ArrayDiffusion

Description

This array kernel implements the following piece of a weak form:

which is expanded as where is the test function, is the finite element solution and is the diffusion coefficients. is an array variable that has number of components. is the scalings of all components of the array variable. The size of the vector test function is the same as the size of . The kernel can be further spelled out as (1) where denotes elements of the mesh; is the number of shape functions on the local element; is the number of quadrature points for doing the spatial integration over an element. and are the expansion coefficients for the test function and the solution respectively, often referred as degrees of freedom. Subscript indicates that the associated quantities are evaluated on a quadrature point. is the determinant of Jacobian, that transform a physical element to a reference element where the shape functions are defined, times local quadrature weighting. It is noted that the test functions of all components are identical because all components of an array variable share the same finite element family and order.

We can rearrange the fully expanded Eq. (1) into where the underlined term is the array provided by ArrayDiffusion::computeQpResidual. The element, shape function and quadrature point summations are taken care of by MOOSE. It is noted that since test functions are arbitrary, can be viewed as an index indicator with which the local residual goes into the global residual vector. Note that represents element-wise multiplication, i.e. is equal to vector whose ith element is , where and are two generic vectors.

In general, the diffusion coefficient is a square matrix with the size of the number of components. When it is a diagonal matrix, it can be represented by an array. In such a case, the components are not coupled with this array diffusion kernel. If all elements of the diffusion coefficient vector are the same, we can use a scalar diffusion coefficient. Thus this kernel gives users an option to set the type of diffusion coefficient with a parameter named as diffusion_coefficient_type. Users can set it to scalar, array or full corresponding to scalar, diagonal matrix and full matrix respectively. Its default value is array.

With some further transformation, the kernel becomes where the underlined part is the local Jacobian evaluated by ArrayDiffusion::computeQpJacobian and ArrayDiffusion::computeQpOffDiagJacobian.

Example Input Syntax

[Kernels]
  [diff]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = dc
  []
[]
(moose/test/tests/kernels/array_kernels/array_diffusion_test.i)

Input Parameters

  • diffusion_coefficientThe name of the diffusivity, can be scalar, vector, or matrix material property.

    C++ Type:MaterialPropertyName

    Controllable:No

    Description:The name of the diffusivity, can be scalar, vector, or matrix material property.

  • 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

  • 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.

  • 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.

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 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<AuxVariableName>

    Controllable:No

    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.)

  • 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 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<AuxVariableName>

    Controllable:No

    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.)

  • 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