INSFVPressureVariable

INSFVPressureVariable is a finite volume variable that toggles the two_term_boundary_expansion to true by default. This is the parameter that determines whether extrapolated boundary face values are determined from both the boundary cell centroid value and boundary cell centroid gradient or just the boundary cell centroid value.

Input Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of blocks (ids or names) that this object will be applied
components1Number of components for an array variable
Default:1
C++ Type:unsigned int
Options:
Description:Number of components for an array variable
familyMONOMIALSpecifies the family of FE shape functions to use for this variable.
Default:MONOMIAL
C++ Type:MooseEnum
Options:LAGRANGE, MONOMIAL, HERMITE, SCALAR, HIERARCHIC, CLOUGH, XYZ, SZABAB, BERNSTEIN, L2_LAGRANGE, L2_HIERARCHIC, NEDELEC_ONE, LAGRANGE_VEC, MONOMIAL_VEC
Description:Specifies the family of FE shape functions to use for this variable.
fvTrueTrue to make this variable a finite volume variable
Default:True
C++ Type:bool
Options:
Description:True to make this variable a finite volume variable
orderCONSTANTOrder of the FE shape function to use for this variable (additional orders not listed here are allowed, depending on the family).
Default:CONSTANT
C++ Type:MooseEnum
Options:CONSTANT, FIRST, SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, EIGHTH, NINTH, TENTH, ELEVENTH, TWELFTH, THIRTEENTH, FOURTEENTH, FIFTEENTH, SIXTEENTH, SEVENTEENTH, EIGHTTEENTH, NINETEENTH, TWENTIETH, TWENTYFIRST, TWENTYSECOND, TWENTYTHIRD, TWENTYFOURTH, TWENTYFIFTH, TWENTYSIXTH, TWENTYSEVENTH, TWENTYEIGHTH, TWENTYNINTH, THIRTIETH, THIRTYFIRST, THIRTYSECOND, THIRTYTHIRD, THIRTYFOURTH, THIRTYFIFTH, THIRTYSIXTH, THIRTYSEVENTH, THIRTYEIGHTH, THIRTYNINTH, FORTIETH, FORTYFIRST, FORTYSECOND, FORTYTHIRD
Description:Order of the FE shape function to use for this variable (additional orders not listed here are allowed, depending on the family).
two_term_boundary_expansionFalseWhether to use a two-term Taylor expansion to calculate boundary face values. The default is to use one-term, e.g. the element centroid value will be used for the boundary face value. If the two-term expansion is used, then the boundary face value depends on the adjoining cell center gradient, which itself depends on the boundary face value. Consequently an implicit solve is used to simultaneously solve for the adjoining cell center gradient and boundary face value(s).
Default:False
C++ Type:bool
Options:
Description:Whether to use a two-term Taylor expansion to calculate boundary face values. The default is to use one-term, e.g. the element centroid value will be used for the boundary face value. If the two-term expansion is used, then the boundary face value depends on the adjoining cell center gradient, which itself depends on the boundary face value. Consequently an implicit solve is used to simultaneously solve for the adjoining cell center gradient and boundary face value(s).
use_dualFalseTrue to use dual basis for Lagrange multipliers
Default:False
C++ Type:bool
Options:
Description:True to use dual basis for Lagrange multipliers
use_extended_stencilFalseWhether to use an extended stencil for gradient computation.
Default:False
C++ Type:bool
Options:
Description:Whether to use an extended stencil for gradient computation.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
eigenFalseTrue to make this variable an eigen variable
Default:False
C++ Type:bool
Options:
Description:True to make this variable an eigen variable
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
scalingSpecifies a scaling factor to apply to this variable
C++ Type:std::vector<double>
Options:
Description:Specifies a scaling factor to apply to this variable

Advanced Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-scalar-transport.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/cylindrical/diverging.i)
(modules/navier_stokes/test/tests/finite_volume/fvbcs/wall_function/Re_t395.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/porosity_jump/2d-rc-epsjump.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-ambient-convection.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/2d-average.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/2d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-no-slip-outflow-bcs.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-boussinesq.i)
(modules/navier_stokes/test/tests/finite_volume/ins/wall_distance_capped_mixing_length_aux/capped_mixing_length.i)
(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/lid-driven.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/2d-rc-friction.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/2d-average-with-temp.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mixing_length_total_viscosity_material/mixing_length_total_viscosity.i)
(modules/navier_stokes/test/tests/finite_volume/fviks/convection/convection_cavity.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/cylindrical/2d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/pins/mms/porosity_change/2d-rc-continuous.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/cylindrical/2d-average-no-slip.i)
(modules/navier_stokes/test/tests/finite_volume/ins/boussinesq/boussinesq.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/2d-average.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/2d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/rc.i)
(modules/navier_stokes/test/tests/postprocessors/conservation_INSFV.i)
(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/lid-driven-with-energy.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/2d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/3d-rc-no-slip.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/plane-poiseuille-flow.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/rotated/rotated-pp-flow.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/1d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/pins/mms/2d-rc.i)
(modules/navier_stokes/examples/pipe_mixing_length/pipe_mixing_length.i)
(modules/navier_stokes/test/tests/finite_volume/fviks/convection/convection_channel.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/2d-average-with-temp.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-no-slip-extrapolated-outlet-pressure.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-no-slip.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/porosity_jump/1d-rc-epsjump.i)
(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/transient-lid-driven-with-energy.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/1d-average.i)
(modules/navier_stokes/test/tests/finite_volume/pins/mms/porosity_change/1d-rc-continuous.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-friction.i)
(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-effective.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/cylindrical/2d-rc-slip.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-mixing-length.i)
(modules/navier_stokes/test/tests/finite_volume/ins/block_restriction/2d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/3d-rc.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mixing_length_eddy_viscosity_aux/mixing_length_eddy_viscosity.i)
(modules/navier_stokes/test/tests/postprocessors/conservation_PINSFV.i)
(modules/navier_stokes/test/tests/finite_volume/pins/mms/1d-rc.i)

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

mu=1
rho=1
k=1e-3
diff=1e-3
cp=1
advected_interp_method='average'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [temperature]
    type = INSFVEnergyVariable
  []
  [scalar]
    type = INSFVScalarFieldVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [energy_advection]
    type = INSFVEnergyAdvection
    variable = temperature
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [energy_diffusion]
    type = FVDiffusion
    coeff = ${k}
    variable = temperature
  []

  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [scalar_diffusion]
    type = FVDiffusion
    coeff = ${diff}
    variable = scalar
  []
  [scalar_src]
    type = FVBodyForce
    variable = scalar
    value = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0
  []
  [inlet_t]
    type = FVDirichletBC
    boundary = 'left'
    variable = temperature
    value = 1
  []
  [inlet_scalar]
    type = FVDirichletBC
    boundary = 'left'
    variable = scalar
    value = 1
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'cp'
    prop_values = '${cp}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
    temperature = 'temperature'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/cylindrical/diverging.i)

mu=1
rho=1
advected_interp_method='average'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  file = diverging.msh
  uniform_refine = 2
[]

[Problem]
  fv_bcs_integrity_check = true
  coord_type = 'RZ'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    # we can think of the axis as a slip wall boundary, no normal velocity and no viscous shear
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  active = 'inlet-u inlet-v free-slip-wall-u free-slip-wall-v outlet-p axis-u axis-v'

  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 0
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 1
  []
  [free-slip-wall-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = u
  []
  [free-slip-wall-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = v
  []
  [no-slip-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 0
  []
  [no-slip-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 0
  []
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 0
  []
  [axis-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [axis-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options = '-options_left'
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'asm      lu           NONZERO                   200'
  line_search = 'none'
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [in]
    type = SideIntegralVariablePostprocessor
    variable = v
    boundary = 'bottom'
  []
  [out]
    type = SideIntegralVariablePostprocessor
    variable = v
    boundary = 'top'
  []
  [num_lin]
    type = NumLinearIterations
    outputs = 'console'
  []
  [num_nl]
    type = NumNonlinearIterations
    outputs = 'console'
  []
  [cum_lin]
    type = CumulativeValuePostprocessor
    outputs = 'console'
    postprocessor = 'num_lin'
  []
  [cum_nl]
    type = CumulativeValuePostprocessor
    outputs = 'console'
    postprocessor = 'num_nl'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/fvbcs/wall_function/Re_t395.i)

von_karman_const = 0.41

H = 1 #halfwidth of the channel
L = 150

Re = 13700

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

advected_interp_method='upwind'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${L}'
    dy = '0.667 0.333'
    ix = '200'
    iy = '10  1'
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [mixing_len]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_shear_stress]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_yplus]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = u
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'x'
    u = u
    v = v
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    p = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = v
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'y'
    u = u
    v = v
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    p = pressure
  []
[]

[AuxKernels]
  [mixing_len]
    type = WallDistanceMixingLengthAux
    walls = 'top'
    variable = mixing_len
    execute_on = 'initial'
    von_karman_const = ${von_karman_const}
  []
  [wall_shear_stress]
    type = WallFunctionWallShearStressAux
    variable = wall_shear_stress
    walls = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [wall_yplus]
    type = WallFunctionYPlusAux
    variable = wall_yplus
    walls = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [wall-u]
    type = INSFVWallFunctionBC
    variable = u
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = x
  []
  [wall-v]
    type = INSFVWallFunctionBC
    variable = v
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = y
  []
  [sym-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [sym-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [symmetry_pressure]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  [restart_out]        # creates input_other.e
   type = Exodus
  []
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/porosity_jump/2d-rc-epsjump.i)

mu=1.1
rho=1.1
advected_interp_method='upwind'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1'
    dy = '0.5'
    ix = '30 30'
    iy = '20'
    subdomain_id = '1 2'
  []
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

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

[ICs]
  inactive = 'porosity_continuous'
  [porosity_1]
    type = ConstantIC
    variable = porosity
    block = 1
    value = 1
  []
  [porosity_2]
    type = ConstantIC
    variable = porosity
    block = 2
    value = 0.5
  []
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    block = '1 2'
    function = smooth_jump
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1)))'
  []
[]

[FVKernels]
  inactive = 'u_advection_porosity_gradient v_advection_porosity_gradient'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity

    momentum_component = 'x'
    vel = 'velocity'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
  [u_advection_porosity_gradient]
    type = PINSFVMomentumAdvectionPorosityGradient
    variable = u
    u = u
    v = v
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity

    momentum_component = 'y'
    vel = 'velocity'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    pressure = pressure
    porosity = porosity
    momentum_component = 'y'
  []
  [v_advection_porosity_gradient]
    type = PINSFVMomentumAdvectionPorosityGradient
    variable = v
    u = u
    v = v
    rho = ${rho}
    porosity = porosity
    momentum_component = 'y'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []

  [walls-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = u
  []
  [walls-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = v
  []

  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0.4
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

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

mu=1
rho=1
k=1e-3
cp=1
advected_interp_method='average'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 5
    ymin = -1
    ymax = 1
    nx = 50
    ny = 16
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [temperature]
    type = INSFVEnergyVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [energy_advection]
    type = INSFVEnergyAdvection
    variable = temperature
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [energy_diffusion]
    type = FVDiffusion
    coeff = ${k}
    variable = temperature
  []
  [ambient_convection]
    type = NSFVEnergyAmbientConvection
    variable = temperature
    T_ambient = 100
    alpha = 'alpha'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0
  []
  [inlet_t]
    type = FVDirichletBC
    boundary = 'left'
    variable = temperature
    value = 1
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'cp alpha'
    prop_values = '${cp} 1'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
    temperature = 'temperature'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/2d-average.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='average'

