LinearFVAdvectionDiffusionScalarSymmetryBC

Description

This object specifies a symmetry boundary condition for a diffusion equation:

$var element = document.getElementById("moose-equation-caea29a4-e7a4-4ede-a3f0-5df6975bce82");katex.render("\\vec{n}_b \\cdot D_b \\nabla u_b~ = 0.0.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where the $var element = document.getElementById("moose-equation-16a78c76-80ea-4f12-b664-6f50e1de5b53");katex.render("\\vec{n}_b", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the boundary normal unit vector and $var element = document.getElementById("moose-equation-37f7ebb7-b216-4902-83c4-aaa6b70c57ba");katex.render("D_b", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the diffusion coefficient at the boundary.

The face value for the advective terms and gradient computations can be computed with or without a linear extrapolation to the face:

$var element = document.getElementById("moose-equation-2011557b-84f0-4e72-8bb3-c9d822bddce7");katex.render("u_b = u_C + (\\vec{d}_{Cb}-(\\vec{d}_Cb \\cdot \\vec{n}_b)\\vec{n}_b)\\nabla u_C", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-e22ae2a3-f6d2-4125-9189-c556af868616");katex.render("\\vec{d}_{Cb}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the vector from the cell center to the boundary face center, while $var element = document.getElementById("moose-equation-6163d8cf-4c54-4255-9507-929b18ebcdae");katex.render("u_C", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-823acb3e-92ec-4c5d-90ea-2bc5f507a6a0");katex.render("\\nabla u_C", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denote the cell center and cell gradient values of $var element = document.getElementById("moose-equation-6742633c-5cbd-41cb-b284-5ce1fdfdcad2");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , respectively.

note

This boundary condition should only be applied to problems involving advection and/or diffusion.
In most cases symmetry boundary conditions don't have cross-flows on the symmetry boundaries. Even though the current formulation can be used with boundaries with flows, it is not recommended.
In its current formulation, the stencil achieves only first-order spatial convergence on meshes composed of triangles and tetrahedra.

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
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)
use_two_term_expansionFalseIf an approximate linear expansion should be used to compute the face value.
Default:False
C++ Type:bool
Controllable:No
Description:If an approximate linear expansion should be used to compute the face value.

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

(test/tests/linearfvkernels/diffusion/diffusion-2d-rz.i)
(test/tests/linearfvbcs/scalar_symmetry/advection-1d-symmetry.i)
(test/tests/linearfvbcs/scalar_symmetry/diffusion-1d-symmetry.i)
(test/tests/linearfvbcs/scalar_symmetry/advection-2d-symmetry.i)
(test/tests/linearfvbcs/scalar_symmetry/diffusion-2d-symmetry.i)

(test/tests/linearfvkernels/diffusion/diffusion-2d-rz.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 1
    ymax = 0.5
  []
  coord_type = RZ
  rz_coord_axis = Y
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 1.0
  []
[]

[LinearFVKernels]
  [diffusion]
    type = LinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func
    use_nonorthogonal_correction = true
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_func
  []
[]

[LinearFVBCs]
  [dir]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "right top bottom"
    functor = analytic_solution
  []
  [symmetry]
    type = LinearFVAdvectionDiffusionScalarSymmetryBC
    variable = u
    boundary = "left"
  []
[]

[Functions]
  [coeff_func]
    type = ParsedFunction
    expression = '1+0.5*x*y'
  []
  [source_func]
    type = ParsedFunction
    expression = '-(-1.0*x^2*y*(1.5 - x^2) + x*(1.5 - x^2)*(-1.0*x*y - 2))/x - (-1.0*x^2*y*(1.5 - y^2) - 4*x*(1.5 - y^2)*(0.5*x*y + 1))/x'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
[]

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

[Convergence]
  [linear]
    type = IterationCountConvergence
    max_iterations = 1
    converge_at_max_iterations = true
  []
[]

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

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [exo]
    type = Exodus
    execute_on = FINAL
  []
[]

(test/tests/linearfvbcs/scalar_symmetry/advection-1d-symmetry.i)

vel = 0.1

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim  = 1
    nx   = 2
    xmin = 0
    xmax = ${fparse pi}
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 1.0
  []
[]

[Functions]
  [u_exact]
    type = ParsedFunction
    expression = 'cos(x)'
  []
  [source_fn]
    type = ParsedFunction
    expression = '-${vel}*sin(x)'
  []
[]

