LinearFVAdvectionDiffusionOutflowBC

Description

LinearFVAdvectionDiffusionOutflowBC will contribute to the system matrix and right hand side of a linear finite volume system. The contributions can be derived using the integral of the advective flux over a boundary face ( $var element = document.getElementById("moose-equation-0e01714b-c979-4130-bf04-d6583cc53034");katex.render("S_b", element, {displayMode:false,throwOnError:false});$ ) of a boundary element:

var element = document.getElementById("moose-equation-5dee9191-b071-447a-acd8-eec4dc068c33");katex.render("\\int\\limits_{S_b} \\vec{v} \\cdot \\vec{n} u dS \\approx \\vec{v}_f \\cdot \\vec{n} u_f |S_b|~,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-ca2c7738-cb8d-4eeb-8268-988547f0f830");katex.render("\\vec{v}_f", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-0b2e06f7-ce08-4261-8892-127146802742");katex.render("\\vec{n}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-d42aa575-048e-411c-957d-6726ac474b03");katex.render("|S_b|", element, {displayMode:false,throwOnError:false});$ are the outlet face velocity, outward pointing surface vector and the surface area,

The value of $var element = document.getElementById("moose-equation-30d75475-f6e0-49ed-bf47-3da37fa1cdb2");katex.render("u_f", element, {displayMode:false,throwOnError:false});$ can be computed two different ways 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-13ff68ae-d437-4c58-b03d-261be3257506");katex.render("u_f = u_C + \\nabla u_C \\cdot \\vec{d}_{Cf}~,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-936f4daf-7442-4000-adc7-8a7d5a772525");katex.render("u_C", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-9aa841aa-45fb-4f3c-8e5a-0654f23cb62b");katex.render("\\nabla u_C", element, {displayMode:false,throwOnError:false});$ are the solution value and gradient in the boundary cell, while $var element = document.getElementById("moose-equation-1143f8b4-92bd-4809-851e-e441e3a92e38");katex.render("\\vec{d}_{Cf}", element, {displayMode:false,throwOnError:false});$ 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-d69e4ae0-78fc-41ad-8020-8f26a709438c");katex.render("u_f = u_C.", element, {displayMode:true,throwOnError:false});

This boundary condition assumes zero normal gradient contribution to the diffusion terms.

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