KKSMultiPhaseConcentration

KKS multi-phase model kernel to enforce . The non-linear variable of this kernel is , the final phase concentration in the list.

Residual

For a KKS model with phases, the residual of the phase concentration constraint equation is

(1)

where is the phase concentration for phase , is the physical solute concentration, and is the interpolation function for phase defined in Folch and Plapp (2005) (referred to as there, but we use to maintain consistency with other interpolation functions in MOOSE).

Jacobian

On-diagonal

Since the non-linear variable for this kernel is , the on-diagonal Jacobian is

(2)

Off-diagonal

For the physical concentration , the off-diagonal Jacobian is

(3)

For phase concentrations other than ,:

(4)

Finally for the order parameters, such as ,

(5)

For the off-diagonal Jacobians we also need to multiply by , the Allen-Cahn mobility.

Input Parameters

  • variableThe name of the variable that this Kernel operates on

    C++ Type:NonlinearVariableName

    Options:

    Description:The name of the variable that this Kernel operates on

  • cjArray of phase concentrations cj. Place in same order as hj_names!

    C++ Type:std::vector

    Options:

    Description:Array of phase concentrations cj. Place in same order as hj_names!

  • cPhysical concentration

    C++ Type:std::vector

    Options:

    Description:Physical concentration

  • hj_namesSwitching Function Materials that provide $h(\eta_1, \eta_2,\dots)$

    C++ Type:std::vector

    Options:

    Description:Switching Function Materials that provide $h(\eta_1, \eta_2,\dots)$

Required Parameters

  • blockThe list of block ids (SubdomainID) that this object will be applied

    C++ Type:std::vector

    Options:

    Description:The list of block ids (SubdomainID) that this object will be applied

  • etasOrder parameters for all phases

    C++ Type:std::vector

    Options:

    Description:Order parameters for all phases

Optional Parameters

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Options:

    Description:Set the enabled status of the MooseObject.

  • 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

    Options:

    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.)

  • 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

    Options:

    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.

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector

    Options:

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Options:

    Description:The seed for the master random number generator

  • 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

    Options:

    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.)

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Options:

    Description:Determines whether this object is calculated using an implicit or explicit form

Advanced Parameters

  • vector_tagsnontimeThe tag for the vectors this Kernel should fill

    Default:nontime

    C++ Type:MultiMooseEnum

    Options:nontime time

    Description:The tag for the vectors this Kernel should fill

  • extra_vector_tagsThe extra tags for the vectors this Kernel should fill

    C++ Type:std::vector

    Options:

    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

    Description:The tag for the matrices this Kernel should fill

  • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

    C++ Type:std::vector

    Options:

    Description:The extra tags for the matrices this Kernel should fill

Tagging Parameters

Input Files