ArrayDGDiffusion

Description

This array DG (discontinuous Galerkin) kernel implements the following piece of a weak form:

$var element = document.getElementById("moose-equation-8b82ab00-1a17-450b-ba28-403c16d7e407");katex.render("\\left([\\![ {\\vec{u}^\\ast} ]\\!] , [\\![ \\vec{\\kappa}\\vec{u} ]\\!] \\right)_{\\Gamma_\\text{int}} + \\left([\\![ \\vec{u}^\\ast ]\\!], \\{\\!\\!\\{ \\vec{D}\\vec{\\nabla}\\vec{u}\\cdot\\vec{n} \\}\\!\\!\\}\\right)_{\\Gamma_\\text{int}} + \\epsilon\\left( \\{\\!\\!\\{ \\vec{D}\\vec{\\nabla}\\vec{u}^\\ast\\cdot\\vec{n} \\}\\!\\!\\}, [\\![ \\vec{u} ]\\!]\\right)_{\\Gamma_\\text{int}},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-29db9a54-ecd5-4e25-8305-c4b15b299f61");katex.render("\\vec{u}^\\ast", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the test function, $var element = document.getElementById("moose-equation-47450039-b3f1-468e-926d-b54c10056081");katex.render("\\vec{u}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the finite element solution and $var element = document.getElementById("moose-equation-ace49ce2-b8c9-4cfc-80e7-86e86e2253a5");katex.render("\\vec{D}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the diffusion coefficients for all components of the array variable. $var element = document.getElementById("moose-equation-8c8eac8d-441e-4fde-9665-4e1823d63cd4");katex.render("[\\![ \\cdot ]\\!]", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-b38a2a05-918e-4ed8-a7d7-d1fc3e9ab030");katex.render("\\{\\!\\!\\{ \\cdot \\}\\!\\!\\}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are the jump and average of the enclosed quantity on the internal sides.

$var element = document.getElementById("moose-equation-7cc1f201-ea87-4394-869c-14c33ae30410");katex.render("\\vec{n}(x)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a unit norm defined on internal sides denoted by $var element = document.getElementById("moose-equation-91af7cf4-18e5-42b2-a342-51fa7208d412");katex.render("\\Gamma_\\text{int}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . $var element = document.getElementById("moose-equation-1ed0477f-ad46-42fa-92cd-907f2a2f6b63");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ can be 1, -1, and 0, corresponding symmetric, asymetric and incomplete interior penalty methods respectively. The penalty coefficients $var element = document.getElementById("moose-equation-c575e14a-bde9-47ab-8c84-ed13755544ec");katex.render("\\kappa", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are evaluated with the following formulation: $var element = document.getElementById("moose-equation-2e3c27f4-342f-4f75-af47-078cf9d56a0c");katex.render("\\vec{\\kappa} = \\sigma \\{\\!\\!\\{ p^2\\frac{\\vec{D}}{h_\\bot} \\}\\!\\!\\}, \\quad x\\in\\Gamma_\\text{int},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-f8aa9db1-e4a6-4c2e-907c-44b1d70c2729");katex.render("p", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the polynomial order of the shape functions; $var element = document.getElementById("moose-equation-9115177a-6a6c-4d3f-8c53-22ed051efeac");katex.render("h_\\bot", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the length of the element orthogonal to the side; $var element = document.getElementById("moose-equation-21f5e9ce-5017-4ac7-8f22-87fde9a228d5");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is an adjustable constant.

Input Parameters

diffThe diffusion (or thermal conductivity or viscosity) coefficient.
C++ Type:MaterialPropertyName
Options:
Description:The diffusion (or thermal conductivity or viscosity) coefficient.
variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this boundary condition applies to

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
diag_save_inThe name of auxiliary variables to save this Kernel'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
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
epsilon1epsilon
Default:1
C++ Type:double
Options:
Description:epsilon
exclude_boundaryThe internal side sets to be excluded from this kernel.
C++ Type:std::vector
Options:
Description:The internal side sets to be excluded from this kernel.
save_inThe name of auxiliary variables to save this Kernel'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
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
sigma4sigma
Default:4
C++ Type:double
Options:
Description:sigma

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
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
Options:
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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
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
Options:
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
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
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

test/tests/kernels/array_kernels/array_save_in.i
test/tests/kernels/array_kernels/array_diffusion_reaction_dg.i

test/tests/kernels/array_kernels/array_save_in.i

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  []
  [subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0.5 0.5 0'
    top_right = '1 1 0'
    block_id = 1
  []
[]

[Variables]
  [u]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []
[]

[AuxVariables]
  [u_diff_save_in]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []
  [u_vacuum_save_in]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []
  [u_dg_save_in]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []

  [u_diff_diag_save_in]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []
  [u_vacuum_diag_save_in]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []
  [u_dg_diag_save_in]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []
[]

[Kernels]
  [diff]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = dc
    save_in = u_diff_save_in
    diag_save_in = u_diff_diag_save_in
  []
  [reaction]
    type = ArrayReaction
    variable = u
    reaction_coefficient = rc
  []
[]

[DGKernels]
  [dgdiff]
    type = ArrayDGDiffusion
    variable = u
    diff = dc
    save_in = u_dg_save_in
    diag_save_in = u_dg_diag_save_in
  []
[]

[BCs]
  [left]
    type = ArrayVacuumBC
    variable = u
    boundary = 1
    save_in = u_vacuum_save_in
    diag_save_in = u_vacuum_diag_save_in
  []

  [right]
    type = ArrayPenaltyDirichletBC
    variable = u
    boundary = 2
    value = '1 2'
    penalty = 4
  []
[]

[Materials]
  [dc0]
    type = GenericConstantArray
    block = 0
    prop_name = dc
    prop_value = '1 1'
  []
  [dc1]
    type = GenericConstantArray
    block = 1
    prop_name = dc
    prop_value = '2 1'
  []
  [rc]
    type = GenericConstant2DArray
    block = '0 1'
    prop_name = rc
    prop_value = '1 0; -0.1 1'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Postprocessors]
  [intu0]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 0
  []
  [intu1]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

test/tests/kernels/array_kernels/array_diffusion_reaction_dg.i

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  []
  [subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0.5 0.5 0'
    top_right = '1 1 0'
    block_id = 1
  []
[]

[Variables]
  [u]
    order = FIRST
    family = L2_LAGRANGE
    components = 2
  []
[]

[Kernels]
  [diff]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = dc
  []
  [reaction]
    type = ArrayReaction
    variable = u
    reaction_coefficient = rc
  []
[]

[DGKernels]
  [dgdiff]
    type = ArrayDGDiffusion
    variable = u
    diff = dc
  []
[]

[BCs]
  [left]
    type = ArrayVacuumBC
    variable = u
    boundary = 1
  []

  [right]
    type = ArrayPenaltyDirichletBC
    variable = u
    boundary = 2
    value = '1 2'
    penalty = 4
  []
[]

[Materials]
  [dc0]
    type = GenericConstantArray
    block = 0
    prop_name = dc
    prop_value = '1 1'
  []
  [dc1]
    type = GenericConstantArray
    block = 1
    prop_name = dc
    prop_value = '2 1'
  []
  [rc]
    type = GenericConstant2DArray
    block = '0 1'
    prop_name = rc
    prop_value = '1 0; -0.1 1'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Postprocessors]
  [intu0]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 0
  []
  [intu1]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

Description
Input Parameters
Input Files

Application Usage

Physics and Syntax

Application Development

Framework Development

MOOSEDocs

Infrastructure

Questions

Information and Tools