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = false
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 'exact_v'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin((1/2)*y*pi)*cos((1/2)*x*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin((1/2)*y*pi)*cos((1/2)*x*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '(1/2)*pi^2*mu*sin((1/2)*y*pi)*cos((1/2)*x*pi) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) + (1/2)*pi*rho*sin((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)^2 - pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) - 1/4*pi*sin((1/4)*x*pi)*sin((3/2)*y*pi)'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = 'sin((1/4)*x*pi)*cos((1/2)*y*pi)'
[]
[exact_rhov]
  type = ParsedFunction
  value = 'rho*sin((1/4)*x*pi)*cos((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = '(5/16)*pi^2*mu*sin((1/4)*x*pi)*cos((1/2)*y*pi) - pi*rho*sin((1/4)*x*pi)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*y*pi) + (1/4)*pi*rho*sin((1/2)*y*pi)*cos((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi) + (3/2)*pi*cos((1/4)*x*pi)*cos((3/2)*y*pi)'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'sin((3/2)*y*pi)*cos((1/4)*x*pi)'
[]
[forcing_p]
  type = ParsedFunction
  value = '-1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi) - 1/2*pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

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

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 'exact_v'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    value = 'sin((1/2)*y*pi)*cos((1/2)*x*pi)'
  []
  [exact_rhou]
    type = ParsedFunction
    value = 'rho*sin((1/2)*y*pi)*cos((1/2)*x*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
  [forcing_u]
    type = ParsedFunction
    value = '(1/2)*pi^2*mu*sin((1/2)*y*pi)*cos((1/2)*x*pi) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) + (1/2)*pi*rho*sin((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)^2 - pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) - 1/4*pi*sin((1/4)*x*pi)*sin((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    value = 'sin((1/4)*x*pi)*cos((1/2)*y*pi)'
  []
  [exact_rhov]
    type = ParsedFunction
    value = 'rho*sin((1/4)*x*pi)*cos((1/2)*y*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
  [forcing_v]
    type = ParsedFunction
    value = '(5/16)*pi^2*mu*sin((1/4)*x*pi)*cos((1/2)*y*pi) - pi*rho*sin((1/4)*x*pi)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*y*pi) + (1/4)*pi*rho*sin((1/2)*y*pi)*cos((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi) + (3/2)*pi*cos((1/4)*x*pi)*cos((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin((3/2)*y*pi)*cos((1/4)*x*pi)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi) - 1/2*pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-no-slip-outflow-bcs.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 0
  []
  [outlet_u]
    type = INSFVMomentumAdvectionOutflowBC
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    u = u
    v = v
    boundary = 'right'
  []
  [outlet_v]
    type = INSFVMomentumAdvectionOutflowBC
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    u = u
    v = v
    boundary = 'right'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-boussinesq.i)

mu=1
rho=1
k=1e-3
cp=1
v_inlet=1
T_inlet=200
advected_interp_method='average'
velocity_interp_method='rc'

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

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${v_inlet}
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [temperature]
    type = INSFVEnergyVariable
  []
[]

[AuxVariables]
  [temp_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
    initial_condition = 100
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.4
  []
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []
  [u_gravity]
    type = PINSFVMomentumGravity
    variable = u
    rho = ${rho}
    gravity = '0 -9.81 0'
    momentum_component = 'x'
    porosity = porosity
  []
  [u_boussinesq]
    type = PINSFVMomentumBoussinesq
    variable = u
    temperature = 'temperature'
    rho = ${rho}
    ref_temperature = 150
    gravity = '0 -9.81 0'
    momentum_component = 'x'
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []
  [v_gravity]
    type = PINSFVMomentumGravity
    variable = v
    rho = ${rho}
    gravity = '-0 -9.81 0'
    momentum_component = 'y'
    porosity = porosity
  []
  [v_boussinesq]
    type = PINSFVMomentumBoussinesq
    variable = v
    temperature = 'temperature'
    rho = ${rho}
    ref_temperature = 150
    gravity = '0 -9.81 0'
    momentum_component = 'y'
    porosity = porosity
  []

  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = temperature
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    k = ${k}
    variable = temperature
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = temperature
    is_solid = false
    temp_fluid = temperature
    temp_solid = temp_solid
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 0
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = ${v_inlet}
  []
  [inlet-T]
    type = FVNeumannBC
    variable = temperature
    value = ${fparse v_inlet * rho * cp * T_inlet}
    boundary = 'bottom'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 0
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'x'
    porosity = porosity
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'y'
    porosity = porosity
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 0
  []
[]

[Materials]
  [constants]
    type = ADGenericConstantMaterial
    prop_names = 'cp h_cv alpha'
    prop_values = '${cp} 1e-3 8e-4'
  []

  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
    temperature = 'temperature'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'top'
  []
  [outlet-v]
    type = SideAverageValue
    variable = v
    boundary = 'top'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = temperature
    boundary = 'top'
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/ins/wall_distance_capped_mixing_length_aux/capped_mixing_length.i)

von_karman_const = 0.41

H = 1 #halfwidth of the channel
L = 150

Re = 13700

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

advected_interp_method='upwind'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${L}'
    dy = '0.667 0.333'
    ix = '200'
    iy = '10  1'
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [mixing_len]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_shear_stress]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_yplus]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = u
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'x'
    u = u
    v = v
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    p = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = v
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'y'
    u = u
    v = v
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    p = pressure
  []
[]

[AuxKernels]
  [mixing_len]
    type = WallDistanceMixingLengthAux
    walls = 'top'
    variable = mixing_len
    execute_on = 'initial'
    von_karman_const = ${von_karman_const}
    delta = 0.5
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [wall-u]
    type = INSFVWallFunctionBC
    variable = u
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = x
  []
  [wall-v]
    type = INSFVWallFunctionBC
    variable = v
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = y
  []
  [sym-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [sym-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [symmetry_pressure]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

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

mu=.01
rho=1

[GlobalParams]
  vel = 'velocity'
  velocity_interp_method = 'rc'
  advected_interp_method = 'average'
  two_term_boundary_expansion = true
[]

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

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

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

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = u
    y = v
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []

  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []

  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top'
    function = 1
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'left right bottom'
    function = 0
  []

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

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

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

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/2d-rc-friction.i)

mu=1.1
rho=1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 5
    ymin = 0
    ymax = 1
    nx = 40
    ny = 20
  []
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  inactive = 'lambda'
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.5
  []
[]

[FVKernels]
  inactive = 'mean-pressure'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []
  [u_friction]
    type = PNSFVMomentumFriction
    variable = u
    momentum_component = 'x'
    porosity = porosity
    Darcy_name = 'Darcy_coefficient'
    Forchheimer_name = 'Forchheimer_coefficient'
    rho = ${rho}
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []
  [v_friction]
    type = PNSFVMomentumFriction
    variable = v
    momentum_component = 'y'
    porosity = porosity
    Darcy_name = 'Darcy_coefficient'
    Forchheimer_name = 'Forchheimer_coefficient'
    rho = ${rho}
  []

  [mean-pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
    phi0 = 0.01
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = u
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = v
    function = 0
  []
  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'x'
    porosity = porosity
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'y'
    porosity = porosity
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
  [darcy]
    type = ADGenericConstantVectorMaterial
    prop_names = 'Darcy_coefficient Forchheimer_coefficient'
    prop_values = '0.1 0.1 0.1 0.1 0.1 0.1'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-14
[]

# Some basic Postprocessors to visually examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/2d-average-with-temp.i)

mu=1.1
rho=1.1
k=1.1
cp=1.1
advected_interp_method='average'
velocity_interp_method='average'
velocity='velocity'

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = false
  []
  [temperature]
    type = INSFVEnergyVariable
    two_term_boundary_expansion = false
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = ${velocity}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = ${velocity}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = ${velocity}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []

  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = temperature
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    vel = ${velocity}
    variable = temperature
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [temp_forcing]
    type = FVBodyForce
    variable = temperature
    function = forcing_t
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 'exact_v'
  []
  [inlet-and-walls-t]
    type = FVFunctionDirichletBC
    boundary = 'left top bottom'
    variable = temperature
    function = 'exact_t'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'k cp'
    prop_values = '${k} ${cp}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'temperature'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin((1/2)*y*pi)*cos((1/2)*x*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin((1/2)*y*pi)*cos((1/2)*x*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '(1/2)*pi^2*mu*sin((1/2)*y*pi)*cos((1/2)*x*pi) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) + (1/2)*pi*rho*sin((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)^2 - pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) - 1/4*pi*sin((1/4)*x*pi)*sin((3/2)*y*pi)'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = 'sin((1/4)*x*pi)*cos((1/2)*y*pi)'
[]
[exact_rhov]
  type = ParsedFunction
  value = 'rho*sin((1/4)*x*pi)*cos((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = '(5/16)*pi^2*mu*sin((1/4)*x*pi)*cos((1/2)*y*pi) - pi*rho*sin((1/4)*x*pi)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*y*pi) + (1/4)*pi*rho*sin((1/2)*y*pi)*cos((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi) + (3/2)*pi*cos((1/4)*x*pi)*cos((3/2)*y*pi)'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'sin((3/2)*y*pi)*cos((1/4)*x*pi)'
[]
[forcing_p]
  type = ParsedFunction
  value = '-1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi) - 1/2*pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[exact_t]
  type = ParsedFunction
  value = 'sin((1/4)*x*pi)*cos((1/2)*y*pi)'
[]
[forcing_t]
  type = ParsedFunction
  value = '-pi*cp*rho*sin((1/4)*x*pi)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) - 1/2*pi*cp*rho*sin((1/4)*x*pi)*sin((1/2)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*y*pi) + (1/4)*pi*cp*rho*sin((1/2)*y*pi)*cos((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi) + (5/16)*pi^2*k*sin((1/4)*x*pi)*cos((1/2)*y*pi)'
  vars = 'k rho cp'
  vals = '${k} ${rho} ${cp}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2t]
    variable = temperature
    function = exact_t
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mixing_length_total_viscosity_material/mixing_length_total_viscosity.i)

von_karman_const = 0.41

H = 1 #halfwidth of the channel
L = 150

Re = 13700

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

advected_interp_method='upwind'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${L}'
    dy = '0.667 0.333'
    ix = '200'
    iy = '10  1'
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [mixing_len]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_shear_stress]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_yplus]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = u
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'x'
    u = u
    v = v
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    p = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = v
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'y'
    u = u
    v = v
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    p = pressure
  []
[]

[AuxKernels]
  [mixing_len]
    type = WallDistanceMixingLengthAux
    walls = 'top'
    variable = mixing_len
    execute_on = 'initial'
    von_karman_const = ${von_karman_const}
    delta = 0.5
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [wall-u]
    type = INSFVWallFunctionBC
    variable = u
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = x
  []
  [wall-v]
    type = INSFVWallFunctionBC
    variable = v
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = y
  []
  [sym-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = total_viscosity
    momentum_component = x
  []
  [sym-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = total_viscosity
    momentum_component = y
  []
  [symmetry_pressure]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
  [total_viscosity]
    type = MixingLengthTurbulentViscosityMaterial
    u = 'u'                             #computes total viscosity = mu_t + mu
    v = 'v'                             #property is called total_viscosity
    mixing_length = mixing_len
    mu = ${mu}
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/fviks/convection/convection_cavity.i)

mu = 1
rho = 1
k = .01
cp = 1
vel = 'velocity'
velocity_interp_method = 'rc'
advected_interp_method = 'average'

