XFEMSingleVariableConstraint

Enforce constraints on the value or flux associated with a variable at an XFEM interface.

Overview

Without any other intervention, the phantom node method used by MOOSE's XFEM system results in Heaviside enrichment of all solution fields at the locations of interfaces, with zero flux conditions. In many cases, there is a need to impose constraints across the interface on one or more of the solutions fields in a multiphysics XFEM simulation, which is the purpose of XFEMSingleVariableConstraint. The object takes in jumps in solutions and fluxes for a single variable and enforces prescribed jumps as a constraint between element fragments.

The variable to be constrained and the UserObject defining the interface upon which the constraint is occurring must both be specified. Next, any jumps in the variable's value or flux at the interface are provided. Lastly, the method by which the constraint is to be enacted is defined in the use_penalty parameter and a parameter dependent upon choice of enforcement method is given in alpha.

Currently, there are two choices of enforcement method: Nitsche's formulation and the penalty method. Nitsche's method has the advantage of providing consistent results but does require the stabilization parameter (alpha) to be as small as possible to maintain solution stability and is only applicable to simple diffusion problems. The penalty method, while stable, does not give results as consistent as Nitsche but can be applied to a wider variety of problems. When using the penalty method, the alpha parameter should be quite large relative to the Jacobian entries for the physics to which the penalty method is being applied.

Example Input File Syntax

[Constraints]
  [./xfem_constraint]
    type = XFEMSingleVariableConstraint
    variable = u
    geometric_cut_userobject = 'level_set_cut_uo'
    jump_flux = jump_flux_func
    use_penalty = true
    alpha = 1e5
  [../]
[]
(modules/xfem/test/tests/moving_interface/verification/1D_xy_discrete2mat.i)

Input Parameters

  • 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

  • alpha100Stabilization parameter in Nitsche's formulation and penalty factor in the Penalty Method. In Nitsche's formulation this should be as small as possible while the method is still stable; while in the Penalty Method you want this to be quite large (e.g. 1e6).

    Default:100

    C++ Type:double

    Controllable:No

    Description:Stabilization parameter in Nitsche's formulation and penalty factor in the Penalty Method. In Nitsche's formulation this should be as small as possible while the method is still stable; while in the Penalty Method you want this to be quite large (e.g. 1e6).

  • geometric_cut_userobjectName of GeometricCutUserObject associated with this constraint.

    C++ Type:UserObjectName

    Controllable:No

    Description:Name of GeometricCutUserObject associated with this constraint.

  • interface_id0The id of the interface.

    Default:0

    C++ Type:unsigned int

    Controllable:No

    Description:The id of the interface.

  • jump0Jump at the interface. Can be a Real or FunctionName.

    Default:0

    C++ Type:FunctionName

    Controllable:No

    Description:Jump at the interface. Can be a Real or FunctionName.

  • jump_flux0Flux jump at the interface. Can be a Real or FunctionName.

    Default:0

    C++ Type:FunctionName

    Controllable:No

    Description:Flux jump at the interface. Can be a Real or FunctionName.

  • use_penaltyFalseUse the Penalty instead of Nitsche (Nitsche only works for simple diffusion problems).

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Use the Penalty instead of Nitsche (Nitsche only works for simple diffusion problems).

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.

  • 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

Input Files