LinearFVPressureFluxBC

Description

This pressure boundary condition is meant to be used with a LinearFVAdvectionDiffusionFunctorDirichletBC applied to the velocity field. It makes the boundary pressure flux consistent with the pressure Poisson equation and the prescribed boundary velocity. The $var element = document.getElementById("moose-equation-f918b512-59ee-47c6-b836-2f922c7c6b6c");katex.render("HbyA", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ flux supplied by RhieChowMassFlux includes the off-diagonal momentum contributions and every assembled non-pressure momentum source.

The boundary velocity functors "u", "v", and "w", together with the density functor "rho", define the prescribed normal mass flux that this boundary condition enforces:

$var element = document.getElementById("moose-equation-571a5458-9826-46a0-8a65-11d4b2a764e1");katex.render("(\\rho \\vec{u} \\cdot \\vec{n})_{bf} = -HbyA_{flux,bf} + (\\rho A^{-1} \\nabla p \\cdot \\vec{n})_{bf}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Anisotropic boundary reconstruction

The boundary condition supplies the complete signed pressure-diffusion flux to the diffusion kernel:

$var element = document.getElementById("moose-equation-1ee493af-0ae9-41ec-ad6f-61f59a937d0d");katex.render("g_{p,bf} = -\\left[HbyA_{flux,bf} + (\\rho \\vec{u} \\cdot \\vec{n})_{bf}\\right].", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Let $var element = document.getElementById("moose-equation-89b160fb-b4c5-4147-8d3d-8a4eef37c28d");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denote the diagonal pressure-diffusion tensor supplied through "Ainv", and let $var element = document.getElementById("moose-equation-11b5b68f-557b-4925-be25-7448bce3d747");katex.render("a_n=\\vec{n}^{T}D\\vec{n}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The normal $var element = document.getElementById("moose-equation-04e4406d-b1c9-4670-92c6-93cb7c6bafae");katex.render("\\vec{n}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ points outward from the cell on which the boundary condition acts. The complete tensor-weighted flux can be decomposed into normal and tangential pressure-gradient contributions:

$var element = document.getElementById("moose-equation-3a7f20e7-bcfc-499f-acdb-1bf3257bcc23");katex.render("g_{p,bf} = a_n \\frac{\\partial p}{\\partial n} + \\left[D\\vec{n} - a_n\\vec{n}\\right] \\cdot \\nabla p.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The boundary condition therefore reconstructs the boundary-normal pressure gradient as

$var element = document.getElementById("moose-equation-a375885b-4aa1-422a-874b-489c4cf9a093");katex.render("\\frac{\\partial p}{\\partial n} = \\frac{g_{p,bf} - \\left[D\\vec{n} - a_n\\vec{n}\\right] \\cdot \\nabla p}{a_n}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The bracketed vector is orthogonal to $var element = document.getElementById("moose-equation-4506a923-520d-49f2-a758-7ac9c3e22031");katex.render("\\vec{n}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , so its dot product contains only the tangential pressure-gradient contribution. This contribution is used only to recover the normal gradient; the kernel does not add it to $var element = document.getElementById("moose-equation-d6a1995e-be59-4ed2-9c6f-c52cf0196a08");katex.render("g_{p,bf}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ because the prescribed flux is already the complete tensor-weighted flux.

For the boundary value, let $var element = document.getElementById("moose-equation-54f340d6-572c-450c-b37e-f2c2e632386c");katex.render("\\vec{d}_{Cf}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ point from the boundary-cell centroid to the boundary face centroid and let $var element = document.getElementById("moose-equation-43f6ff6d-90b3-489b-a6dc-516427adaa68");katex.render("\\vec{d}_t=\\vec{d}_{Cf}-(\\vec{d}_{Cf}\\cdot\\vec{n})\\vec{n}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The reconstructed pressure is

$var element = document.getElementById("moose-equation-9f04165d-5493-4b3b-b517-5a1aad4f6bb3");katex.render("p_{bf} = p_C + |\\vec{d}_{Cf}\\cdot\\vec{n}|\\frac{\\partial p}{\\partial n} + \\vec{d}_t\\cdot\\nabla p.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The last term provides the geometric tangential correction on a nonorthogonal boundary cell. At startup, before momentum assembly has populated $var element = document.getElementById("moose-equation-9b6b2c42-d17b-4cef-a333-d37f225924c3");katex.render("A^{-1}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-0cf45c63-8983-4753-99f7-4536f912b410");katex.render("a_n", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is exactly zero. The boundary condition then uses the cell pressure as the boundary pressure and a zero normal gradient until a valid inverse momentum diagonal is available.