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 0.5'
    dy = '1'
    ix = '8 5'
    iy = '8'
    subdomain_id = '0 1'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = 'cmg'
    primary_block = 0
    paired_block = 1
    new_boundary = 'interface'
  []
  [secondary_interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = 'interface'
    primary_block = 1
    paired_block = 0
    new_boundary = 'secondary_interface'
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    block = 0
  []
  [v]
    type = INSFVVelocityVariable
    block = 0
  []
  [pressure]
    type = INSFVPressureVariable
    block = 0
  []
  [T]
    type = INSFVEnergyVariable
    block = 0
  []
  [Ts]
    type = INSFVEnergyVariable
    block = 1
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[ICs]
  [T]
    type = ConstantIC
    variable = T
    value = 1
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    vel = ${vel}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    u = u
    v = v
    pressure = pressure
    mu = ${mu}
    rho = ${rho}
    block = 0
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
    block = 0
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    block = 0
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
    block = 0
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
    block = 0
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    block = 0
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
    block = 0
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
    block = 0
  []

  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
    block = 0
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    block = 0
  []

  [solid_temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = Ts
    block = 1
  []
[]

[FVInterfaceKernels]
  [convection]
    type = FVConvectionCorrelationInterface
    variable1 = T
    variable2 = Ts
    boundary = 'interface'
    h = 5
    temp_solid = Ts
    temp_fluid = T
    subdomain1 = 0
    subdomain2 = 1
    bulk_distance = 0.3
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top'
    function = 'lid_function'
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'left interface bottom'
    function = 0
  []

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

  [T_hot]
    type = FVDirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  []

  [T_cold]
    type = FVDirichletBC
    variable = Ts
    boundary = 'right'
    value = 0
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'k cp'
    prop_values = '${k} ${cp}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'T'
    rho = ${rho}
    block = 0
  []
[]

[Functions]
  [lid_function]
    type = ParsedFunction
    value = '4*x*(1-x)'
  []
[]


[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'asm      lu           NONZERO                   200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
  l_max_its = 200
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/cylindrical/2d-rc.i)

mu=1.1
rho=1.1

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

[Problem]
  coord_type = 'RZ'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = 'average'
    velocity_interp_method = 'rc'
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = 'average'
    velocity_interp_method = 'rc'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = 'average'
    velocity_interp_method = 'rc'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [no-slip-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'left right top bottom'
    variable = u
    function = 'exact_u'
  []

  [no-slip-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'left right top bottom'
    variable = v
    function = 'exact_v'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = u
    v = v
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin(y)*sin(x*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin(y)*sin(x*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = 'mu*sin(y)*sin(x*pi) - (-x*pi^2*mu*sin(y)*sin(x*pi) + pi*mu*sin(y)*cos(x*pi))/x + (2*x*pi*rho*sin(y)^2*sin(x*pi)*cos(x*pi) + rho*sin(y)^2*sin(x*pi)^2)/x + (-1/2*x*pi*rho*sin(x)*sin(y)*sin(x*pi)*sin((1/2)*y*pi) + x*rho*sin(x)*sin(x*pi)*cos(y)*cos((1/2)*y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = 'sin(x)*cos((1/2)*y*pi)'
[]
[exact_rhov]
  type = ParsedFunction
  value = 'rho*sin(x)*cos((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = '(1/4)*pi^2*mu*sin(x)*cos((1/2)*y*pi) - pi*rho*sin(x)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) + cos(y) - (-x*mu*sin(x)*cos((1/2)*y*pi) + mu*cos(x)*cos((1/2)*y*pi))/x + (x*pi*rho*sin(x)*sin(y)*cos(x*pi)*cos((1/2)*y*pi) + x*rho*sin(y)*sin(x*pi)*cos(x)*cos((1/2)*y*pi) + rho*sin(x)*sin(y)*sin(x*pi)*cos((1/2)*y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'sin(y)'
[]
[forcing_p]
  type = ParsedFunction
  value = '-1/2*pi*rho*sin(x)*sin((1/2)*y*pi) + (x*pi*rho*sin(y)*cos(x*pi) + rho*sin(y)*sin(x*pi))/x'
  vars = 'rho'
  vals = '${rho}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      30                 lu           NONZERO'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/pins/mms/porosity_change/2d-rc-continuous.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = -1
    ymax = 1
    nx = 8
    ny = 8
  []
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

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

[ICs]
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    function = smooth_jump
  []
[]

[GlobalParams]
  porosity = porosity
[]

[FVKernels]
  inactive = 'u_pressure_porosity u_pressure_porosity_gradient
              v_pressure_porosity v_pressure_porosity_gradient'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    smooth_porosity = true
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    smooth_porosity = true
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
    smooth_porosity = false
    vel = 'velocity'
    momentum_component = 'x'
  []
  # Option 1: eps * pressure gradient
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []

  # Option 2: gradient (eps * pressure) - P * gradient(eps)
  [u_pressure_porosity]
    type = PINSFVMomentumPressureFlux
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure_porosity_gradient]
    type = PINSFVMomentumPressurePorosityGradient
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    smooth_porosity = true
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
    smooth_porosity = false
    vel = 'velocity'
    momentum_component = 'y'
  []
  # Option 1: eps * pressure gradient
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    pressure = pressure
    porosity = porosity
    momentum_component = 'y'
  []

  # Option 2: gradient (eps * pressure) - P * gradient(eps)
  [v_pressure_porosity]
    type = PINSFVMomentumPressureFlux
    variable = v
    pressure = pressure
    porosity = porosity
    momentum_component = 'y'
  []
  [v_pressure_porosity_gradient]
    type = PINSFVMomentumPressurePorosityGradient
    variable = v
    pressure = pressure
    porosity = porosity
    momentum_component = 'y'
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 'exact_v'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1))) - 0.01 * y'
  []

  # Output from compute-functions-2d.py
  [exact_u]
    type = ParsedFunction
    value = 'sin((1/2)*y*pi)*cos((1/2)*x*pi)'
  []
  [forcing_u]
    type = ParsedFunction
    value = '(1/2)*pi^2*mu*sin((1/2)*y*pi)*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - 0.005*pi*mu*cos((1/2)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 + 7.5*pi*mu*exp(30 - 30*x)*sin((1/2)*x*pi)*sin((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + (1/2)*pi*rho*sin((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)^2/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.01*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 + 15.0*rho*exp(30 - 30*x)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi)^2/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) - 1/4*pi*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*sin((1/4)*x*pi)*sin((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    value = 'sin((1/4)*x*pi)*cos((1/2)*y*pi)'
  []
  [forcing_v]
    type = ParsedFunction
    value = '(5/16)*pi^2*mu*sin((1/4)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.005*pi*mu*sin((1/4)*x*pi)*sin((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 - 3.75*pi*mu*exp(30 - 30*x)*cos((1/4)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) - pi*rho*sin((1/4)*x*pi)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) - 1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + (1/4)*pi*rho*sin((1/2)*y*pi)*cos((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1)) + 0.01*rho*sin((1/4)*x*pi)^2*cos((1/2)*y*pi)^2/(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2 + 15.0*rho*exp(30 - 30*x)*sin((1/4)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)/((exp(30 - 30*x) + 1)^2*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))^2) + (3/2)*pi*(-0.01*y + 1 - 0.5/(exp(30 - 30*x) + 1))*cos((1/4)*x*pi)*cos((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin((3/2)*y*pi)*cos((1/4)*x*pi)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi) - 1/2*pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/cylindrical/2d-average-no-slip.i)

mu=1
rho=1
advected_interp_method='average'
velocity_interp_method='average'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 4
    nx = 10
    ny = 40
  []
[]

[Problem]
  fv_bcs_integrity_check = true
  coord_type = 'RZ'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 0
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 1
  []
  [no-slip-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 0
  []
  [no-slip-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 0
  []
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 0
  []
  [axis-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [axis-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Postprocessors]
  [in]
    type = SideIntegralVariablePostprocessor
    variable = v
    boundary = 'bottom'
  []
  [out]
    type = SideIntegralVariablePostprocessor
    variable = v
    boundary = 'top'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/boussinesq/boussinesq.i)

mu = 1
rho = 1
k = 1
cp = 1
alpha = 1
vel = 'velocity'
velocity_interp_method = 'rc'
advected_interp_method = 'upwind'
rayleigh=1e3
hot_temp=${rayleigh}
temp_ref=${fparse hot_temp / 2.}

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 32
    ny = 32
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [T]
    type = INSFVEnergyVariable
    scaling = 1e-4
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[AuxVariables]
  [U]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [vel_x]
    order = FIRST
    family = MONOMIAL
  []
  [vel_y]
    order = FIRST
    family = MONOMIAL
  []
  [viz_T]
    order = FIRST
    family = MONOMIAL
  []
[]

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = u
    y = v
    execute_on = 'initial timestep_end'
  []
  [vel_x]
    type = ParsedAux
    variable = vel_x
    function = 'u'
    execute_on = 'initial timestep_end'
    args = 'u'
  []
  [vel_y]
    type = ParsedAux
    variable = vel_y
    function = 'v'
    execute_on = 'initial timestep_end'
    args = 'v'
  []
  [viz_T]
    type = ParsedAux
    variable = viz_T
    function = 'T'
    execute_on = 'initial timestep_end'
    args = 'T'
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    vel = ${vel}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    u = u
    v = v
    pressure = pressure
    mu = ${mu}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_buoyancy]
    type = INSFVMomentumBoussinesq
    variable = u
    temperature = T
    gravity = '0 -1 0'
    rho = ${rho}
    ref_temperature = ${temp_ref}
    momentum_component = 'x'
  []
  [u_gravity]
    type = INSFVMomentumGravity
    variable = u
    gravity = '0 -1 0'
    rho = ${rho}
    momentum_component = 'x'
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_buoyancy]
    type = INSFVMomentumBoussinesq
    variable = v
    temperature = T
    gravity = '0 -1 0'
    rho = ${rho}
    ref_temperature = ${temp_ref}
    momentum_component = 'y'
  []
  [v_gravity]
    type = INSFVMomentumGravity
    variable = v
    gravity = '0 -1 0'
    rho = ${rho}
    momentum_component = 'y'
  []

  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top'
    function = 'lid_function'
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'left right bottom'
    function = 0
  []

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

  [T_hot]
    type = FVDirichletBC
    variable = T
    boundary = left
    value = ${hot_temp}
  []

  [T_cold]
    type = FVDirichletBC
    variable = T
    boundary = right
    value = 0
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'k cp alpha'
    prop_values = '${k} ${cp} ${alpha}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'T'
    rho = ${rho}
  []
[]

[Functions]
  [lid_function]
    type = ParsedFunction
    value = '4*x*(1-x)'
  []
[]


[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      300                lu           NONZERO'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/2d-average.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='average'

