KokkosLinearFVFunctorNeumannBC

This object provides prescribed outward normal gradient data for Kokkos linear finite volume kernels. The outward normal gradient is supplied through a KokkosParsedFunction via the "functor" parameter.

The primitive relation supplied by this BC is

var element = document.getElementById("moose-equation-299afbaa-746a-4c7b-aa21-055a07d50867");katex.render("\\nabla_n u = g", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-25be0831-c5f2-4967-84ca-8c7ffb71766a");katex.render("g", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the prescribed outward normal gradient. Kernels apply their own physics coefficients when consuming this relation; for example, a diffusion kernel multiplies by its diffusion coefficient and face area. This BC therefore prescribes a normal gradient, not a total diffusive flux.

For kernels that need a boundary value, this object also supplies the orthogonal extrapolation

var element = document.getElementById("moose-equation-9c000f53-94e5-49ff-87d1-272c684e936e");katex.render("u_b = u_C + g d_{Cf}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-a42d99f1-f53c-4b87-986c-5f81b8b497f3");katex.render("u_C", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the cell value and $var element = document.getElementById("moose-equation-63faaa4a-2b7b-4d1c-a37d-fadcc1394484");katex.render("d_{Cf}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the cell-center-to-face-center distance.

Example Syntax

[LinearFVBCs<<<{"href": "../../../syntax/LinearFVBCs/index.html"}>>>]
  [dirichlet_lr]
    type = KokkosLinearFVFunctorDirichletBC<<<{"description": "Kokkos LinearFV Dirichlet boundary condition.", "href": "KokkosLinearFVFunctorDirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable this boundary condition supplies data for"}>>> = u
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left right'
    functor<<<{"description": "The boundary-value functor."}>>> = analytic_solution_kokkos
  []
  [neumann_bottom]
    type = KokkosLinearFVFunctorNeumannBC<<<{"description": "Kokkos LinearFV Neumann boundary condition.", "href": "KokkosLinearFVFunctorNeumannBC.html"}>>>
    variable<<<{"description": "The name of the variable this boundary condition supplies data for"}>>> = u
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'bottom'
    functor<<<{"description": "The prescribed outward normal gradient functor on the boundary."}>>> = neumann_bottom_gradient
  []
  [neumann_top]
    type = KokkosLinearFVFunctorNeumannBC<<<{"description": "Kokkos LinearFV Neumann boundary condition.", "href": "KokkosLinearFVFunctorNeumannBC.html"}>>>
    variable<<<{"description": "The name of the variable this boundary condition supplies data for"}>>> = u
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'top'
    functor<<<{"description": "The prescribed outward normal gradient functor on the boundary."}>>> = neumann_top_gradient
  []
[]

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
functorThe prescribed outward normal gradient functor on the boundary.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The prescribed outward normal gradient functor on the boundary.
variableThe name of the variable this boundary condition supplies data for
C++ Type:LinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable this boundary condition supplies data for

Required 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

Advanced Parameters

Input Files

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-internal-neumann.i)
(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-neumann.i)
(test/tests/kokkos/linearfvkernels/advection-diffusion/kokkos_advection_diffusion-1d.i)

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-neumann.i)

# 2D diffusion MMS test with mixed Dirichlet (left/right) and Neumann (top/bottom) BCs.
# Exact solution:  u = (1.5 - x^2)(1.5 - y^2)
# Diffusion coeff: D = 1 + 0.5*x*y
# Neumann normal gradient on bottom (n = -y): -du/dy|_{y=0} = 0  (du/dy = 0 at y=0)
# Neumann normal gradient on top   (n = +y):  du/dy|_{y=ymax}

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    ymax = 0.5
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [dirichlet_lr]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = 'left right'
    functor = analytic_solution_kokkos
  []
  [neumann_bottom]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = 'bottom'
    functor = neumann_bottom_gradient
  []
  [neumann_top]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = 'top'
    functor = neumann_top_gradient
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [coeff_func_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + 0.5*x*y'
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = '2*(1.5-y*y) + 2*x*y*(1.5-y*y) + 2*(1.5-x*x) + 2*x*y*(1.5-x*x)'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  # Outward normal gradient on bottom (n = -y): -du/dy|_{y=0} = 0
  [neumann_bottom_gradient]
    type = KokkosParsedFunction
    expression = 0.0
  []
  # Outward normal gradient on top (n = +y): du/dy|_{y=ymax}
  # du/dy = (1.5-x^2)*(-2*ymax)
  [neumann_top_gradient]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(-2.0*0.5)'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-internal-neumann.i)

