LevelSetOlssonReinitialization

This kernel implements the non-time portion of the conservative "re-initialization" algorithm of Olsson et al. (2007) that transforms into a smooth function in the range rather than a signed distance, which is useful for certain types of problems such as phase identification. The weak form of the original re-initialization equation is: find such that

where is the pseudo time during the re-initialization, is the normal vector computed from the level set variable at pseudo time , is the interface thickness, , and .

To avoid any tangential diffusion, a modified re-initialization formulation is proposed by restricting compressive flux to normal direction. The weak form of the modified re-initialization equation is: find such that

where is the pseudo time during the re-initialization, is the normal vector computed from the level set variable at pseudo time , is the interface thickness, , and .

When steady-state for is detected when (see LevelSetOlssonTerminator the entire process is repeated at time .

Our preliminary numerical tests indicate that the original re-initialization formulation works better to maintain the smoothness of an interface, so the original re-initialization formulation is set to be default. The modified re-initialization formulation can be used by setting use_modified_reinitilization_step = true although additional work needs to be done to investigate its numerical instability issue.

Example Syntax

The LevelSetOlssonReinitialization kernel is typically employed in a reinitialization sub-app (see the MOOSE MultiApp system), within this context this Kernel is invoked with the [Kernels] as follows.

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.05
  [../]
[]
(modules/level_set/test/tests/reinitialization/reinit.i)

Input Parameters

  • epsilonThe epsilon coefficient to be used in the reinitialization calculation.

    C++ Type:PostprocessorName

    Controllable:No

    Description:The epsilon coefficient to be used in the reinitialization calculation.

  • phi_0The level set variable to be reinitialized as signed distance function.

    C++ Type:std::vector<VariableName>

    Controllable:No

    Description:The level set variable to be reinitialized as signed distance function.

  • 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.

  • use_modified_reinitilization_formulationFalseUse the modified reinitilization formulation (Olsson et. al. (2007), section 2.2.1).

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Use the modified reinitilization formulation (Olsson et. al. (2007), section 2.2.1).

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

Input Files

References

  1. Elin Olsson, Gunilla Kreiss, and Sara Zahedi. A conservative level set method for two phase flow ii. Journal of Computational Physics, 225(1):785–807, 2007. URL: http://dx.doi.org/10.1016/j.jcp.2006.12.027.[BibTeX]