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

[Problem]
  kernel_coverage_check = false
  fv_bcs_integrity_check = true
  coord_type = 'RZ'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = false
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 'exact_v'
  []
  [no-slip-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 'exact_u'
  []
  [no-slip-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 'exact_v'
  []
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 'exact_p'
  []
  [axis-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [axis-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin(x*pi)*sin((1/2)*y*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin(x*pi)*sin((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '(1/4)*pi^2*mu*sin(x*pi)*sin((1/2)*y*pi) - pi*sin(x*pi)*cos((1/2)*y*pi) - (-x*pi^2*mu*sin(x*pi)*sin((1/2)*y*pi) + pi*mu*sin((1/2)*y*pi)*cos(x*pi))/x + (2*x*pi*rho*sin(x*pi)*sin((1/2)*y*pi)^2*cos(x*pi) + rho*sin(x*pi)^2*sin((1/2)*y*pi)^2)/x + (-x*pi*rho*sin(x*pi)*sin((1/2)*y*pi)*sin(y*pi)*cos(x*pi) + (1/2)*x*pi*rho*sin(x*pi)*cos(x*pi)*cos((1/2)*y*pi)*cos(y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = 'cos(x*pi)*cos(y*pi)'
[]
[exact_rhov]
  type = ParsedFunction
  value = 'rho*cos(x*pi)*cos(y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = 'pi^2*mu*cos(x*pi)*cos(y*pi) - 2*pi*rho*sin(y*pi)*cos(x*pi)^2*cos(y*pi) - 1/2*pi*sin((1/2)*y*pi)*cos(x*pi) - (-x*pi^2*mu*cos(x*pi)*cos(y*pi) - pi*mu*sin(x*pi)*cos(y*pi))/x + (-x*pi*rho*sin(x*pi)^2*sin((1/2)*y*pi)*cos(y*pi) + x*pi*rho*sin((1/2)*y*pi)*cos(x*pi)^2*cos(y*pi) + rho*sin(x*pi)*sin((1/2)*y*pi)*cos(x*pi)*cos(y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'cos(x*pi)*cos((1/2)*y*pi)'
[]
[forcing_p]
  type = ParsedFunction
  value = '-pi*rho*sin(y*pi)*cos(x*pi) + (x*pi*rho*sin((1/2)*y*pi)*cos(x*pi) + rho*sin(x*pi)*sin((1/2)*y*pi))/x'
  vars = 'rho'
  vals = '${rho}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

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

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

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

[Problem]
  kernel_coverage_check = false
  fv_bcs_integrity_check = true
  coord_type = 'RZ'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 'exact_v'
  []
  [no-slip-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 'exact_u'
  []
  [no-slip-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 'exact_v'
  []
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 'exact_p'
  []
  [axis-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [axis-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin(x*pi)*sin((1/2)*y*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin(x*pi)*sin((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '(1/4)*pi^2*mu*sin(x*pi)*sin((1/2)*y*pi) - pi*sin(x*pi)*cos((1/2)*y*pi) - (-x*pi^2*mu*sin(x*pi)*sin((1/2)*y*pi) + pi*mu*sin((1/2)*y*pi)*cos(x*pi))/x + (2*x*pi*rho*sin(x*pi)*sin((1/2)*y*pi)^2*cos(x*pi) + rho*sin(x*pi)^2*sin((1/2)*y*pi)^2)/x + (-x*pi*rho*sin(x*pi)*sin((1/2)*y*pi)*sin(y*pi)*cos(x*pi) + (1/2)*x*pi*rho*sin(x*pi)*cos(x*pi)*cos((1/2)*y*pi)*cos(y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = 'cos(x*pi)*cos(y*pi)'
[]
[exact_rhov]
  type = ParsedFunction
  value = 'rho*cos(x*pi)*cos(y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = 'pi^2*mu*cos(x*pi)*cos(y*pi) - 2*pi*rho*sin(y*pi)*cos(x*pi)^2*cos(y*pi) - 1/2*pi*sin((1/2)*y*pi)*cos(x*pi) - (-x*pi^2*mu*cos(x*pi)*cos(y*pi) - pi*mu*sin(x*pi)*cos(y*pi))/x + (-x*pi*rho*sin(x*pi)^2*sin((1/2)*y*pi)*cos(y*pi) + x*pi*rho*sin((1/2)*y*pi)*cos(x*pi)^2*cos(y*pi) + rho*sin(x*pi)*sin((1/2)*y*pi)*cos(x*pi)*cos(y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'cos(x*pi)*cos((1/2)*y*pi)'
[]
[forcing_p]
  type = ParsedFunction
  value = '-pi*rho*sin(y*pi)*cos(x*pi) + (x*pi*rho*sin((1/2)*y*pi)*cos(x*pi) + rho*sin(x*pi)*sin((1/2)*y*pi))/x'
  vars = 'rho'
  vals = '${rho}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/rc.i)

mu=1.1
rho=1.1
velocity_interp_method='rc'

[GlobalParams]
  force_boundary_execution = false
  two_term_boundary_expansion = false
[]

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

[Problem]
  fv_bcs_integrity_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = 'average'
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = 'average'
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = 'average'
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [no-slip-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'left right top bottom'
    variable = u
    function = 'exact_u'
  []

  [no-slip-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'left right top bottom'
    variable = v
    function = 'exact_v'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin(y)*cos((1/2)*x*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin(y)*cos((1/2)*x*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = 'mu*sin(y)*cos((1/2)*x*pi) + (1/4)*pi^2*mu*sin(y)*cos((1/2)*x*pi) - 1/2*pi*rho*sin(x)*sin(y)*sin((1/2)*y*pi)*cos((1/2)*x*pi) + rho*sin(x)*cos(y)*cos((1/2)*x*pi)*cos((1/2)*y*pi) - pi*rho*sin(y)^2*sin((1/2)*x*pi)*cos((1/2)*x*pi) + sin(y)*cos(x)'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = 'sin(x)*cos((1/2)*y*pi)'
[]
[exact_rhov]
  type = ParsedFunction
  value = 'rho*sin(x)*cos((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = 'mu*sin(x)*cos((1/2)*y*pi) + (1/4)*pi^2*mu*sin(x)*cos((1/2)*y*pi) - pi*rho*sin(x)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) - 1/2*pi*rho*sin(x)*sin(y)*sin((1/2)*x*pi)*cos((1/2)*y*pi) + rho*sin(y)*cos(x)*cos((1/2)*x*pi)*cos((1/2)*y*pi) + sin(x)*cos(y)'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'sin(x)*sin(y)'
[]
[forcing_p]
  type = ParsedFunction
  value = '-1/2*pi*rho*sin(x)*sin((1/2)*y*pi) - 1/2*pi*rho*sin(y)*sin((1/2)*x*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      30                lu           NONZERO'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    variable = v
    function = exact_v
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/postprocessors/conservation_INSFV.i)

mu=1.1
rho=1
advected_interp_method='average'
velocity_interp_method='average'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  inactive = 'mesh internal_boundary_bot internal_boundary_top'
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1'
    dy = '1 1 1'
    ix = '5'
    iy = '5 5 5'
    subdomain_id = '1
                    2
                    3'
  []
  [internal_boundary_bot]
    type = SideSetsBetweenSubdomainsGenerator
    input = mesh
    new_boundary = 'internal_bot'
    primary_block = 1
    paired_block = 2
  []
  [internal_boundary_top]
    type = SideSetsBetweenSubdomainsGenerator
    input = internal_boundary_bot
    new_boundary = 'internal_top'
    primary_block = 2
    paired_block = 3
  []
  [diverging_mesh]
    type = FileMeshGenerator
    file = 'expansion_quad.e'
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 0
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [temperature]
    type = INSFVEnergyVariable
  []
[]

[AuxVariables]
  [advected_density]
    order = CONSTANT
    family = MONOMIAL
    fv = true
    initial_condition = ${rho}
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
    force_boundary_execution = true
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
    force_boundary_execution = true
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [temp_advection]
    type = INSFVEnergyAdvection
    vel = 'velocity'
    variable = temperature
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [temp_source]
    type = FVBodyForce
    variable = temperature
    function = 10
    block = 1
  []
[]

[FVBCs]
  inactive = 'noslip-u noslip-v'
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 0
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 1
  []
  [noslip-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 0
  []
  [noslip-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 0
  []
  [free-slip-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = u
  []
  [free-slip-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = v
  []
  [axis-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [axis-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 0
  []
  [inlet_temp]
    type = FVNeumannBC
    boundary = 'bottom'
    variable = temperature
    value = 300
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'temperature'
    rho = ${rho}
  []
  [advected_material_property]
    type = ADGenericConstantMaterial
    prop_names = 'advected_rho cp'
    prop_values ='${rho} 1'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Postprocessors]
  [inlet_mass_variable]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = advected_density
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [inlet_mass_constant]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = ${rho}
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [inlet_mass_matprop]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_mat_prop = 'advected_rho'
    fv = true
  []
  [mid1_mass]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid2_mass]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [outlet_mass]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []

  [inlet_momentum_x]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid1_momentum_x]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid2_momentum_x]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [outlet_momentum_x]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []

  [inlet_momentum_y]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid1_momentum_y]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid2_momentum_y]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [outlet_momentum_y]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []

  [inlet_advected_energy]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
  []
  [mid1_advected_energy]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid2_advected_energy]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [outlet_advected_energy]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
  []
[]

[Outputs]
  exodus = false
  csv = true
  inactive = 'console_mass console_momentum_x console_momentum_y console_energy'
  [console_mass]
    type = Console
    start_step = 1
    show = 'inlet_mass_variable inlet_mass_constant inlet_mass_matprop mid1_mass mid2_mass outlet_mass'
  []
  [console_momentum_x]
    type = Console
    start_step = 1
    show = 'inlet_momentum_x mid1_momentum_x mid2_momentum_x outlet_momentum_x'
  []
  [console_momentum_y]
    type = Console
    start_step = 1
    show = 'inlet_momentum_y mid1_momentum_y mid2_momentum_y outlet_momentum_y'
  []
  [console_energy]
    type = Console
    start_step = 1
    show = 'inlet_advected_energy mid1_advected_energy mid2_advected_energy outlet_advected_energy'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/lid-driven-with-energy.i)

mu = 1
rho = 1
k = .01
cp = 1
vel = 'velocity'
velocity_interp_method = 'rc'
advected_interp_method = 'average'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 32
    ny = 32
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [T]
    type = INSFVEnergyVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

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

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = u
    y = v
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    vel = ${vel}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    u = u
    v = v
    pressure = pressure
    mu = ${mu}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []

  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []

  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [temp-condution]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []

  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top'
    function = 'lid_function'
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'left right bottom'
    function = 0
  []

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

  [T_hot]
    type = FVDirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  []

  [T_cold]
    type = FVDirichletBC
    variable = T
    boundary = 'top'
    value = 0
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'k cp'
    prop_values = '${k} ${cp}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'T'
    rho = ${rho}
  []
[]

[Functions]
  [lid_function]
    type = ParsedFunction
    value = '4*x*(1-x)'
  []
[]


[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      300                lu           NONZERO'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

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

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 5
    ymin = 0
    ymax = 1
    nx = 20
    ny = 10
  []
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  inactive = 'lambda'
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.5
  []
[]

[FVKernels]
  inactive = 'mean-pressure'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [mean-pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
    phi0 = 0.01
  []
[]

[FVBCs]
  # Select desired boundary conditions
  active = 'inlet-u inlet-v outlet-p free-slip-u free-slip-v'

  # Possible inlet boundary conditions
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [inlet-p]
    type = INSFVOutletPressureBC
    boundary = 'left'
    variable = pressure
    function = 1
  []

