DiffusionFluxBC

Computes a boundary residual contribution consistent with the Diffusion Kernel. Does not impose a boundary condition; instead computes the boundary contribution corresponding to the current value of grad(u) and accumulates it in the residual vector.

Description

DiffusionFluxBC is a FluxBC which is appropriate for use with the boundary terms arising from the Diffusion Kernel. DiffusionFluxBC does not "enforce" a boundary condition per-se (see, e.g. DirichletBC, NeumannBC, and related classes for that). Instead, this class is responsible for computing the residual (and Jacobian) contributions due to the boundary contribution arising from integration by parts on the Diffusion Kernel.

note

The standard theory of elliptic operators requires the specification of boundary conditions on all parts of the boundary, so "implicitly" computing a residual contribution in this manner (instead of replacing it with the correct "data") falls outside of this theory. That said, there are instances where such an approach gives reasonable results in practice, see, for example, the paper by Griffiths (1997).

As an example, consider the Poisson problem with mixed boundary conditions: $var element = document.getElementById("moose-equation-46e913d4-43cf-42c1-8e4e-de7418440559");katex.render("\\begin{aligned} -\\nabla^2 u &= f && \\quad \\in \\Omega \\\\ u &= g && \\quad \\in \\partial \\Omega_D \\\\ \\frac{\\partial u}{\\partial n} &= h && \\quad \\in \\partial \\Omega_N, \\end{aligned}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-cf66f2be-e401-42b2-a3a8-b797eacf78fa");katex.render("\\Omega \\subset \\mathbb{R}^n", element, {displayMode:false,throwOnError:false});$ is the domain, and $var element = document.getElementById("moose-equation-c5a5f75d-7b41-4d9f-83bb-ec1739d1c8af");katex.render("\\partial \\Omega = \\partial \\Omega_D \\cup \\partial \\Omega_N \\cup \\partial \\Omega_F", element, {displayMode:false,throwOnError:false});$ is its boundary, and no boundary conditions are specified on $var element = document.getElementById("moose-equation-df562df9-ec85-496b-950c-25c52ef96dff");katex.render("\\partial \\Omega_F", element, {displayMode:false,throwOnError:false});$ . The weak formulation of this problem is: find $var element = document.getElementById("moose-equation-872a99b3-298e-4e10-b0f7-eda18681f19c");katex.render("u", element, {displayMode:false,throwOnError:false});$ satisfying the Dirichlet boundary conditions and such that $(1)var element = document.getElementById("moose-equation-f2349151-094d-45b1-9cf7-7b95487a2095");katex.render(" \\int_{\\Omega} \\left( \\nabla u \\cdot \\nabla v - fv \\right) \\,\\text{d}x -\\int_{\\partial \\Omega_N} hv \\,\\text{d}s -\\underbrace{\\int_{\\partial \\Omega_F} \\frac{\\partial u}{\\partial n} v \\,\\text{d}s}_{\\texttt{DiffusionFluxBC}} = 0", element, {displayMode:true,throwOnError:false});$ holds for every $var element = document.getElementById("moose-equation-dfd3b873-9be2-48ef-a4fc-8790381e4e84");katex.render("v \\in \\mathcal{V} = \\{v : v \\in H^1(\\Omega), v=0 \\text{ on } \\partial \\Omega_D \\}", element, {displayMode:false,throwOnError:false});$ , i.e. test functions that vanish on the Dirichlet boundary. The DiffusionFluxBC class would then be used to compute the last term in Eq. (1).

References

D. F. Griffiths. The `No Boundary Condition' outflow boundary condition. International Journal of Numerical Methods in Fluids, 24(4):393–411, 1997. URL: http://tinyurl.com/y77au2k.

@article{griffiths1997noboundary,
    author = "Griffiths, D. F.",
    title = "{The `No Boundary Condition' outflow boundary condition}",
    journal = "International Journal of Numerical Methods in Fluids",
    year = "1997",
    volume = "24",
    number = "4",
    pages = "393--411",
    url = "http://tinyurl.com/y77au2k"
}

Example Input Syntax

  [./all]
    type = DiffusionFluxBC
    variable = u
    boundary = '2 4 100 101'
  [../]

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 residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

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_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, 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.
diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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
save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

(moose/test/tests/mortar/continuity-2d-conforming/equalgradient.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-conf.e
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lmx]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]
  [./lmy]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]
[]

[ICs]
  [./block1]
    type = FunctionIC
    variable = u
    block = 1
    function = y
  [../]
  [./block2]
    type = FunctionIC
    variable = u
    block = 2
    function = y-0.5
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./dt]
    type = TimeDerivative
    variable = u
  [../]
[]

[Constraints]
  [./cedx]
    type = EqualGradientConstraint
    secondary_variable = u
    variable = lmx
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
    component = 0
  [../]
  [./cedy]
    type = EqualGradientConstraint
    secondary_variable = u
    variable = lmy
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
    component = 1
  [../]
[]

[BCs]
  [./all]
    type = DiffusionFluxBC
    variable = u
    boundary = '2 4 100 101'
  [../]
  [./boundary]
    type = DirichletBC
    boundary = 1
    variable = u
    value = 0.0
  [../]
  [./top]
    type = FunctionDirichletBC
    boundary = 3
    variable = u
    function = 0.5-t
  [../]
[]

[Preconditioning]
  [./fmp]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  nl_rel_tol = 1e-11
  l_tol = 1e-10
  l_max_its = 10
  dt = 0.05
  num_steps = 3
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

Description
References
Example Input Syntax
Input Parameters