LinearFVAdvectionDiffusionExtrapolatedBC

Description

LinearFVAdvectionDiffusionExtrapolatedBC will contribute to the system matrix and right hand side of a linear finite volume system.

To approximate the boundary value ( $var element = document.getElementById("moose-equation-17faf5aa-f713-4273-b192-a16f3bea2fdd");katex.render("u_f", element, {displayMode:false,throwOnError:false});$ ) two different approaches are supported depending on the setting of the "use_two_term_expansion" parameter. When the two-term expansion is enabled the face value is approximated as:

var element = document.getElementById("moose-equation-47f6a685-9356-4294-a645-571884a6e9bf");katex.render("u_f = u_C + \\nabla u_C \\cdot \\vec{d}_{Cf}~,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-701b9890-8163-4c3d-b9ce-fdf8f034f5fc");katex.render("u_C", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-8e7c8bf1-51db-47c1-a5b1-e519a0a863b9");katex.render("\\nabla u_C", element, {displayMode:false,throwOnError:false});$ are the solution value and gradient in the boundary cell, while $var element = document.getElementById("moose-equation-45a64cfb-5c9d-4164-a78e-6042ab55ad13");katex.render("\\vec{d}_{Cf}", element, {displayMode:false,throwOnError:false});$ is the vector pointing to the face center from the boundary cell centroid. When "use_two_term_expansion" is disabled the following first-order approximation is used:

var element = document.getElementById("moose-equation-6ee9e3f7-cb9d-4243-bc18-8d09860aa3ec");katex.render("u_f = u_C.", element, {displayMode:true,throwOnError:false});

The contributions to the system matrix and right hand side resulting from the boundary value and the boundary normal gradient are computed accordingly.

note

This boundary condition should only be used for problems which involve advection and/or diffusion problems.

Example Syntax

[LinearFVBCs]
  [inflow]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "left top bottom"
    functor = analytic_solution
  []
  [outflow]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = u
    boundary = "right"
    use_two_term_expansion = false
  []
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
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

use_two_term_expansionFalseIf an approximate linear expansion should be used to compute the face value.
Default:False
C++ Type:bool
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Options:rhs, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form

Advanced Parameters

(moose/test/tests/linearfvkernels/advection/advection-2d.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny= 1
    ymax = 0.5
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

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

[LinearFVKernels]
  [advection]
    type = LinearFVAdvection
    variable = u
    velocity = "0.5 0 0"
    advected_interp_method = upwind
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inflow]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "left top bottom"
    functor = analytic_solution
  []
  [outflow]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = u
    boundary = "right"
    use_two_term_expansion = false
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = '0.5*pi*sin(2*y*pi)*cos(x*pi)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = 'sin(x*pi)*sin(2*y*pi) + 1.5'
  []
[]

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

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

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

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

Description
Example Syntax
Input Parameters