  # Possible wall boundary conditions
  [free-slip-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = u
  []
  [free-slip-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = v
  []
  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 0
  []
  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'x'
    porosity = porosity
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'y'
    porosity = porosity
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  # Possible outlet boundary conditions
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0
  []
  [outlet-p-novalue]
    type = INSFVMassAdvectionOutflowBC
    boundary = 'right'
    variable = pressure
    u = u
    v = v
    rho = ${rho}
  []
  [outlet-u]
    type = PINSFVMomentumAdvectionOutflowBC
    boundary = 'right'
    variable = u
    vel = velocity
    u = u
    v = v
    porosity = porosity
  []
  [outlet-v]
    type = PINSFVMomentumAdvectionOutflowBC
    boundary = 'right'
    variable = v
    vel = velocity
    u = u
    v = v
    porosity = porosity
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-14
[]

# Some basic Postprocessors to visually examine the solution
[Postprocessors]
  [inlet-p]
    type = SideIntegralVariablePostprocessor
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/3d-rc-no-slip.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 10
    ymin = -1
    ymax = 1
    zmin = -1
    zmax = 1
    nx = 20
    ny = 4
    nz = 4
    elem_type = TET4
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [w]
    type = INSFVVelocityVariable
    initial_condition = 1e-15
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [w_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhow'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []
  [w_viscosity]
    type = FVDiffusion
    variable = w
    coeff = ${mu}
  []
  [w_pressure]
    type = INSFVMomentumPressure
    variable = w
    momentum_component = 'z'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [inlet-w]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = w
    function = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom front back'
    variable = u
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom front back'
    variable = v
    function = 0
  []
  [walls-w]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom front back'
    variable = w
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    w = 'w'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -pc_factor_shift_type'
  petsc_options_value = 'lu       mumps                      NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/plane-poiseuille-flow.i)

mu=0.5
rho=1.1
advected_interp_method='average'
velocity_interp_method='average'
two_term_boundary_expansion=true

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = ${two_term_boundary_expansion}
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = ${two_term_boundary_expansion}
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = ${two_term_boundary_expansion}
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top bottom'
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'top bottom'
    function = 'exact_v'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = '0.5*(1.0 - y^2)/mu'
  vars = 'mu'
  vals = '${mu}'
[]
[exact_rhou]
  type = ParsedFunction
  value = '0.5*rho*(1.0 - y^2)/mu'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '0'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = '0.0'
[]
[exact_rhov]
  type = ParsedFunction
  value = '0'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = '0'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = '10.0 - x'
[]
[forcing_p]
  type = ParsedFunction
  value = '0'
  vars = 'rho mu'
  vals = '${rho} ${mu}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

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

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [walls-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = u
  []
  [walls-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom'
    variable = v
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/rotated/rotated-pp-flow.i)

mu=0.5
rho=1.1
advected_interp_method='average'
velocity_interp_method='average'
two_term_boundary_expansion=true

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 10
    ymin = -1
    ymax = 1
    nx = 10
    ny = 2
  []
  [rotate]
    type = TransformGenerator
    input = gen
    transform = 'rotate'
    vector_value = '45 0 0'
  []
[]

[Problem]
  kernel_coverage_check = false
  fv_bcs_integrity_check = true
[]

[AuxVariables]
  [vel_exact_x][]
  [vel_exact_y][]
  [p_exact][]
[]

[AuxKernels]
  [u_exact]
    type = FunctionAux
    variable = vel_exact_x
    function = exact_u
  []
  [v_exact]
    type = FunctionAux
    variable = vel_exact_y
    function = exact_v
  []
  [p_exact]
    type = FunctionAux
    variable = p_exact
    function = exact_p
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = ${two_term_boundary_expansion}
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = ${two_term_boundary_expansion}
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = ${two_term_boundary_expansion}
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top bottom'
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'top bottom'
    function = 'exact_v'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = '0.25*sqrt(2)*(1.0 - 1/2*(-x + y)^2)/mu'
  vars = 'mu'
  vals = '${mu}'
[]
[exact_rhou]
  type = ParsedFunction
  value = '0.25*sqrt(2)*rho*(1.0 - 1/2*(-x + y)^2)/mu'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '0'
[]
[exact_v]
  type = ParsedFunction
  value = '0.25*sqrt(2)*(1.0 - 1/2*(-x + y)^2)/mu'
  vars = 'mu'
  vals = '${mu}'
[]
[exact_rhov]
  type = ParsedFunction
  value = '0.25*sqrt(2)*rho*(1.0 - 1/2*(-x + y)^2)/mu'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = '0'
[]
[exact_p]
  type = ParsedFunction
  value = '-1/2*sqrt(2)*(x + y) + 10.0'
[]
[forcing_p]
  type = ParsedFunction
  value = '0'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/1d-rc.i)

mu=1.1
rho=1.1
advected_interp_method='upwind'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 1
    dx = '1 1'
    ix = '30 30'
    subdomain_id = '1 2'
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 1
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/pins/mms/2d-rc.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = -1
    ymax = 1
    nx = 8
    ny = 8
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.8
  []
[]

[GlobalParams]
  porosity = porosity
  two_term_boundary_expansion = true
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 'exact_v'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 'exact_u'
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 'exact_v'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    value = 'sin((1/2)*y*pi)*cos((1/2)*x*pi)'
  []
  [forcing_u]
    type = ParsedFunction
    value = '0.625*pi^2*mu*sin((1/2)*y*pi)*cos((1/2)*x*pi) - 0.625*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) + 0.625*pi*rho*sin((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi)^2 - 1.25*pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)^2*cos((1/2)*x*pi) - 0.2*pi*sin((1/4)*x*pi)*sin((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    value = 'sin((1/4)*x*pi)*cos((1/2)*y*pi)'
  []
  [forcing_v]
    type = ParsedFunction
    value = '0.390625*pi^2*mu*sin((1/4)*x*pi)*cos((1/2)*y*pi) - 1.25*pi*rho*sin((1/4)*x*pi)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) - 0.625*pi*rho*sin((1/4)*x*pi)*sin((1/2)*x*pi)*sin((1/2)*y*pi)*cos((1/2)*y*pi) + 0.3125*pi*rho*sin((1/2)*y*pi)*cos((1/4)*x*pi)*cos((1/2)*x*pi)*cos((1/2)*y*pi) + 1.2*pi*cos((1/4)*x*pi)*cos((3/2)*y*pi)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin((3/2)*y*pi)*cos((1/4)*x*pi)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-1/2*pi*rho*sin((1/4)*x*pi)*sin((1/2)*y*pi) - 1/2*pi*rho*sin((1/2)*x*pi)*sin((1/2)*y*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    type = ElementL2Error
    variable = pressure
    function = exact_p
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/examples/pipe_mixing_length/pipe_mixing_length.i)

# This example demonstrates how the mixing length model can be tuned to match an
# established correlation for pressure drop in a smooth circular pipe.

# The primary input parameters for this example are the system Reynolds number
# and the von Karman constant for the mixing length model. These two parameters
# can be changed here:
Re = 1e5
von_karman_const = 0.22

# Note that for this model (using the wall-distance mixing length for the entire
# pipe) different von Karman constants are optimal for different Reynolds
# numbers.

# This model has been non-dimensionalized. The diameter (D), density (rho), and
# bulk velocity (bulk_u) are all considered unity.
D = 1
total_len = ${fparse 40 * D}
rho = 1
bulk_u = 1

# With those parameters set, the viscosity is then computed in order to reach
# the desired Reynolds number.
mu = ${fparse rho * bulk_u * D / Re}

# Here the DeltaP will be evaluted by using a postprocessor to find the pressure
# at a point that is 10 diameters away from the outlet. (The outlet pressure is
# set to zero.)
L = ${fparse 10 * D}

# We will use the McAdams correlation to find the Darcy friction factor. Note
# that this correlation is valid for fully developed flow in smooth circular
# tubes at 3e4 < Re < 1e6.
f = ${fparse 0.316 * Re^(-0.25)}

# The DeltaP can then be computed using this friction factor as,
ref_delta_P = ${fparse f * L / D * rho * bulk_u^2 / 2}

# The upwind and Rhie-Chow interpolation schemes are used here.
advected_interp_method='upwind'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${total_len}
    ymin = 0
    ymax = ${fparse 0.5 * D}
    nx = 200
    ny = 40
    bias_y = ${fparse 1 / 1.2}
  []
  [rename1]
    type = RenameBoundaryGenerator
    input = gen
    old_boundary = 'left'
    new_boundary = 'inlet'
  []
  [rename2]
    type = RenameBoundaryGenerator
    input = rename1
    old_boundary = 'right'
    new_boundary = 'outlet'
  []
  [rename3]
    type = RenameBoundaryGenerator
    input = rename2
    old_boundary = 'bottom'
    new_boundary = 'symmetry'
  []
  [rename4]
    type = RenameBoundaryGenerator
    input = rename3
    old_boundary = 'top'
    new_boundary = 'wall'
  []
[]

[Outputs]
  exodus = true
[]

[Problem]
  kernel_coverage_check = false
  fv_bcs_integrity_check = true
  coord_type = 'RZ'
  rz_coord_axis = 'X'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

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

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = u
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'x'
    u = u
    v = v
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = v
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'y'
    u = u
    v = v
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[AuxKernels]
  [mixing_len]
    type = WallDistanceMixingLengthAux
    walls = 'wall'
    variable = mixing_len
    execute_on = 'initial'
    von_karman_const = ${von_karman_const}
  []
[]

[FVBCs]
  [inlet_u]
    type = INSFVInletVelocityBC
    boundary = 'inlet'
    variable = u
    function = ${bulk_u}
  []
  [inlet_v]
    type = INSFVInletVelocityBC
    boundary = 'inlet'
    variable = v
    function = '0'
  []
  [walls_u]
    type = INSFVNoSlipWallBC
    boundary = 'wall'
    variable = u
    function = 0
  []
  [walls_v]
    type = INSFVNoSlipWallBC
    boundary = 'wall'
    variable = v
    function = 0
  []
  [sym_u]
    type = INSFVSymmetryVelocityBC
    boundary = 'symmetry'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [sym_v]
    type = INSFVSymmetryVelocityBC
    boundary = 'symmetry'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [sym_p]
    type = INSFVSymmetryPressureBC
    boundary = 'symmetry'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'outlet'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
[]

[Postprocessors]
  [delta_P]
    type = PointValue
    variable = 'pressure'
    point = '${fparse total_len - L} 0 0'
  []
  [reference_delta_P]
    type = Receiver
    default = ${ref_delta_P}
  []
[]

(modules/navier_stokes/test/tests/finite_volume/fviks/convection/convection_channel.i)

mu = 1
rho = 1
k = .01
cp = 1
vel = 'velocity'
velocity_interp_method = 'rc'
advected_interp_method = 'average'

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 0.5'
    dy = '1'
    ix = '8 5'
    iy = '8'
    subdomain_id = '0 1'
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = 'cmg'
    primary_block = 0
    paired_block = 1
    new_boundary = 'interface'
  []
  [fluid_side]
    type = BreakBoundaryOnSubdomainGenerator
    input = 'interface'
    boundaries = 'top bottom'
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    block = 0
    initial_condition = 1e-6
  []
  [v]
    type = INSFVVelocityVariable
    block = 0
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
    block = 0
  []
  [T]
    type = INSFVEnergyVariable
    block = 0
    initial_condition = 1
  []
  [Ts]
    type = INSFVEnergyVariable
    block = 1
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    vel = ${vel}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    u = u
    v = v
    pressure = pressure
    mu = ${mu}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [solid_temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = Ts
  []
[]

