FVAnisotropicDiffusion

Computes residual for anisotropic diffusion operator for finite volume method.

An anisotropic diffusion term that is discretized using the finite-volume method:

var element = document.getElementById("moose-equation-195b66c7-9bcc-45bc-b256-40181554325e");katex.render("- \\nabla \\cdot \\mathbf{k} \\nabla \\phi,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-48bc0842-0f2d-471c-a7b5-12d4d9713394");katex.render("\\mathbf{k}", element, {displayMode:false,throwOnError:false});$ is the diagonal tensor diffusion coefficient and $var element = document.getElementById("moose-equation-e7655017-33de-4469-aaa4-e02d47ac4b23");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$ is the diffusing variable. The discretized form of the equation above over en element is the following:

var element = document.getElementById("moose-equation-c1e52feb-e718-4039-85ce-f12049e8579a");katex.render("- \\sum\\limits_f \\mathbf{k}_f (\\nabla \\phi)_f \\mathbf{S}_f", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-0c98cb93-878c-4982-856b-530964a3f8c7");katex.render("\\mathbf{S}_f", element, {displayMode:false,throwOnError:false});$ denotes the surface vector of face $var element = document.getElementById("moose-equation-8bc6fb6b-216c-4191-811f-4e8085cd9c89");katex.render("f", element, {displayMode:false,throwOnError:false});$ of the element. Furthermore, the face gradient, (\nabla \phi)_f, is determined using a central difference scheme combined with non-orthogonal correction. Lastly, components of the diffusion (diagonal) tensor can be either interpolated to the face using a geometric arithmetic average:

var element = document.getElementById("moose-equation-43729d1b-7ee7-4ebb-b5fa-6a9f2e01ceeb");katex.render("(k_i)_f = g (k_i)_C + (1 - g) (k_i)_N,", element, {displayMode:true,throwOnError:false});

or a harmonic average:

var element = document.getElementById("moose-equation-d883171f-61b3-4df1-bc07-06b08303861c");katex.render("1 / (k_i)_f = g / (k_i)_C + (1 - g) / (k_i)_N,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-fea22468-d172-4ac4-b071-3200b42ef3f5");katex.render("g", element, {displayMode:false,throwOnError:false});$ is the interpolation weight, and subscripts $var element = document.getElementById("moose-equation-174dec45-e8cd-46dd-b339-3fcd32cf38d2");katex.render("C", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-d3bdb450-0689-44de-a7d0-6f0b4245c051");katex.render("N", element, {displayMode:false,throwOnError:false});$ represent element and neighbor values.

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '10 10'
    ix = '2 2'
    dy = '20'
    iy = '4'
    subdomain_id = '1 2'
  []
[]

[Variables]
  [v]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []

  [u]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [fem_diff1]
    type = AnisotropicDiffusion
    variable = u
    tensor_coeff = '1 0 0
                    0 10 0
                    0 0 0'
    block = 1
  []

  [fem_diff2]
    type = AnisotropicDiffusion
    variable = u
    tensor_coeff = '10 0 0
                    0 10 0
                    0 0 0'
    block = 2
  []
[]

[BCs]
  [fem_left_bottom]
    type = NeumannBC
    variable = u
    boundary = 'left bottom'
    value = 1
  []
  [fem_top_right]
    type = DirichletBC
    variable = u
    boundary = 'right top'
    value = 0
  []
[]

[FVKernels]
  [diff]
    type = FVAnisotropicDiffusion
    variable = v
    coeff = coeff
  []
[]

[FVBCs]
  [left_bottom]
    type = FVNeumannBC
    variable = v
    boundary = 'left bottom'
    value = 1
  []
  [top_right]
    type = FVDirichletBC
    variable = v
    boundary = 'right top'
    value = 0
  []
[]

[Materials]
  [diff1]
    type = ADGenericVectorFunctorMaterial
    prop_names = 'coeff'
    prop_values = '1 10 1'
    block = 1
  []

  [diff2]
    type = ADGenericVectorFunctorMaterial
    prop_names = 'coeff'
    prop_values = '10 10 1'
    block = 2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

Input Parameters

coeffThe diagonal coefficients of a diffusion tensor.
C++ Type:MooseFunctorName
Controllable:No
Description:The diagonal coefficients of a diffusion tensor.
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

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
coeff_interp_methodharmonicSwitch that can select face interpolation method for diffusion coefficients.
Default:harmonic
C++ Type:MooseEnum
Options:average, harmonic
Controllable:No
Description:Switch that can select face interpolation method for diffusion coefficients.
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.

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

boundaries_to_avoidThe set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.
boundaries_to_forceThe set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.
force_boundary_executionFalseWhether to force execution of this object on all external boundaries.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to force execution of this object on all external boundaries.

Boundary Execution Modification 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.
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
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

ghost_layers2The number of layers of elements to ghost.
Default:2
C++ Type:unsigned short
Controllable:No
Description:The number of layers of elements to ghost.
use_point_neighborsFalseWhether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters

(moose/test/tests/fvkernels/fv_anisotropic_diffusion/fv_anisotropic_diffusion.i)

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '10 10'
    ix = '2 2'
    dy = '20'
    iy = '4'
    subdomain_id = '1 2'
  []
[]

[Variables]
  [v]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []

  [u]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [fem_diff1]
    type = AnisotropicDiffusion
    variable = u
    tensor_coeff = '1 0 0
                    0 10 0
                    0 0 0'
    block = 1
  []

  [fem_diff2]
    type = AnisotropicDiffusion
    variable = u
    tensor_coeff = '10 0 0
                    0 10 0
                    0 0 0'
    block = 2
  []
[]

[BCs]
  [fem_left_bottom]
    type = NeumannBC
    variable = u
    boundary = 'left bottom'
    value = 1
  []
  [fem_top_right]
    type = DirichletBC
    variable = u
    boundary = 'right top'
    value = 0
  []
[]

[FVKernels]
  [diff]
    type = FVAnisotropicDiffusion
    variable = v
    coeff = coeff
  []
[]

[FVBCs]
  [left_bottom]
    type = FVNeumannBC
    variable = v
    boundary = 'left bottom'
    value = 1
  []
  [top_right]
    type = FVDirichletBC
    variable = v
    boundary = 'right top'
    value = 0
  []
[]

[Materials]
  [diff1]
    type = ADGenericVectorFunctorMaterial
    prop_names = 'coeff'
    prop_values = '1 10 1'
    block = 1
  []

  [diff2]
    type = ADGenericVectorFunctorMaterial
    prop_names = 'coeff'
    prop_values = '10 10 1'
    block = 2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]