The reconstruction can be disabled explicitly by setting "use_two_term_expansion" to false. In that case, the boundary pressure is approximated by the adjacent cell pressure and the boundary-normal gradient used for reconstruction is zero. The complete pressure-diffusion flux imposed on the pressure equation is unchanged. This one-term option avoids division by $var element = document.getElementById("moose-equation-a24c280c-cce4-480c-b7fe-30666934a020");katex.render("a_n", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for configurations in which the boundary-normal inverse momentum coefficient may remain zero.

Input Parameters

AinvThe 1/A where A is the momentum system diagonal vector. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The 1/A where A is the momentum system diagonal vector. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
HbyA_fluxThe total HbyA face flux value. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The total HbyA face flux value. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
rhoThe density functor used together with the prescribed boundary velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The density functor used together with the prescribed boundary velocity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
uThe x-velocity functor on the boundary. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The x-velocity functor on the boundary. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
variableThe name of the variable that this boundary condition applies to
C++ Type:LinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this boundary condition applies to

Required Parameters

use_two_term_expansionTrueWhether to reconstruct the boundary pressure using the pressure flux and cell gradient. If false, the boundary pressure is approximated by the adjacent cell pressure.
Default:True
C++ Type:bool
Controllable:No
Description:Whether to reconstruct the boundary pressure using the pressure flux and cell gradient. If false, the boundary pressure is approximated by the adjacent cell pressure.
vThe y-velocity functor on the boundary. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The y-velocity functor on the boundary. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
wThe z-velocity functor on the boundary. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The z-velocity functor on the boundary. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsrhsThe tag for the vectors this Kernel should fill
Default:rhs
C++ Type:MultiMooseEnum
Options:rhs, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).

Advanced Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/ins/natural_convection/linear_segregated/2d/diff_heated_cavity_linear_segregated.i)
(modules/navier_stokes/test/tests/finite_volume/ins/linear_fv_pressure_flux_bc/internal-neighbor.i)
(modules/navier_stokes/test/tests/finite_volume/ins/linear_fv_pressure_flux_bc/errors.i)
(modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/linear-segregated/2d/2d-velocity-pressure.i)
(modules/navier_stokes/test/tests/finite_volume/ins/natural_convection/linear_segregated/2d/diff_heated_cavity_linear_buoyancy.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex/2d-symmetric-vortex.i)

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

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

walls = 'right left top bottom'

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

  continue_on_max_its = true
[]

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

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

(modules/navier_stokes/test/tests/finite_volume/ins/linear_fv_pressure_flux_bc/internal-neighbor.i)

# Unit properties and speed give the exact constant plug-flow solution used by the CSV comparisons.
mu = 1
rho = 1
flow_block = 2
inlet_speed = 1

[Mesh]
  [blocks]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1'
    dy = '1'
    ix = '1 2'
    iy = '1'
    subdomain_id = '1 ${flow_block}'
  []
  [internal_inlet]
    type = SideSetsBetweenSubdomainsGenerator
    input = blocks
    primary_block = ${flow_block}
    paired_block = 1
    new_boundary = internal_inlet
  []
  [delete_inlet_block]
    type = BlockDeletionGenerator
    input = internal_inlet
    block = 1
  []
[]

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

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

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = ${inlet_speed}
    solver_sys = u_system
    block = ${flow_block}
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    solver_sys = v_system
    block = ${flow_block}
  []
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
    block = ${flow_block}
  []
[]

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

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

[LinearFVBCs]
  [prescribed-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'internal_inlet top bottom'
    variable = vel_x
    functor = ${inlet_speed}
  []
  [prescribed-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'internal_inlet top bottom'
    variable = vel_y
    functor = 0
  []
  [pressure-flux]
    type = LinearFVPressureFluxBC
    boundary = 'internal_inlet top bottom'
    variable = pressure
    HbyA_flux = HbyA
    Ainv = Ainv
    u = vel_x
    v = vel_y
    rho = ${rho}
  []
  [outlet-pressure]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = right
    variable = pressure
    functor = 0
  []
  [outlet-u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet-v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