[FVInterfaceKernels]
  [convection]
    type = FVConvectionCorrelationInterface
    variable1 = T
    variable2 = Ts
    boundary = 'interface'
    h = 5
    temp_solid = Ts
    temp_fluid = T
    subdomain1 = 0
    subdomain2 = 1
    wall_cell_is_bulk = true
  []
[]

[FVBCs]
  [walls_u]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'interface left'
    function = 0
  []
  [walls_v]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'interface left'
    function = 0
  []

  [inlet_u]
    type = INSFVInletVelocityBC
    variable = u
    boundary = 'bottom_to_0'
    function = 0
  []
  [inlet_v]
    type = INSFVInletVelocityBC
    variable = v
    boundary = 'bottom_to_0'
    function = 1
  []

  [inlet_T]
    type = FVDirichletBC
    variable = T
    boundary = 'bottom_to_0'
    value = 0.5
  []

  [outlet]
    type = INSFVMassAdvectionOutflowBC
    variable = pressure
    boundary = 'top_to_0'
    u = u
    v = v
    rho = ${rho}
  []
  [outlet_u]
    type = INSFVMomentumAdvectionOutflowBC
    variable = u
    boundary = 'top_to_0'
    u = u
    v = v
    vel = 'velocity'
  []
  [outlet_v]
    type = INSFVMomentumAdvectionOutflowBC
    variable = v
    boundary = 'top_to_0'
    u = u
    v = v
    vel = 'velocity'
  []

  [heater]
    type = FVDirichletBC
    variable = 'Ts'
    boundary = 'right'
    value = 10
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'k cp'
    prop_values = '${k} ${cp}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'T'
    rho = ${rho}
    block = 0
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'asm      lu           NONZERO                   200'
  line_search = 'none'

  nl_abs_tol = 1e-14
[]

[Postprocessors]
  [max_T]
    type = ElementExtremeValue
    variable = T
    block = 0
  []
  [max_Ts]
    type = ElementExtremeValue
    variable = Ts
    block = 1
  []
  [mdot_out]
    type = VolumetricFlowRate
    boundary = 'top_to_0'
    vel_x = u
    vel_y = v
    advected_interp_method = ${advected_interp_method}
  []
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/cylindrical/2d-average-with-temp.i)

mu=1.1
rho=1.1
k=1.1
cp=1.1
advected_interp_method='average'
velocity_interp_method='average'
velocity='velocity'

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

[Problem]
  kernel_coverage_check = false
  fv_bcs_integrity_check = true
  coord_type = 'RZ'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = false
  []
  [temperature]
    type = INSFVEnergyVariable
    two_term_boundary_expansion = false
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = ${velocity}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = ${velocity}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = ${velocity}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_forcing]
    type = FVBodyForce
    variable = v
    function = forcing_v
  []

  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = temperature
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    vel = ${velocity}
    variable = temperature
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [temp_forcing]
    type = FVBodyForce
    variable = temperature
    function = forcing_t
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 'exact_u'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 'exact_v'
  []
  [no-slip-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 'exact_u'
  []
  [no-slip-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 'exact_v'
  []
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 'exact_p'
  []
  [axis-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [axis-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
  [axis-inlet-wall-t]
    type = FVFunctionDirichletBC
    boundary = 'left bottom right'
    variable = temperature
    function = 'exact_t'
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'k cp'
    prop_values = '${k} ${cp}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'temperature'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin(x*pi)*sin((1/2)*y*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin(x*pi)*sin((1/2)*y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '(1/4)*pi^2*mu*sin(x*pi)*sin((1/2)*y*pi) - pi*sin(x*pi)*cos((1/2)*y*pi) - (-x*pi^2*mu*sin(x*pi)*sin((1/2)*y*pi) + pi*mu*sin((1/2)*y*pi)*cos(x*pi))/x + (2*x*pi*rho*sin(x*pi)*sin((1/2)*y*pi)^2*cos(x*pi) + rho*sin(x*pi)^2*sin((1/2)*y*pi)^2)/x + (-x*pi*rho*sin(x*pi)*sin((1/2)*y*pi)*sin(y*pi)*cos(x*pi) + (1/2)*x*pi*rho*sin(x*pi)*cos(x*pi)*cos((1/2)*y*pi)*cos(y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_v]
  type = ParsedFunction
  value = 'cos(x*pi)*cos(y*pi)'
[]
[exact_rhov]
  type = ParsedFunction
  value = 'rho*cos(x*pi)*cos(y*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_v]
  type = ParsedFunction
  value = 'pi^2*mu*cos(x*pi)*cos(y*pi) - 2*pi*rho*sin(y*pi)*cos(x*pi)^2*cos(y*pi) - 1/2*pi*sin((1/2)*y*pi)*cos(x*pi) - (-x*pi^2*mu*cos(x*pi)*cos(y*pi) - pi*mu*sin(x*pi)*cos(y*pi))/x + (-x*pi*rho*sin(x*pi)^2*sin((1/2)*y*pi)*cos(y*pi) + x*pi*rho*sin((1/2)*y*pi)*cos(x*pi)^2*cos(y*pi) + rho*sin(x*pi)*sin((1/2)*y*pi)*cos(x*pi)*cos(y*pi))/x'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'cos(x*pi)*cos((1/2)*y*pi)'
[]
[forcing_p]
  type = ParsedFunction
  value = '-pi*rho*sin(y*pi)*cos(x*pi) + (x*pi*rho*sin((1/2)*y*pi)*cos(x*pi) + rho*sin(x*pi)*sin((1/2)*y*pi))/x'
  vars = 'rho'
  vals = '${rho}'
[]
[exact_t]
  type = ParsedFunction
  value = 'sin(x*pi)*sin((1/2)*y*pi)'
[]
[forcing_t]
  type = ParsedFunction
  value = '(1/4)*pi^2*k*sin(x*pi)*sin((1/2)*y*pi) - (-x*pi^2*k*sin(x*pi)*sin((1/2)*y*pi) + pi*k*sin((1/2)*y*pi)*cos(x*pi))/x + (2*x*pi*cp*rho*sin(x*pi)*sin((1/2)*y*pi)^2*cos(x*pi) + cp*rho*sin(x*pi)^2*sin((1/2)*y*pi)^2)/x + (-x*pi*cp*rho*sin(x*pi)*sin((1/2)*y*pi)*sin(y*pi)*cos(x*pi) + (1/2)*x*pi*cp*rho*sin(x*pi)*cos(x*pi)*cos((1/2)*y*pi)*cos(y*pi))/x'
  vars = 'k rho cp'
  vals = '${k} ${rho} ${cp}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2v]
    type = ElementL2Error
    variable = v
    function = exact_v
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2t]
    variable = temperature
    function = exact_t
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated.i)

mu=1
rho=1
k=1e-3
cp=1
u_inlet=1
T_inlet=200
advected_interp_method='average'
velocity_interp_method='rc'

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

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  inactive = 'temp_solid'
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [temperature]
    type = INSFVEnergyVariable
  []
  [temp_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
  []
[]

[AuxVariables]
  [temp_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
    initial_condition = 100
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.5
  []
[]

[FVKernels]
  inactive = 'solid_energy_diffusion solid_energy_convection'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = temperature
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [energy_diffusion]
    type = PINSFVEnergyDiffusion
    k = ${k}
    variable = temperature
    porosity = porosity
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = temperature
    is_solid = false
    temp_fluid = temperature
    temp_solid = temp_solid
    h_solid_fluid = 'h_cv'
  []

  [solid_energy_diffusion]
    type = FVDiffusion
    coeff = ${k}
    variable = temp_solid
  []
  [solid_energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = temp_solid
    is_solid = true
    temp_fluid = temperature
    temp_solid = temp_solid
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  inactive = 'heated-side'
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [inlet-T]
    type = FVNeumannBC
    variable = temperature
    value = ${fparse u_inlet * rho * cp * T_inlet}
    boundary = 'left'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = u
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = v
    function = 0
  []
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'temp_solid'
    value = 150
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'x'
    porosity = porosity
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'y'
    porosity = porosity
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0.1
  []
[]

[Materials]
  [constants]
    type = ADGenericConstantMaterial
    prop_names = 'cp h_cv'
    prop_values = '${cp} 1'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
    temperature = 'temperature'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideAverageValue
    variable = u
    boundary = 'right'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = temperature
    boundary = 'right'
  []
  [solid-temp]
    type = ElementAverageValue
    variable = temp_solid
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-no-slip-extrapolated-outlet-pressure.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 0
  []
  [outlet_u]
    type = INSFVMomentumAdvectionOutflowBC
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    u = u
    v = v
    boundary = 'right'
  []
  [outlet_v]
    type = INSFVMomentumAdvectionOutflowBC
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    u = u
    v = v
    boundary = 'right'
  []
  [outlet_p]
    type = INSFVMassAdvectionOutflowBC
    boundary = 'right'
    variable = pressure
    u = u
    v = v
    rho = ${rho}
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-no-slip.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

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

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/porosity_jump/1d-rc-epsjump.i)

mu=1.1
rho=1.1
advected_interp_method='upwind'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 1
    dx = '1 1'
    ix = '30 30'
    subdomain_id = '1 2'
  []
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

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

[ICs]
  inactive = 'porosity_continuous'
  [porosity_1]
    type = ConstantIC
    variable = porosity
    block = 1
    value = 1
  []
  [porosity_2]
    type = ConstantIC
    variable = porosity
    block = 2
    value = 0.5
  []
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    block = '1 2'
    function = smooth_jump
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1)))'
  []
[]

[FVKernels]
  inactive = 'u_advection_porosity_gradient'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
  [u_advection_porosity_gradient]
    type = PINSFVMomentumAdvectionPorosityGradient
    variable = u
    u = u
    rho = ${rho}
    porosity = porosity
    momentum_component = 'x'
    smooth_porosity = true
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 1
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/transient-lid-driven-with-energy.i)

mu = 1
rho = 1
k = .01
cp = 1
vel = 'velocity'
velocity_interp_method = 'rc'
advected_interp_method = 'average'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 32
    ny = 32
  []
  [pin]
    type = ExtraNodesetGenerator
    input = gen
    new_boundary = 'pin'
    nodes = '0'
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [T]
    type = INSFVEnergyVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[ICs]
  [T]
    type = ConstantIC
    variable = T
    value = 1
  []
[]

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

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = u
    y = v
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    vel = ${vel}
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    u = u
    v = v
    pressure = pressure
    mu = ${mu}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVScalarLagrangeMultiplier
    variable = pressure
    lambda = lambda
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = 'u'
    rho = ${rho}
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = v
    rho = ${rho}
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [temp_time]
    type = INSFVEnergyTimeDerivative
    variable = T
    rho = ${rho}
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
    vel = ${vel}
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top'
    function = 'lid_function'
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'left right bottom'
    function = 0
  []

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

  [T_hot]
    type = FVDirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  []

  [T_cold]
    type = FVDirichletBC
    variable = T
    boundary = 'top'
    value = 0
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'k cp'
    prop_values = '${k} ${cp}'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'T'
    rho = ${rho}
  []
[]

[Functions]
  [lid_function]
    type = ParsedFunction
    value = '4*x*(1-x)'
  []
[]


[Executioner]
  type = Transient
  solve_type = NEWTON
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'asm      lu           NONZERO                   200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
  l_max_its = 200
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mms/channel-flow/1d-average.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='average'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 0
    xmax = 1
    nx = 2
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    two_term_boundary_expansion = false
  []
  [pressure]
    type = INSFVPressureVariable
    two_term_boundary_expansion = false
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []

