DGFunctionDiffusionDirichletBC

Diffusion Dirichlet boundary condition for discontinuous Galerkin method.

Note that these boundary conditions are specific to DG and to a diffusion problem. Using a Functions System for the Dirichlet boundary conditions means that the spatial and time dependence is either known or imposed.

More information about Dirichlet boundary conditions and their mathematical meaning may be found in the DirichletBC documentation, and more information may be found about the discontinuous Galerkin discretization in the DGKernels documentation

Example input syntax

In this example, a 2D diffusion problem is solved with DG. A Dirichlet boundary condition is imposed on all boundaries using the exact_fn function. The epsilon and sigma parameters are DG parameters.

[BCs]
  active = 'all'

  [all]
    type = DGFunctionDiffusionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
    epsilon = -1
    sigma = 6
  []
[]

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
epsilonEpsilon
C++ Type:double
Controllable:No
Description:Epsilon
functionThe forcing function.
C++ Type:FunctionName
Controllable:No
Description:The forcing function.
sigmaSigma
C++ Type:double
Controllable:No
Description:Sigma
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

diff1The diffusion (or thermal conductivity or viscosity) coefficient.
Default:1
C++ Type:MaterialPropertyName
Controllable:No
Description:The diffusion (or thermal conductivity or viscosity) coefficient.
displacementsThe displacements
C++ Type:std::vector<VariableName>
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
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.
value0The value the variable should have on the boundary
Default:0
C++ Type:double
Controllable:No
Description:The value the variable should have on the boundary

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_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
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>
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>
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
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
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>
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
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
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/dgkernels/2d_diffusion_dg/2d_diffusion_dg_test.i)

###########################################################
# This is a test of the Discontinuous Galerkin System.
# Discontinous basis functions are used (Monomials) and
# a Laplacian DGKernel contributes to the
# internal edges around each element. Jumps are allowed
# but penalized by this method.
#
# @Requirement F3.60
###########################################################


[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
#  xmin = -1
#  xmax = 1
#  ymin = -1
#  ymax = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  elem_type = QUAD4
[]

[Variables]
  active = 'u'

  [u]
    order = FIRST
    family = MONOMIAL

    [InitialCondition]
      type = ConstantIC
      value = 1
    []
  []
[]

[Functions]
  active = 'forcing_fn exact_fn'

  [forcing_fn]
    type = ParsedFunction
#    function = -4.0+(x*x)+(y*y)
#    function = x
#    function = (x*x)-2.0
    expression = 2*pow(e,-x-(y*y))*(1-2*y*y)
#    function = (x*x*x)-6.0*x
  []

  [exact_fn]
    type = ParsedGradFunction
#    function = x
#    grad_x = 1
#    grad_y = 0

#    function = (x*x)+(y*y)
#    grad_x = 2*x
#    grad_y = 2*y

#    function = (x*x)
#    grad_x = 2*x
#    grad_y = 0

    expression = pow(e,-x-(y*y))
    grad_x = -pow(e,-x-(y*y))
    grad_y = -2*y*pow(e,-x-(y*y))

#    function = (x*x*x)
#    grad_x = 3*x*x
#    grad_y = 0
  []
[]

[Kernels]
  active = 'diff abs forcing'

  [diff]
    type = Diffusion
    variable = u
  []

  [abs]          # u * v
    type = Reaction
    variable = u
  []

  [forcing]
    type = BodyForce
    variable = u
    function = forcing_fn
  []
[]

[DGKernels]
  active = 'dg_diff'

  [dg_diff]
    type = DGDiffusion
    variable = u
    epsilon = -1
    sigma = 6
  []
[]

[BCs]
  active = 'all'

  [all]
    type = DGFunctionDiffusionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
    epsilon = -1
    sigma = 6
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
#  petsc_options = '-snes_mf'
#  petsc_options_iname = '-pc_type -pc_hypre_type'
#  petsc_options_value = 'hypre    boomeramg'

#  petsc_options = '-snes_mf'
#  max_r_steps = 2
  [Adaptivity]
    steps = 2
    refine_fraction = 1.0
    coarsen_fraction = 0
    max_h_level = 8
  []

  nl_rel_tol = 1e-10

#  nl_rel_tol = 1e-12
[]

[Postprocessors]
  active = 'h dofs l2_err'

  [h]
    type = AverageElementSize
  []

  [dofs]
    type = NumDOFs
  []

  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  []
[]

[Outputs]
  file_base = out
  exodus = true
[]