[Functions]
  [exact-u]
    type = ParsedFunction
    expression = ${inlet_speed}
  []
  [exact-zero]
    type = ParsedFunction
    expression = 0
  []
[]

[Postprocessors]
  [inlet-mass-flow]
    type = VolumetricFlowRate
    boundary = internal_inlet
    vel_x = vel_x
    vel_y = vel_y
    advected_quantity = ${rho}
    rhie_chow_user_object = rc
  []
  [u-error]
    type = ElementL2FunctorError
    approximate = vel_x
    exact = exact-u
    block = ${flow_block}
  []
  [v-error]
    type = ElementL2FunctorError
    approximate = vel_y
    exact = exact-zero
    block = ${flow_block}
  []
  [pressure-error]
    type = ElementL2FunctorError
    approximate = pressure
    exact = exact-zero
    block = ${flow_block}
  []
[]

[Executioner]
  type = SIMPLE
  # Tight algebraic tolerances make the reported errors sensitive to the internal-boundary sign.
  momentum_l_abs_tol = 1e-12
  pressure_l_abs_tol = 1e-12
  momentum_l_tol = 0
  pressure_l_tol = 0
  rhie_chow_user_object = rc
  momentum_systems = 'u_system v_system'
  pressure_system = pressure_system
  # These standard SIMPLE relaxation factors provide stable convergence for the tiny test mesh.
  momentum_equation_relaxation = 0.8
  pressure_variable_relaxation = 0.3
  # Fifty iterations is a conservative cap; the exact initialized solution converges much sooner.
  num_iterations = 50
  # These nonlinear tolerances keep the final CSV errors below the comparison threshold.
  pressure_absolute_tolerance = 1e-10
  momentum_absolute_tolerance = 1e-10
  momentum_petsc_options_iname = '-pc_type'
  momentum_petsc_options_value = 'lu'
  pressure_petsc_options_iname = '-pc_type'
  pressure_petsc_options_value = 'lu'
  print_fields = false
[]

[Outputs]
  csv = true
  execute_on = FINAL
[]

(modules/navier_stokes/test/tests/finite_volume/ins/linear_fv_pressure_flux_bc/errors.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
  []
[]

[Problem]
  linear_sys_names = pressure_system
[]

[Variables]
  [pressure]
    type = MooseLinearVariableFVReal
    solver_sys = pressure_system
  []
[]

[LinearFVKernels]
  [diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
  []
[]

[LinearFVBCs]
  active = pressure_flux
  [pressure_flux]
    type = LinearFVPressureFluxBC
    variable = pressure
    boundary = left
    HbyA_flux = 0
    Ainv = Ainv
    u = 0
    rho = 1
  []
[]

[FunctorMaterials]
  [inverse_diagonal]
    type = GenericVectorFunctorMaterial
    prop_names = Ainv
    prop_values = '1 1 1'
  []
[]

[Executioner]
  type = Steady
  system_names = pressure_system
[]

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

mu = 2.6
rho = 1.0
advected_interp_method = 'average'

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

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

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

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

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

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

[LinearFVBCs]
  inactive = 'inlet_and_wall_pressure_flux'

  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '1.1'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top bottom'
    variable = vel_y
    functor = 0.0
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 1.4
  []
  [inlet_and_wall_pressure_flux]
    type = LinearFVPressureFluxBC
    boundary = 'left top bottom'
    variable = pressure
    HbyA_flux = HbyA
    Ainv = Ainv
    u = vel_x
    v = vel_y
    rho = ${rho}
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_x
    use_two_term_expansion = false
    boundary = right
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = vel_y
    use_two_term_expansion = false
    boundary = right
  []
[]

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

[Outputs]
  exodus = true
[]

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

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

walls = 'right left top bottom'

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  continue_on_max_its = true
[]

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

[Outputs]
  exodus = true
[]

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

mu = 1.2
rho = 1.5
advected_interp_method = 'average'

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

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

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

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

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

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

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

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

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

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

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

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

Description
Anisotropic boundary reconstruction
Input Parameters
Input Files