[]

[FVBCs]
  [inlet_u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Functions]
[exact_u]
  type = ParsedFunction
  value = 'sin((1/2)*x*pi)'
[]
[exact_rhou]
  type = ParsedFunction
  value = 'rho*sin((1/2)*x*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[forcing_u]
  type = ParsedFunction
  value = '(1/4)*pi^2*mu*sin((1/2)*x*pi) + pi*rho*sin((1/2)*x*pi)*cos((1/2)*x*pi) - 1/2*pi*sin((1/2)*x*pi)'
  vars = 'mu rho'
  vals = '${mu} ${rho}'
[]
[exact_p]
  type = ParsedFunction
  value = 'cos((1/2)*x*pi)'
[]
[forcing_p]
  type = ParsedFunction
  value = '(1/2)*pi*rho*cos((1/2)*x*pi)'
  vars = 'rho'
  vals = '${rho}'
[]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  []

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [./L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

(modules/navier_stokes/test/tests/finite_volume/pins/mms/porosity_change/1d-rc-continuous.i)

mu=1.5
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 1
    dx = '1 1'
    ix = '15 15'
  []
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Problem]
  error_on_jacobian_nonzero_reallocation = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

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

[ICs]
  [porosity_continuous]
    type = FunctionIC
    variable = porosity
    function = smooth_jump
  []
[]

[Functions]
  [smooth_jump]
    type = ParsedFunction
    value = '1 - 0.5 * 1 / (1 + exp(-30*(x-1)))'
  []

  # Generated by compute-functions-1d.py
  [exact_u]
    type = ParsedFunction
    value = 'cos((1/2)*x*pi)'
  []
  [forcing_u]
    type = ParsedFunction
    value = '-mu*(-1/4*pi^2*cos((1/2)*x*pi)/(1 - 0.5/(exp(30 - 30*x) + 1)) - 15.0*pi*exp(30 - 30*x)*sin((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^2) - 450.0*exp(30 - 30*x)*cos((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^2) + 900.0*exp(60 - 60*x)*cos((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^3) + 450.0*exp(60 - 60*x)*cos((1/2)*x*pi)/((1 - 0.5/(exp(30 - 30*x) + 1))^3*(exp(30 - 30*x) + 1)^4)) - pi*rho*sin((1/2)*x*pi)*cos((1/2)*x*pi)/(1 - 0.5/(exp(30 - 30*x) + 1)) + 15.0*rho*exp(30 - 30*x)*cos((1/2)*x*pi)^2/((1 - 0.5/(exp(30 - 30*x) + 1))^2*(exp(30 - 30*x) + 1)^2) + (1 - 0.5/(exp(30 - 30*x) + 1))*cos(x)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin(x)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-1/2*pi*rho*sin((1/2)*x*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[FVKernels]
  inactive = 'u_pressure_porosity u_pressure_porosity_gradient'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
    smooth_porosity = true
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
    smooth_porosity = true
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity

    vel = 'velocity'
    momentum_component = 'x'
    smooth_porosity = true
  []

  # Option 1: eps * pressure gradient
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []

  # Option 2: gradient (eps * pressure) - P * gradient(eps)
  [u_pressure_porosity]
    type = PINSFVMomentumPressureFlux
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
  [u_pressure_porosity_gradient]
    type = PINSFVMomentumPressurePorosityGradient
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []

  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'

  # ksp_gmres_restart bumped to 200 for linear convergence
  nl_max_its = 100
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

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

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 5
    ymin = -1
    ymax = 1
    nx = 50
    ny = 10
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  inactive='u_friction_quad v_friction_quad'
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []
  [u_friction_linear]
    type = NSFVMomentumFriction
    variable = u
    linear_coef_name = friction_coefficient
  []
  [u_friction_quad]
    type = NSFVMomentumFriction
    variable = u
    quadratic_coef_name = friction_coefficient
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
  [v_friction_linear]
    type = NSFVMomentumFriction
    variable = v
    linear_coef_name = friction_coefficient
  []
  [v_friction_quad]
    type = NSFVMomentumFriction
    variable = v
    quadratic_coef_name = friction_coefficient
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [walls-u]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = u
    function = 0
  []
  [walls-v]
    type = INSFVNoSlipWallBC
    boundary = 'top bottom'
    variable = v
    function = 0
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
  [friction_coefficient]
    type = ADGenericConstantMaterial
    prop_names = 'friction_coefficient'
    prop_values = '25'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/pins/channel-flow/heated/2d-rc-heated-effective.i)

mu=1
rho=1
k=1e-3
cp=1
u_inlet=1
T_inlet=200
advected_interp_method='average'
velocity_interp_method='rc'

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

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  inactive = 'temp_solid'
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${u_inlet}
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [temperature]
    type = INSFVEnergyVariable
  []
  [temp_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
  []
[]

[AuxVariables]
  [temp_solid]
    family = 'MONOMIAL'
    order = 'CONSTANT'
    fv = true
    initial_condition = 100
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.5
  []
[]

[FVKernels]
  inactive = 'solid_energy_diffusion solid_energy_convection'
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    porosity = porosity
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [energy_advection]
    type = PINSFVEnergyAdvection
    variable = temperature
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [energy_diffusion]
    type = PINSFVEnergyEffectiveDiffusion
    kappa = 'kappa'
    variable = temperature
  []
  [energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = temperature
    is_solid = false
    temp_fluid = temperature
    temp_solid = temp_solid
    h_solid_fluid = 'h_cv'
  []

  [solid_energy_diffusion]
    type = FVDiffusion
    coeff = ${k}
    variable = temp_solid
  []
  [solid_energy_convection]
    type = PINSFVEnergyAmbientConvection
    variable = temp_solid
    is_solid = true
    temp_fluid = temperature
    temp_solid = temp_solid
    h_solid_fluid = 'h_cv'
  []
[]

[FVBCs]
  inactive = 'heated-side'
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = ${u_inlet}
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [inlet-T]
    type = FVNeumannBC
    variable = temperature
    value = ${fparse u_inlet * rho * cp * T_inlet}
    boundary = 'left'
  []

  [no-slip-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = u
    function = 0
  []
  [no-slip-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = v
    function = 0
  []
  [heated-side]
    type = FVDirichletBC
    boundary = 'top'
    variable = 'temp_solid'
    value = 150
  []

  [symmetry-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'x'
    porosity = porosity
  []
  [symmetry-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = 'y'
    porosity = porosity
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []

  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0.1
  []
[]

[Materials]
  [constants]
    type = ADGenericConstantMaterial
    prop_names = 'cp h_cv'
    prop_values = '${cp} 1'
  []
  [kappa]
    type = ADGenericConstantVectorMaterial
    prop_names = 'kappa'
    prop_values = '1e-3 1e-2 1e-1'
  []
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
    temperature = 'temperature'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

# Some basic Postprocessors to examine the solution
[Postprocessors]
  [inlet-p]
    type = SideAverageValue
    variable = pressure
    boundary = 'left'
  []
  [outlet-u]
    type = SideAverageValue
    variable = u
    boundary = 'right'
  []
  [outlet-temp]
    type = SideAverageValue
    variable = temperature
    boundary = 'right'
  []
  [solid-temp]
    type = ElementAverageValue
    variable = temp_solid
  []
[]

[Outputs]
  exodus = true
  csv = false
[]

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

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    nx = 10
    ny = 50
  []
[]

[Problem]
  fv_bcs_integrity_check = true
  coord_type = 'RZ'
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 0
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 1
  []
  [free-slip-wall-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = u
  []
  [free-slip-wall-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = v
  []
  [outlet-p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 0
  []
  [axis-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [axis-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-mixing-length.i)

Re = 1e4
von_karman_const = 0.2

D = 1
rho = 1
bulk_u = 1
mu = ${fparse rho * bulk_u * D / Re}

advected_interp_method='upwind'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 5
    ymin = 0
    ymax = ${fparse 0.5 * D}
    nx = 20
    ny = 10
    bias_y = ${fparse 1 / 1.2}
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [scalar]
    type = INSFVScalarFieldVariable
  []
[]

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

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = u
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'x'
    u = u
    v = v
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = v
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'y'
    u = u
    v = v
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [scalar_diffusion_rans]
    type = INSFVMixingLengthScalarDiffusion
    variable = scalar
    mixing_length = mixing_len
    u = u
    v = v
    schmidt_number = 1.0
  []
  [scalar_src]
    type = FVBodyForce
    variable = scalar
    value = 0.1
  []
[]

[AuxKernels]
  [mixing_len]
    type = WallDistanceMixingLengthAux
    walls = 'top bottom'
    variable = mixing_len
    execute_on = 'initial'
    von_karman_const = ${von_karman_const}
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [inlet_scalar]
    type = FVDirichletBC
    boundary = 'left'
    variable = scalar
    value = 1
  []
  [wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = u
    function = 0
  []
  [wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'top'
    variable = v
    function = 0
  []
  [sym-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [sym-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/block_restriction/2d-rc.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

restricted_blocks = '1'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  parallel_type = 'replicated'
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1'
    dy = '1'
    ix = '7 7'
    iy = 10
    subdomain_id = '1 2'
  []
  [mid]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    input = mesh
    new_boundary = 'middle'
  []
  [break_top]
    type = PatchSidesetGenerator
    boundary = 'top'
    n_patches = 2
    input = mid
  []
  [break_bottom]
    type = PatchSidesetGenerator
    boundary = 'bottom'
    n_patches = 2
    input = break_top
  []
[]

[Problem]
  kernel_coverage_check = false
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
    block = ${restricted_blocks}
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1
    block = ${restricted_blocks}
  []
  [pressure]
    type = INSFVPressureVariable
    block = ${restricted_blocks}
  []
  [temperature]
    type = INSFVEnergyVariable
    block = ${restricted_blocks}
  []
  [scalar]
    type = INSFVScalarFieldVariable
    block = ${restricted_blocks}
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [energy_advection]
    type = INSFVEnergyAdvection
    variable = temperature
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [energy_diffusion]
    type = FVDiffusion
    coeff = 1.1
    variable = temperature
  []
  [energy_loss]
    type = FVBodyForce
    variable = temperature
    value = -0.1
  []

  [scalar_advection]
    type = INSFVScalarFieldAdvection
    variable = scalar
    vel = 'velocity'
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [scalar_diffusion]
    type = FVDiffusion
    coeff = 1
    variable = scalar
  []
  [scalar_src]
    type = FVBodyForce
    variable = scalar
    value = 0.1
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [top-wall-u]
    type = INSFVNoSlipWallBC
    boundary = 'top_0'
    variable = u
    function = 0
  []
  [top-wall-v]
    type = INSFVNoSlipWallBC
    boundary = 'top_0'
    variable = v
    function = 0
  []
  [bottom-wall-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom_0'
    variable = u
    mu = ${mu}
    u = u
    v = v
    momentum_component = 'x'
  []
  [bottom-wall-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom_0'
    variable = v
    mu = ${mu}
    u = u
    v = v
    momentum_component = 'y'
  []
  [bottom-wall-p]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom_0'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'middle'
    variable = pressure
    function = 0
  []
  [inlet_t]
    type = FVDirichletBC
    boundary = 'left'
    variable = temperature
    value = 1
  []
  [outlet_scalar]
    type = FVDirichletBC
    boundary = 'middle'
    variable = scalar
    value = 1
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'temperature'
    rho = ${rho}
    block = ${restricted_blocks}
  []
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'cp'
    prop_values = '2'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

