s}
    thermal_conductivity = ${k_s}
    incoming_flux = heat_flux_to_solid_interface
    surface_temperature = interface_temperature_fluid_interface
  []
[]

[FunctorMaterials]
  [rhocpT]
    property_name = 'rhocpT'
    type = ParsedFunctorMaterial
    functor_names = 'T_fluid'
    expression = '${rho}*${cp}*T_fluid'
  []
[]

[Postprocessors]
  [h_in]
    type = VolumetricFlowRate
    boundary = 'ent_left'
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    subtract_mesh_velocity = false
  []
  [h_out]
    type = VolumetricFlowRate
    boundary = 'fluid_right fluid_top ent_top interface'
    vel_x = vel_x
    vel_y = vel_y
    rhie_chow_user_object = rc
    advected_quantity = 'rhocpT'
    advected_interp_method = upwind
    subtract_mesh_velocity = false
  []
[]

[VectorPostprocessors]
  [y_vs_ts]
    type = LineValueSampler
    variable = 'T_solid'
    start_point = '0.05 -1e-9 0' # making sure we are always in the domain
    end_point = '0.05 ${fparse -b+1e-9} 0'
    num_points = 8
    sort_by = id
    warn_discontinuous_face_values = false
  []
  [y_vs_tf]
    type = LineValueSampler
    variable = 'T_fluid'
    start_point = '0.05 1e-9 0' # making sure we are always in the domain
    end_point = '0.05 ${fparse b-1e-9} 0'
    num_points = 12
    sort_by = id
    warn_discontinuous_face_values = false
  []
[]

[Executioner]
  type = SIMPLE

  num_iterations = 1000

  momentum_systems = 'u_system v_system'
  pressure_system = 'pressure_system'
  rhie_chow_user_object = 'rc'
  momentum_l_abs_tol = 1e-10
  pressure_l_abs_tol = 1e-10
  momentum_l_tol = 0
  pressure_l_tol = 0
  momentum_equation_relaxation = 0.9
  pressure_variable_relaxation = 0.3
  momentum_absolute_tolerance = 1e-7
  pressure_absolute_tolerance = 1e-7
  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'
  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_system = 'energy_system'
  solid_energy_system = 'solid_energy_system'
  energy_l_abs_tol = 1e-10
  solid_energy_l_abs_tol = 1e-10
  energy_l_tol = 0
  solid_energy_l_tol = 0
  energy_equation_relaxation = 1.0
  energy_absolute_tolerance = 1e-7
  solid_energy_absolute_tolerance = 1e-7
  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  solid_energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  solid_energy_petsc_options_value = 'hypre boomeramg'

  cht_interfaces = 'interface'
  cht_solid_flux_relaxation = 0.4
  cht_fluid_flux_relaxation = 0.4
  cht_solid_temperature_relaxation = 0.4
  cht_fluid_temperature_relaxation = 0.4
  max_cht_fpi = 3

  print_fields = false
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h.i)

L = 30
nx = 600
bulk_u = 0.01
q_source = 50000.
A_cp = 976.78
B_cp = 1.0634
T_in = 860.
p_ref = 101325.0
rho = 2000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

[Problem]
  linear_sys_names = 'u_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*1900.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = 860.
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u} #${bulk_u} #'fully_developed_velocity'
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = ${q_source}
  []
  [T_analytical]
    type = ParsedFunction
    expression = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    h_from_p_T_functor = h_from_p_T_functor
    T_from_p_h_functor = T_from_p_h_functor
  []
  [h_from_p_T_functor]
    type = ParsedFunctorMaterial
    property_name = 'h_from_p_T_functor'
    functor_names = 'T'
    expression = '${A_cp}*T+${B_cp}/2*(T^2)'
  []
  [T_from_p_h_functor]
    type = ParsedFunctorMaterial
    property_name = 'T_from_p_h_functor'
    functor_names = 'h'
    expression = '(-${A_cp}+sqrt(${A_cp}^2+2*h*${B_cp}))/${B_cp}'
  []
  [rho]
    type = ADParsedFunctorMaterial
    property_name = 'rho'
    functor_names = 'T'
    expression = ${rho}
  []
  [cp]
    type = ADParsedFunctorMaterial
    property_name = 'cp'
    functor_names = 'T'
    expression = '${A_cp}+${B_cp}*T'
  []
  [mu]
    type = ADParsedFunctorMaterial
    property_name = 'mu'
    functor_names = 'T'
    expression = '4.5e-3'
  []
  [k]
    type = ADParsedFunctorMaterial
    property_name = 'k'
    functor_names = 'T'
    expression = 0.7
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
  [T_out_analytic]
    type = FunctionValuePostprocessor
    function = T_analytical
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

(modules/navier_stokes/test/tests/finite_volume/wcns/enthalpy_equation/1d_test_h_fp.i)

L = 30
nx = 600
bulk_u = 0.01
p_ref = 101325.0
T_in = 860.
q_source = 20000.
advected_interp_method = 'upwind'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = ${L}
    nx = ${nx}
  []
  allow_renumbering = false
[]

