Issue Running Axisymmetric Case with k-epsilon Model and linear finite volume discretization

[Scarafia99]

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Question

Hi everyone,

I read in the MOOSE Newsletter (July 2025) that the standard k-epsilon turbulence model was implemented for the linear finite volume approach. I was excited to try out this new capability on an axisymmetric problem.

I successfully ran my real case using Cartesian (xy) coordinates without any issues. However, when switching to axisymmetric (rz) coordinates, the simulation diverged.

To investigate further, I modified the ERCOFTAC test case that was used to validate the axisymmetric implementation, but unfortunately, that also failed to run properly.

At this point, I'm not sure whether the current implementation supports axisymmetric cases with the k-epsilon model, or if I'm missing something in the setup.

I'd really appreciate any tips or guidance on this issue. Thank you so much for your time!

Below is the input file I used:

H = 1 #halfwidth of the channel
L = 100

Re = 13700

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

advected_interp_method = 'upwind'

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

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

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

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

[Problem]
  type = FEProblem
  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_time]
    type = LinearFVTimeDerivative
    variable = vel_x
    factor = ${rho}
  []
  [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 = true
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_time]
    type = LinearFVTimeDerivative
    variable = vel_y
    factor = ${rho}
  []
  [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 = true
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []

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

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

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

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = vel_y
    functor = 0.0
  []
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []
  # symmetry BCs
  [vel_y_symmetry]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'bottom'
    functor = '0'
    variable = vel_y
  []
  [vel_x_symmetry]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'bottom'
    functor = '0'
    variable = vel_x
  []
  [pressure_symmetry]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'bottom'
    functor = '0'
    variable = pressure
  []
  [TKED_symmetry]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'bottom'
    functor = '0'
    variable = TKED
  []
  [TKE_symmetry]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'bottom'
    functor = '0'
    variable = TKE
  []

  [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 = 'top'
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
[]

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

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

[Executioner]
  type = PIMPLE

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

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

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

  print_fields = false
  continue_on_max_its = true
  dt = 1.0
  num_steps = 4
[]

[Outputs]
  csv = true
  exodus = true
[]

Additional information

Reynolds number: 13700
Discretization (finite element CG/DG, finite volume, etc): finite volume
Models (turbulence, porous media, etc): k-epsilon
Solver method (fully coupled, segregated, multiapps, etc): [linear-segregated-transient]
Base input you started from: channel_ERCOFTAC (https://github.com/idaholab/moose/tree/next/modules/navier_stokes/test/tests/finite_volume/ins/turbulence/channel/linear-segregated-transient)

[GiudGiud]

hello

We have not worked on that. For 2D and 2D-RZ work, the Newton-FV works fine for us.

Can you simulate a 3D pipe? This solver is fast enough for 3D

[GiudGiud]

mind sharing the 3D input? we can look at that, that should work
2D-RZ I think there might be development to do, I m not sure

[Scarafia99]

Hi, I've included the input file I used below. I managed to get it working by reducing the turbulence intensity. However, I'm concerned about the computational cost in a real complex case .

I'm exploring whether a strategy similar to what’s used in OpenFOAM could be applied in MOOSE for axisymmetric simulations. Instead of rotating the 2D geometry a full 360 degrees—which greatly increases computational expense—I’m considering rotating it only 1 to 6 degrees and adding a single cell in the theta direction to create a 3D model.

Would this approach be feasible in MOOSE?

thanks you so much for your time

# command to run it
# mpirun --allow-run-as-root -n 10 moose-opt -i coolant_3D.i --no-color > output.log &

H = 1 #halfwidth of the channel
L = 100

Re = 13700

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

advected_interp_method = 'upwind'

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

### Initial and Boundary Conditions ###
intensity = 0.001 #0.01
k_init = '${fparse 1.5*(intensity * bulk_u)^2}'
eps_init = '${fparse C_mu^0.75 * k_init^1.5 / (2*H)}'

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

[Mesh]

