LinearFVVelocitySymmetryBC

Description

LinearFVVelocitySymmetryBC mirrors the segregated momentum solution at a symmetry plane for linear finite-volume velocity variables. The boundary value is obtained by reflecting the cell-centered velocity across the symmetry normal, removing the normal component while preserving the tangential components. This provides the classical symmetry condition of zero normal velocity together with a zero-gradient tangential velocity, making the operator consistent with the linearised momentum fluxes used by SIMPLE-like algorithms. The implementation is based on the methodology in Greenshields and Weller (2022).

Let $var element = document.getElementById("moose-equation-aecc16a8-cdd8-4293-af4e-a34f91f8194f");katex.render("\\mathbf{u}_P", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denote the cell-center velocity adjacent to the face with unit normal $var element = document.getElementById("moose-equation-9394a845-36d0-4d13-b946-71dc16aa1ebf");katex.render("\\mathbf{n}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The boundary condition projects out the normal contribution,

$var element = document.getElementById("moose-equation-34fd6d5e-edfa-47ae-b1e6-1cf224be2699");katex.render("\\mathbf{u}_f = \\mathbf{u}_P - (\\mathbf{u}_P \\cdot \\mathbf{n}) \\mathbf{n},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

which enforces $ \mathbf{u}_f \cdot \mathbf{n} = 0$ while keeping the tangential velocity from the cell.

The object couples to the momentum component being solved. The parameter "momentum_component" selects which velocity equation the boundary condition contributes to, and the velocity components must be supplied through "u", "v", and "w". Only the velocity components present in the problem dimension are required.

This boundary condition is typically paired with the momentum flux kernel LinearWCNSFVMomentumFlux and LinearFVPressureSymmetryBC on symmetry planes of channel flows, as demonstrated in:

note

The current approximation of the face value assumes that the face centroid is close to the point where the line from the cell center in the normal direction intersects the face. This means that on unstructured meshes, this results a spatially first-order discretization.

[LinearFVBCs<<<{"href": "../../syntax/LinearFVBCs/index.html"}>>>]
  [symmetry-u]
    type = LinearFVVelocitySymmetryBC<<<{"description": "Adds a symmetry boundary condition for the velocity.", "href": "LinearFVVelocitySymmetryBC.html"}>>>
    variable<<<{"description": "The name of the variable that this boundary condition applies to"}>>> = vel_x
    momentum_component<<<{"description": "The component of the momentum equation that this kernel applies to."}>>> = x
    u<<<{"description": "The velocity in the x direction."}>>> = vel_x
    v<<<{"description": "The velocity in the y direction."}>>> = vel_y
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'bottom'
  []
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
momentum_componentThe component of the momentum equation that this kernel applies to.
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:The component of the momentum equation that this kernel applies to.
uThe velocity in the x direction.
C++ Type:SolverVariableName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the x direction.
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

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)
vThe velocity in the y direction.
C++ Type:SolverVariableName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the y direction.
wThe velocity in the z direction.
C++ Type:SolverVariableName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the z direction.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_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/channel-flow/linear-segregated/2d-symmetric/channel.i)
(modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated/channel_ERCOFTAC_symmetric.i)
(modules/navier_stokes/test/tests/finite_volume/ins/mms/linear-segregated/2d-symmetric-vortex/2d-symmetric-vortex.i)

References

Christopher Greenshields and Henry Weller. Notes on Computational Fluid Dynamics: General Principles. CFD Direct Ltd, Reading, UK, 2022.

@book{greenshieldsweller2022,
    author = "Greenshields, Christopher and Weller, Henry",
    title = "Notes on Computational Fluid Dynamics: General Principles",
    year = "2022",
    publisher = "CFD Direct Ltd",
    address = "Reading, UK"
}

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

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

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

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

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

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

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method = ${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 = ${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 = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

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

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

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

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

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

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

[Outputs]
  csv = true
  execute_on = timestep_end
[]

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

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

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

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

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

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

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method = ${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 = ${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 = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []
[]

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

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

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

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

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

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

[Outputs]
  csv = true
  execute_on = timestep_end
[]

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

H = 1 #halfwidth of the channel
L = 100

Re = 13700

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

advected_interp_method = 'upwind'

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[Executioner]
  type = SIMPLE

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

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

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

  print_fields = false
  continue_on_max_its = true
[]

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

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

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

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

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

mu = 1.2
rho = 1.5
advected_interp_method = 'average'

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

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

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

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

[LinearFVKernels]
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method = ${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 = ${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 = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = 'Ainv' # Functor created in the RhieChowMassFlux UO
    use_nonorthogonal_correction = false
    use_nonorthogonal_correction_on_boundary = false
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = 'HbyA' # Functor created in the RhieChowMassFlux UO
    force_boundary_execution = true
  []
[]

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

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

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

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

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

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

Description
Input Parameters
Input Files
References