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

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 10
    ymin = -1
    ymax = 1
    zmin = -1
    zmax = 1
    nx = 21
    ny = 7
    nz = 7
  []
[]

[Problem]
  fv_bcs_integrity_check = true
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [w]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [w_advection]
    type = INSFVMomentumAdvection
    variable = w
    advected_quantity = 'rhow'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    w = w
    mu = ${mu}
    rho = ${rho}
  []
  [w_viscosity]
    type = FVDiffusion
    variable = w
    coeff = ${mu}
  []
  [w_pressure]
    type = INSFVMomentumPressure
    variable = w
    momentum_component = 'z'
    pressure = pressure
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = 0
  []
  [inlet-w]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = w
    function = 0
  []

  [walls-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom front back'
    variable = u
  []
  [walls-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom front back'
    variable = v
  []
  [walls-w]
    type = INSFVNaturalFreeSlipBC
    boundary = 'top bottom front back'
    variable = w
  []

  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 0
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    w = 'w'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
  nl_abs_tol = 1e-13
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/mixing_length_eddy_viscosity_aux/mixing_length_eddy_viscosity.i)

von_karman_const = 0.41

H = 1 #halfwidth of the channel
L = 150

Re = 13700

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

advected_interp_method='upwind'
velocity_interp_method='rc'

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${L}'
    dy = '0.667 0.333'
    ix = '200'
    iy = '10  1'
  []
[]

[Problem]
  fv_bcs_integrity_check = false
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [v]
    type = INSFVVelocityVariable
    initial_condition = 1e-6
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [mixing_len]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_shear_stress]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [wall_yplus]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
  [eddy_viscosity]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []

  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [u_viscosity]
    type = FVDiffusion
    variable = u
    coeff = ${mu}
  []
  [u_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = u
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'x'
    u = u
    v = v
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    p = pressure
  []

  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
  []
  [v_viscosity]
    type = FVDiffusion
    variable = v
    coeff = ${mu}
  []
  [v_viscosity_rans]
    type = INSFVMixingLengthReynoldsStress
    variable = v
    rho = ${rho}
    mixing_length = mixing_len
    momentum_component = 'y'
    u = u
    v = v
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    p = pressure
  []
[]

[AuxKernels]
  [mixing_len]
    type = WallDistanceMixingLengthAux
    walls = 'top'
    variable = mixing_len
    execute_on = 'initial'
    von_karman_const = ${von_karman_const}
    delta = 0.5
  []
  [turbulent_viscosity]
    type = INSFVMixingLengthTurbulentViscosityAux
    variable = eddy_viscosity
    mixing_length = mixing_len
    u = u
    v = v
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = '1'
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = v
    function = '0'
  []
  [wall-u]
    type = INSFVWallFunctionBC
    variable = u
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = x
  []
  [wall-v]
    type = INSFVWallFunctionBC
    variable = v
    boundary = 'top'
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    momentum_component = y
  []
  [sym-u]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
  []
  [sym-v]
    type = INSFVSymmetryVelocityBC
    boundary = 'bottom'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
  []
  [symmetry_pressure]
    type = INSFVSymmetryPressureBC
    boundary = 'bottom'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = '0'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/postprocessors/conservation_PINSFV.i)

mu=1.1
rho=1
advected_interp_method='average'
velocity_interp_method='average'

[Mesh]
  inactive = 'mesh internal_boundary_bot internal_boundary_top'
  [mesh]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1'
    dy = '1 1 1'
    ix = '5'
    iy = '5 5 5'
    subdomain_id = '1
                    2
                    3'
  []
  [internal_boundary_bot]
    type = SideSetsBetweenSubdomainsGenerator
    input = mesh
    new_boundary = 'internal_bot'
    primary_block = 1
    paired_block = 2
  []
  [internal_boundary_top]
    type = SideSetsBetweenSubdomainsGenerator
    input = internal_boundary_bot
    new_boundary = 'internal_top'
    primary_block = 2
    paired_block = 3
  []
  [diverging_mesh]
    type = FileMeshGenerator
    file = 'expansion_quad.e'
  []
[]

[Problem]
  kernel_coverage_check = false
  fv_bcs_integrity_check = true
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 0
  []
  [v]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [temperature]
    type = INSFVEnergyVariable
  []
[]

[AuxVariables]
  [advected_density]
    order = CONSTANT
    family = MONOMIAL
    fv = true
    initial_condition = ${rho}
  []
  [porosity]
    order = CONSTANT
    family = MONOMIAL
    fv = true
    initial_condition = 0.5
  []
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    force_boundary_execution = true
    porosity = porosity
    mu = ${mu}
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
    porosity = porosity
  []

  [v_advection]
    type = PINSFVMomentumAdvection
    variable = v
    advected_quantity = 'rhov'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [v_viscosity]
    type = PINSFVMomentumDiffusion
    variable = v
    force_boundary_execution = true
    porosity = porosity
    mu = ${mu}
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
    porosity = porosity
  []

  [temp_advection]
    type = PINSFVEnergyAdvection
    vel = 'velocity'
    variable = temperature
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    v = v
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [temp_source]
    type = FVBodyForce
    variable = temperature
    function = 10
    block = 1
  []
[]

[FVBCs]
  inactive = 'noslip-u noslip-v'
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = u
    function = 0
  []
  [inlet-v]
    type = INSFVInletVelocityBC
    boundary = 'bottom'
    variable = v
    function = 1
  []
  [noslip-u]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = u
    function = 0
  []
  [noslip-v]
    type = INSFVNoSlipWallBC
    boundary = 'right'
    variable = v
    function = 0
  []
  [free-slip-u]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = u
  []
  [free-slip-v]
    type = INSFVNaturalFreeSlipBC
    boundary = 'right'
    variable = v
  []
  [axis-u]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = u
    u = u
    v = v
    mu = ${mu}
    momentum_component = x
    porosity = porosity
  []
  [axis-v]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = v
    u = u
    v = v
    mu = ${mu}
    momentum_component = y
    porosity = porosity
  []
  [axis-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = pressure
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'top'
    variable = pressure
    function = 0
  []
  [inlet_temp]
    type = FVNeumannBC
    boundary = 'bottom'
    variable = temperature
    value = 300
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    v = 'v'
    pressure = 'pressure'
    temperature = 'temperature'
    rho = ${rho}
  []
  [advected_material_property]
    type = ADGenericConstantMaterial
    prop_names = 'advected_rho cp'
    prop_values ='${rho} 1'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      200                lu           NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Postprocessors]
  [inlet_mass_variable]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = advected_density
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [inlet_mass_constant]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = ${rho}
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [inlet_mass_matprop]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_mat_prop = 'advected_rho'
    fv = true
  []
  [mid1_mass]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid2_mass]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [outlet_mass]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []

  [inlet_momentum_x]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid1_momentum_x]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid2_momentum_x]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [outlet_momentum_x]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    advected_variable = u
    fv = true
    advected_interp_method = ${advected_interp_method}
  []

  [inlet_momentum_y]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid1_momentum_y]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [mid2_momentum_y]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []
  [outlet_momentum_y]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    advected_variable = v
    fv = true
    advected_interp_method = ${advected_interp_method}
  []

  [inlet_advected_energy]
    type = VolumetricFlowRate
    boundary = bottom
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
  []
  [mid1_advected_energy]
    type = InternalVolumetricFlowRate
    boundary = internal_bot
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
  []
  [mid2_advected_energy]
    type = InternalVolumetricFlowRate
    boundary = internal_top
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
  []
  [outlet_advected_energy]
    type = VolumetricFlowRate
    boundary = top
    vel_x = u
    vel_y = v
    advected_mat_prop = 'rho_cp_temp'
    fv = true
  []
[]

[Outputs]
  exodus = false
  csv = true
  inactive = 'console_mass console_momentum_x console_momentum_y console_energy'
  [console_mass]
    type = Console
    start_step = 1
    show = 'inlet_mass_variable inlet_mass_constant inlet_mass_matprop mid1_mass mid2_mass outlet_mass'
  []
  [console_momentum_x]
    type = Console
    start_step = 1
    show = 'inlet_momentum_x mid1_momentum_x mid2_momentum_x outlet_momentum_x'
  []
  [console_momentum_y]
    type = Console
    start_step = 1
    show = 'inlet_momentum_y mid1_momentum_y mid2_momentum_y outlet_momentum_y'
  []
  [console_energy]
    type = Console
    start_step = 1
    show = 'inlet_advected_energy mid1_advected_energy mid2_advected_energy outlet_advected_energy'
  []
[]

(modules/navier_stokes/test/tests/finite_volume/pins/mms/1d-rc.i)

mu=1.1
rho=1.1
advected_interp_method='average'
velocity_interp_method='rc'

[Mesh]
  [mesh]
    type = CartesianMeshGenerator
    dim = 1
    dx = '1 1'
    ix = '5 5'
    subdomain_id = '1 2'
  []
[]

[GlobalParams]
  two_term_boundary_expansion = true
[]

[Variables]
  [u]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = 1
  []
  [pressure]
    type = INSFVPressureVariable
  []
[]

[AuxVariables]
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 0.8
  []
[]

[Problem]
  error_on_jacobian_nonzero_reallocation = true
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    value = 'cos((1/2)*x*pi)'
  []
  [forcing_u]
    type = ParsedFunction
    value = '0.3125*pi^2*mu*cos((1/2)*x*pi) - 1.25*pi*rho*sin((1/2)*x*pi)*cos((1/2)*x*pi) + 0.8*cos(x)'
    vars = 'mu rho'
    vals = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    value = 'sin(x)'
  []
  [forcing_p]
    type = ParsedFunction
    value = '-1/2*pi*rho*sin((1/2)*x*pi)'
    vars = 'rho'
    vals = '${rho}'
  []
[]

[FVKernels]
  [mass]
    type = PINSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    vel = 'velocity'
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [mass_forcing]
    type = FVBodyForce
    variable = pressure
    function = forcing_p
  []

  [u_advection]
    type = PINSFVMomentumAdvection
    variable = u
    advected_quantity = 'rhou'
    vel = 'velocity'
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    pressure = pressure
    u = u
    mu = ${mu}
    rho = ${rho}
    porosity = porosity
  []
  [u_viscosity]
    type = PINSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    porosity = porosity
  []
  [u_pressure]
    type = PINSFVMomentumPressureFlux
    variable = u
    pressure = pressure
    porosity = porosity
    momentum_component = 'x'
  []
  [u_forcing]
    type = FVBodyForce
    variable = u
    function = forcing_u
  []
[]

[FVBCs]
  [inlet-u]
    type = INSFVInletVelocityBC
    boundary = 'left'
    variable = u
    function = 'exact_u'
  []
  [outlet_p]
    type = INSFVOutletPressureBC
    boundary = 'right'
    variable = pressure
    function = 'exact_p'
  []
[]

[Materials]
  [ins_fv]
    type = INSFVMaterial
    u = 'u'
    pressure = 'pressure'
    rho = ${rho}
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      100                lu           NONZERO'
  line_search = 'none'
[]

[Postprocessors]
  [inlet_p]
    type = SideAverageValue
    variable = 'pressure'
    boundary = 'left'
  []
  [outlet-u]
    type = SideIntegralVariablePostprocessor
    variable = u
    boundary = 'right'
  []
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

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INSFVPressureVariable

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