  # parece que no funciona en coordenas cilindricas!!!
  # tendria que usar el mesh 3D que funciona en openFoam
  [block_1]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${L}
    ymin = 0
    ymax = ${H}
    nx = 4
    ny = 3
    bias_y = 0.7
  []
  [rg]
    type = RevolveGenerator
    input = block_1
    axis_point = '0.0 0.0 0.0'
    axis_direction = '1.0 0.0 0.0'
    nums_azimuthal_intervals = 30
    revolving_angles = 360
  []
  allow_renumbering = true
[]

[Problem]

  type = FEProblem
  linear_sys_names = 'u_system v_system w_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
    w = vel_z
    pressure = pressure
    rho = ${rho}
    p_diffusion_kernel = p_diffusion
  []
[]

[Variables]
  [vel_x]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = u_system
  []
  [vel_y]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = v_system
  []
  [vel_z]
    type = MooseLinearVariableFVReal
    initial_condition = 1e-8
    solver_sys = w_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_time]
    type = LinearFVTimeDerivative
    variable = vel_x
    factor = ${rho}
  []
  [u_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_x
    advected_interp_method = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'x'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true #false
    use_deviatoric_terms = yes
  []
  [u_diffusion]
    type = LinearFVDiffusion
    variable = vel_x
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [u_pressure]
    type = LinearFVMomentumPressure
    variable = vel_x
    pressure = pressure
    momentum_component = 'x'
  []

  [v_time]
    type = LinearFVTimeDerivative
    variable = vel_y
    factor = ${rho}
  []
  [v_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_y
    advected_interp_method = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'y'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
    use_deviatoric_terms = yes
  []
  [v_diffusion]
    type = LinearFVDiffusion
    variable = vel_y
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [v_pressure]
    type = LinearFVMomentumPressure
    variable = vel_y
    pressure = pressure
    momentum_component = 'y'
  []
  [w_time]
    type = LinearFVTimeDerivative
    variable = vel_z
    factor = ${rho}
  []
  [w_advection_stress]
    type = LinearWCNSFVMomentumFlux
    variable = vel_z
    advected_interp_method = ${advected_interp_method}
    mu = 'mu_t'
    u = vel_x
    v = vel_y
    w = vel_z
    momentum_component = 'z'
    rhie_chow_user_object = 'rc'
    use_nonorthogonal_correction = true
    use_deviatoric_terms = yes
  []
  [w_diffusion]
    type = LinearFVDiffusion
    variable = vel_z
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [w_pressure]
    type = LinearFVMomentumPressure
    variable = vel_z
    pressure = pressure
    momentum_component = 'z'
  []
  [p_diffusion]
    type = LinearFVAnisotropicDiffusion
    variable = pressure
    diffusion_tensor = Ainv
    use_nonorthogonal_correction = true
  []
  [HbyA_divergence]
    type = LinearFVDivergence
    variable = pressure
    face_flux = HbyA
    force_boundary_execution = true
  []

  [TKE_time]
    type = LinearFVTimeDerivative
    variable = TKE
    factor = ${rho}
  []
  [TKE_advection]
    type = LinearFVTurbulentAdvection
    variable = TKE
  []
  [TKE_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
  []
  [TKE_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKE
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_k}
    use_nonorthogonal_correction = true
  []
  [TKE_source_sink]
    type = LinearFVTKESourceSink
    variable = TKE
    u = vel_x
    v = vel_y
    w = vel_z
    epsilon = TKED
    rho = ${rho}
    mu = ${mu}
    mu_t = 'mu_t'
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    C_pl = 50 # 1e10
  []

  [TKED_time]
    type = LinearFVTimeDerivative
    variable = TKED
    factor = ${rho}
  []
  [TKED_advection]
    type = LinearFVTurbulentAdvection
    variable = TKED
    walls = ${walls}
  []
  [TKED_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = ${mu}
    use_nonorthogonal_correction = true
    walls = ${walls}
  []
  [TKED_turb_diffusion]
    type = LinearFVTurbulentDiffusion
    variable = TKED
    diffusion_coeff = 'mu_t'
    scaling_coeff = ${sigma_eps}
    use_nonorthogonal_correction = true
    walls = ${walls}
  []
  [TKED_source_sink]
    type = LinearFVTKEDSourceSink
    variable = TKED
    u = vel_x
    v = vel_y
    w = vel_z
    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 = 50 # 1e10
  []
[]