[GlobalParams]
  rhie_chow_user_object = 'rc'
  advected_interp_method = ${advected_interp_method}
  u = vel_x
[]

[Problem]
  linear_sys_names = 'u_system pressure_system energy_system'
  previous_nl_solution_required = true
[]

[UserObjects]
  [rc]
    type = RhieChowMassFlux
    u = vel_x
    pressure = pressure
    rho = 'rho'
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    solver_sys = u_system
    initial_condition = ${bulk_u}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    initial_condition = ${p_ref}
  []
  [h]
    type = MooseLinearVariableFVReal
    solver_sys = energy_system
    initial_condition = ${fparse 860.*240.}
  []
[]

[AuxVariables]
  [rho_var]
    type = MooseLinearVariableFVReal
  []
  [cp_var]
    type = MooseLinearVariableFVReal
  []
  [mu_var]
    type = MooseLinearVariableFVReal
  []
  [k_var]
    type = MooseLinearVariableFVReal
  []
  [T]
    type = MooseLinearVariableFVReal
    initial_condition = ${T_in}
  []
  [h_aux]
    type = MooseLinearVariableFVReal
  []
[]

[FVInterpolationMethods]
  [upwind]
    type = FVAdvectedUpwind
  []
[]

[LinearFVKernels]

  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method_name = ${advected_interp_method}
    mu = 'mu'
    momentum_component = 'x'
    use_nonorthogonal_correction = false
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [p_diffusion]
    type = LinearFVPressureCorrectionDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [temp_advection]
    type = LinearFVEnergyAdvection
    variable = h
  []
  [source]
    type = LinearFVSource
    variable = h
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inlet_u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = ${bulk_u}
  []
  [inlet_h]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = h
    boundary = 'left'
    functor = 'h_from_p_T'
  []
  [inlet_T]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = T
    boundary = 'left'
    functor = ${T_in}
  []

  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = ${p_ref}
  []
  [outlet_h]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = h
    use_two_term_expansion = false
    boundary = 'right'
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = 'right'
  []
[]

[FluidProperties]
  [lead]
    type = LeadFluidProperties
  []
[]

[FunctorMaterials]
  [enthalpy_material]
    type = LinearFVEnthalpyFunctorMaterial
    pressure = ${p_ref}
    T_fluid = T
    h = h
    fp = lead
  []
  [fluid_props_to_mat_props]
    type = GeneralFunctorFluidProps
    fp = lead
    pressure = ${p_ref}
    T_fluid = 'T'
    speed = 1
    porosity = 1
    characteristic_length = 1
  []
  [source_func]
    type = ADParsedFunctorMaterial
    property_name = source_func
    functor_names = 'rho'
    expression = ${q_source}
  []
[]

[AuxKernels]
  [rho_out]
    type = FunctorAux
    functor = 'rho'
    variable = 'rho_var'
    execute_on = 'NONLINEAR'
  []
  [cp_out]
    type = FunctorAux
    functor = 'cp'
    variable = 'cp_var'
    execute_on = 'NONLINEAR'
  []
  [mu_out]
    type = FunctorAux
    functor = 'mu'
    variable = 'mu_var'
    execute_on = 'NONLINEAR'
  []
  [k_out]
    type = FunctorAux
    functor = 'k'
    variable = 'k_var'
    execute_on = 'NONLINEAR'
  []
  [T_from_h_functor_aux]
    type = FunctorAux
    functor = 'T_from_p_h'
    variable = 'T'
    execute_on = 'NONLINEAR'
  []
  [h_from_T_functor_aux]
    type = FunctorAux
    functor = 'h_from_p_T'
    variable = 'h_aux'
    execute_on = 'NONLINEAR'
  []
[]

[Postprocessors]
  [T_out_sim]
    type = ElementalVariableValue
    variable = T
    elementid = ${fparse nx-1}
  []
[]

[Executioner]
  type = SIMPLE
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  energy_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  energy_l_tol = 0
  rhie_chow_user_object = 'rc'
  momentum_systems = 'u_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  momentum_equation_relaxation = 0.7
  pressure_variable_relaxation = 0.3
  energy_equation_relaxation = 0.95
  num_iterations = 100
  pressure_absolute_tolerance = 1e-8
  momentum_absolute_tolerance = 1e-8
  energy_absolute_tolerance = 1e-6
  print_fields = false
  momentum_l_max_its = 200

  momentum_petsc_options_iname = '-pc_type -pc_hypre_type'
  momentum_petsc_options_value = 'hypre boomeramg'

  pressure_petsc_options_iname = '-pc_type -pc_hypre_type'
  pressure_petsc_options_value = 'hypre boomeramg'

  energy_petsc_options_iname = '-pc_type -pc_hypre_type'
  energy_petsc_options_value = 'hypre boomeramg'
  continue_on_max_its = true
[]

[Outputs]
  [out]
    type = CSV
  []
[]

Selecting Interpolation
Input Parameters
Input Files