# 2D diffusion MMS test with Neumann normal-gradient BCs on internal block boundaries.
# Exact solution:  u = v = 1.5 - x^2
# Diffusion coeff: D = 1 + 0.5*x*y

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.5 0.5'
    ix = '2 2'
    dy = '0.5'
    iy = '2'
    subdomain_id = '1 2'
  []
  [left_internal]
    type = SideSetsBetweenSubdomainsGenerator
    input = cmg
    new_boundary = left_internal
    primary_block = 1
    paired_block = 2
  []
  [right_internal]
    type = SideSetsBetweenSubdomainsGenerator
    input = left_internal
    new_boundary = right_internal
    primary_block = 2
    paired_block = 1
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    block = 1
  []
  [v]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    block = 2
  []
[]

[LinearFVKernels]
  [diffusion_left]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
    block = 1
  []
  [source_left]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
    block = 1
  []
  [diffusion_right]
    type = KokkosLinearFVDiffusion
    variable = v
    diffusion_coeff = coeff_func_kokkos
    block = 2
  []
  [source_right]
    type = KokkosLinearFVSource
    variable = v
    source_density = source_func_kokkos
    scaling_factor = unit_fn
    block = 2
  []
[]

[LinearFVBCs]
  [dirichlet_left]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = left
    functor = analytic_solution_kokkos
  []
  [neumann_left_internal]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = left_internal
    functor = left_internal_gradient
  []
  [dirichlet_right]
    type = KokkosLinearFVFunctorDirichletBC
    variable = v
    boundary = right
    functor = analytic_solution_kokkos
  []
  [neumann_right_internal]
    type = KokkosLinearFVFunctorNeumannBC
    variable = v
    boundary = right_internal
    functor = right_internal_gradient
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [coeff_func_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + 0.5*x*y'
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = '2.0 + 2.0*x*y'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '1.5 - x*x'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '1.5 - x*x'
  []
  [left_internal_gradient]
    type = KokkosParsedFunction
    expression = '-1.0'
  []
  [right_internal_gradient]
    type = KokkosParsedFunction
    expression = '1.0'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [left_error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
    block = 1
  []
  [right_error]
    type = ElementL2FunctorError
    approximate = v
    exact = analytic_solution
    execute_on = FINAL
    block = 2
  []
  [error]
    type = ParsedPostprocessor
    expression = 'sqrt(left*left + right*right)'
    pp_names = 'left_error right_error'
    pp_symbols = 'left right'
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-neumann.i)

# 2D diffusion MMS test with mixed Dirichlet (left/right) and Neumann (top/bottom) BCs.
# Exact solution:  u = (1.5 - x^2)(1.5 - y^2)
# Diffusion coeff: D = 1 + 0.5*x*y
# Neumann normal gradient on bottom (n = -y): -du/dy|_{y=0} = 0  (du/dy = 0 at y=0)
# Neumann normal gradient on top   (n = +y):  du/dy|_{y=ymax}

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    ymax = 0.5
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [dirichlet_lr]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = 'left right'
    functor = analytic_solution_kokkos
  []
  [neumann_bottom]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = 'bottom'
    functor = neumann_bottom_gradient
  []
  [neumann_top]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = 'top'
    functor = neumann_top_gradient
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [coeff_func_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + 0.5*x*y'
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = '2*(1.5-y*y) + 2*x*y*(1.5-y*y) + 2*(1.5-x*x) + 2*x*y*(1.5-x*x)'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  # Outward normal gradient on bottom (n = -y): -du/dy|_{y=0} = 0
  [neumann_bottom_gradient]
    type = KokkosParsedFunction
    expression = 0.0
  []
  # Outward normal gradient on top (n = +y): du/dy|_{y=ymax}
  # du/dy = (1.5-x^2)*(-2*ymax)
  [neumann_top_gradient]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(-2.0*0.5)'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/linearfvkernels/advection-diffusion/kokkos_advection_diffusion-1d.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 2
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [advection]
    type = KokkosLinearFVAdvection
    variable = u
    velocity = '0.5 0 0'
  []
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = unit_fn
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [inflow]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = left
    functor = analytic_solution_kokkos
  []
  [outflow]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = right
    functor = zero_fn
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [zero_fn]
    type = KokkosParsedFunction
    expression = 0.0
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = 'x - 3.0'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + (1.0 - x) * (1.0 - x)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '1.0 + (1.0 - x) * (1.0 - x)'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -pc_factor_mat_solver_type -mat_mumps_icntl_14'
  petsc_options_value = 'lu       NONZERO               1e-12                     mumps                    50'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

Example Syntax
Input Parameters
Input Files