[LinearFVBCs]
  [inlet-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_x
    functor = '${bulk_u}'
  []
  [inlet-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_y
    functor = '0.0'
  []
  [inlet-w]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = vel_z
    functor = '0'
  []
  [inlet_TKE]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKE
    functor = '${k_init}'
  []
  [inlet_TKED]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'left'
    variable = TKED
    functor = '${eps_init}'
  []

  [walls-u]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = vel_x
    functor = 0.0
  []
  [walls-v]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = vel_y
    functor = 0.0
  []
  [walls-w]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'top'
    variable = vel_z
    functor = 0.0
  []
  [walls_p]
    type = LinearFVAdvectionDiffusionFunctorNeumannBC
    boundary = 'top'
    variable = pressure
    functor = '0'
  []

  [walls_mu_t]
    type = LinearFVTurbulentViscosityWallFunctionBC
    boundary = 'top'
    variable = 'mu_t'
    u = vel_x
    v = vel_y
    w = vel_z
    rho = ${rho}
    mu = ${mu}
    tke = TKE
    wall_treatment = ${wall_treatment}
  []
  # # outlet conditions
  [outlet_u]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_x
    use_two_term_expansion = false
  []
  [outlet_v]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_y
    use_two_term_expansion = false
  []
  [outlet_w]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = vel_z
    use_two_term_expansion = false
  []
  [outlet_p]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    boundary = 'right'
    variable = pressure
    functor = 0.0
  []
  [outlet_TKE]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKE
    use_two_term_expansion = false
  []
  [outlet_TKED]
    type = LinearFVAdvectionDiffusionOutflowBC
    boundary = 'right'
    variable = TKED
    use_two_term_expansion = false
  []
[]

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

[AuxKernels]
  [compute_mu_t]
    type = kEpsilonViscosityAux
    variable = mu_t
    C_mu = ${C_mu}
    tke = TKE
    epsilon = TKED
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    w = vel_z
    bulk_wall_treatment = ${bulk_wall_treatment}
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
    mu_t_ratio_max = 50
  []
  [compute_y_plus]
    type = RANSYPlusAux
    variable = yplus
    tke = TKE
    mu = ${mu}
    rho = ${rho}
    u = vel_x
    v = vel_y
    w = vel_z
    walls = ${walls}
    wall_treatment = ${wall_treatment}
    execute_on = 'NONLINEAR'
  []
  [compute_mu_eff]
    type = ParsedAux
    variable = 'mu_eff'
    coupled_variables = 'mu_t'
    expression = 'mu_t + ${mu}'
    execute_on = 'NONLINEAR'
  []
[]

[Executioner]
  type = PIMPLE

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

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

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

  print_fields = false
  continue_on_max_its = true
  dt = 1.0
  num_steps = 4
[]

[Outputs]
  csv = true
  exodus = true
[]

[Postprocessors]
  [k_max]
    type = ElementExtremeValue
    variable = TKE
  []
  [k_min]
    type = ElementExtremeValue
    variable = TKE
    value_type = min
  []
  [eps_max]
    type = ElementExtremeValue
    variable = TKED
  []
  [eps_min]
    type = ElementExtremeValue
    variable = TKED
    value_type = min
  []
  [mut_max]
    type = ElementExtremeValue
    variable = mu_t
  []
  [mut_min]
    type = ElementExtremeValue
    variable = mu_t
    value_type = min
  []
[]

[GiudGiud]

Thanks I ll take a look

Would this approach be feasible in MOOSE?

It could with reflective BCs. Periodic BCs are not set up for linear FV but would not too be hard for this case i think since it's a single cell in theta.
But that is another thing that is not within our current scope of work. So we likely won't be developing these BCs for you.

[grmnptr]

Oh yes, we don't have symmetry BCs yet for linearFV. However, I have some time next week to add them.
If you want to keep track of the progress just visit this guy:
#27756

[Scarafia99]

Thanks you so much @grmnptr , @GiudGiud . I appreciate it