DivergenceAux

Computes the divergence of a vector of functors.

note

Using this AuxKernel to compute a term in a nonlinear equation will discard derivatives when using automatic differentiation (AD), and will make it more difficult to write down the Jacobian contributions when not using AD.

Example input syntax

In this example, the divergence of a finite volume vector field (u, v) is computed over a block, and compared to the flux on the sides of the block, verifying the divergence theorem as a sanity check.

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [divergence]
    type = ADDivergenceAux<<<{"description": "Computes the divergence of a vector of functors.", "href": "DivergenceAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = div
    u<<<{"description": "x-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number."}>>> = 'u'
    v<<<{"description": "y-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number."}>>> = 'v'
  []
[]

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [int_divergence]
    type = ElementL1Error<<<{"description": "Computes L1 error between an elemental field variable and an analytical function.", "href": "../postprocessors/ElementL1Error.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 2
    variable<<<{"description": "The name of the variable that this object operates on"}>>> = div
    function<<<{"description": "The analytic solution to compare against"}>>> = 0
  []
  [sum_surface_current]
    type = ParsedPostprocessor<<<{"description": "Computes a parsed expression with post-processors", "href": "../postprocessors/ParsedPostprocessor.html"}>>>
    expression<<<{"description": "function expression"}>>> = 's1 - s2 + s3 - s4'
    pp_names<<<{"description": "Post-processors arguments"}>>> = 's1 s2 s3 s4'
  []
  [s1]
    type = ADSideIntegralFunctorPostprocessor<<<{"description": "Computes a surface integral of the specified functor, using the single-sided face argument, which usually means that the functor will be evaluated from a single side of the surface, not interpolated between both sides.", "href": "../postprocessors/SideIntegralFunctorPostprocessor.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'block_2_right'
    functor<<<{"description": "The name of the functor that this postprocessor integrates. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number."}>>> = 'u'
  []
  [s2]
    type = ADSideIntegralFunctorPostprocessor<<<{"description": "Computes a surface integral of the specified functor, using the single-sided face argument, which usually means that the functor will be evaluated from a single side of the surface, not interpolated between both sides.", "href": "../postprocessors/SideIntegralFunctorPostprocessor.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'block_2_left'
    functor<<<{"description": "The name of the functor that this postprocessor integrates. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number."}>>> = 'u'
  []
  [s3]
    type = ADSideIntegralFunctorPostprocessor<<<{"description": "Computes a surface integral of the specified functor, using the single-sided face argument, which usually means that the functor will be evaluated from a single side of the surface, not interpolated between both sides.", "href": "../postprocessors/SideIntegralFunctorPostprocessor.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'block_2_top'
    functor<<<{"description": "The name of the functor that this postprocessor integrates. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number."}>>> = 'v'
  []
  [s4]
    type = ADSideIntegralFunctorPostprocessor<<<{"description": "Computes a surface integral of the specified functor, using the single-sided face argument, which usually means that the functor will be evaluated from a single side of the surface, not interpolated between both sides.", "href": "../postprocessors/SideIntegralFunctorPostprocessor.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'block_2_bot'
    functor<<<{"description": "The name of the functor that this postprocessor integrates. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number."}>>> = 'v'
  []
[]

Input Parameters

ux-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:x-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to

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
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
vy-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:y-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
wz-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:z-component of the vector. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

Optional 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.
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

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
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.

Material Property Retrieval Parameters

(moose/test/tests/auxkernels/divergence_aux/test_fv.i)

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1.5 1 0.1'
    dy = '1.3 1 0.9'
    ix = '2 4 1'
    iy = '2 3 3'
    subdomain_id = '1 1 1
                    1 2 1
                    1 1 1'
  []
  [add_inner_boundaries_top]
    type = SideSetsAroundSubdomainGenerator
    input = cmg
    new_boundary = 'block_2_top'
    block = 2
    normal = '0 1 0'
  []
  [add_inner_boundaries_bot]
    type = SideSetsAroundSubdomainGenerator
    input = add_inner_boundaries_top
    new_boundary = 'block_2_bot'
    block = 2
    normal = '0 -1 0'
  []
  [add_inner_boundaries_right]
    type = SideSetsAroundSubdomainGenerator
    input = add_inner_boundaries_bot
    new_boundary = 'block_2_right'
    block = 2
    normal = '1 0 0'
  []
  [add_inner_boundaries_left]
    type = SideSetsAroundSubdomainGenerator
    input = add_inner_boundaries_right
    new_boundary = 'block_2_left'
    block = 2
    normal = '-1 0 0'
  []
[]

[Variables]
  [u]
    type = MooseVariableFVReal
  []
  [v]
    type = MooseVariableFVReal
  []
[]

[FVKernels]
  [diff_u]
    type = FVDiffusion
    variable = u
    coeff = 1
  []
  [reaction_u]
    type = FVReaction
    variable = u
  []
  [diff_v]
    type = FVDiffusion
    variable = v
    coeff = 2
  []
  [reaction_v]
    type = FVReaction
    variable = v
  []
[]

[AuxVariables]
  [div]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [divergence]
    type = ADDivergenceAux
    variable = div
    u = 'u'
    v = 'v'
  []
[]

[FVBCs]
  [left]
    type = FVDirichletBC
    variable = u
    boundary = left
    value = 2
  []
  [right]
    type = FVDirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [top]
    type = FVDirichletBC
    variable = v
    boundary = top
    value = 2
  []
  [bottom]
    type = FVDirichletBC
    variable = v
    boundary = bottom
    value = 1
  []
[]

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

[Postprocessors]
  [int_divergence]
    type = ElementL1Error
    block = 2
    variable = div
    function = 0
  []
  [sum_surface_current]
    type = ParsedPostprocessor
    expression = 's1 - s2 + s3 - s4'
    pp_names = 's1 s2 s3 s4'
  []
  [s1]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'block_2_right'
    functor = 'u'
  []
  [s2]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'block_2_left'
    functor = 'u'
  []
  [s3]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'block_2_top'
    functor = 'v'
  []
  [s4]
    type = ADSideIntegralFunctorPostprocessor
    boundary = 'block_2_bot'
    functor = 'v'
  []
[]

[Outputs]
  csv = true
  hide = 's1 s2 s3 s4'
[]