[LinearFVKernels]
  [advection]
    type = LinearFVAdvection
    variable = u
    velocity = "${vel} 0 0"
    advected_interp_method = average
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_fn
  []
[]

[LinearFVBCs]
  [rob_l]
    type = LinearFVAdvectionDiffusionScalarSymmetryBC
    variable = u
    boundary = "left"
    use_two_term_expansion = true
  []
  [dirichlet]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "right"
    functor = u_exact
  []
[]

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

[Convergence]
  [linear]
    type = IterationCountConvergence
    max_iterations = 4
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-7
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-10'
  linear_convergence = linear
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
[]

(test/tests/linearfvbcs/scalar_symmetry/diffusion-1d-symmetry.i)

diff = 0.1

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim  = 1
    nx   = 2
    xmin = 0
    xmax = ${fparse pi}
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 1.0
  []
[]

[Functions]
  [u_exact]
    type = ParsedFunction
    expression = 'cos(x)'
  []
  [source_fn]
    type = ParsedFunction
    expression = '${diff}*cos(x)'
  []
[]

[LinearFVKernels]
  [advection]
    type = LinearFVDiffusion
    variable = u
    diffusion_coeff = ${diff}
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_fn
  []
[]

[LinearFVBCs]
  [rob_l]
    type = LinearFVAdvectionDiffusionScalarSymmetryBC
    variable = u
    boundary = "left"
    use_two_term_expansion = true
  []
  [dirichlet]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "right"
    functor = u_exact
  []
[]

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

[Convergence]
  [linear]
    type = IterationCountConvergence
    max_iterations = 4
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-7
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  linear_convergence = linear
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
[]

(test/tests/linearfvbcs/scalar_symmetry/advection-2d-symmetry.i)

vel_x = -0.1
two_term_bc=true

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    xmin = 0
    xmax = ${fparse pi/3}
    ymin = 0
    ymax = ${fparse pi/3}
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 0.02
  []
[]

[Functions]
  [u_exact]
    type = ParsedFunction
    expression = 'cos(x)*cos(y)'
  []
  [source_fn]
    type = ParsedFunction
    expression = '-${vel_x}*sin(x)*cos(y)'
  []
[]

[LinearFVKernels]
  [advection]
    type = LinearFVAdvection
    variable = u
    velocity = "${vel_x} 0 0"
    advected_interp_method = average
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_fn
  []
[]

[LinearFVBCs]
  [symm]
    type = LinearFVAdvectionDiffusionScalarSymmetryBC
    variable = u
    boundary = "bottom"
    use_two_term_expansion = ${two_term_bc}
  []
  [outflow]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = u
    boundary = "left"
    use_two_term_expansion = ${two_term_bc}
  []
  [dir]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "right top"
    functor = u_exact
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = 'TIMESTEP_END'
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = u_exact
    execute_on = 'TIMESTEP_END'
  []
[]

[Convergence]
  [linear]
    type = IterationCountConvergence
    max_iterations = 1
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-9
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-10'
  multi_system_fixed_point = true
  multi_system_fixed_point_convergence = linear
[]

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

(test/tests/linearfvbcs/scalar_symmetry/diffusion-2d-symmetry.i)

diff = 0.1 # diffusion coeff.

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim  = 2
    nx   = 2
    ny   = 2
    xmin = 0
    xmax = ${fparse pi/3}
    ymin = 0
    ymax = ${fparse pi/3}
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 0.0
  []
[]

[Functions]
  [u_exact]
    type = ParsedFunction
    expression = 'cos(x)*cos(y)'
  []
  [source_fn]
    type = ParsedFunction
    expression = '2*${diff}*cos(x)*cos(y)'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = LinearFVDiffusion
    variable = u
    diffusion_coeff = ${diff}
    use_nonorthogonal_correction = true
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_fn
  []
[]

[LinearFVBCs]
  [dir]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "right top"
    functor = u_exact
  []
  [symm]
    type = LinearFVAdvectionDiffusionScalarSymmetryBC
    variable = u
    boundary = "bottom left"
    use_two_term_expansion = true
  []
[]

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

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
[]

[Convergence]
  [linear]
    type = IterationCountConvergence
    max_iterations = 10
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-7
  multi_system_fixed_point = true
  multi_system_fixed_point_convergence = linear
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  linear_convergence = linear
[]

Description
Input Parameters
Input Files