- Fj_namesList of free energies for each phase. Place in same order as hj_names!
C++ Type:std::vector
Description:List of free energies for each phase. Place in same order as hj_names!
- cj_namesArray of phase concentrations cj. Place in same order as Fj_names!
C++ Type:std::vector
Description:Array of phase concentrations cj. Place in same order as Fj_names!
- eta_iOrder parameter that derivatives are taken with respect to
C++ Type:std::vector
Description:Order parameter that derivatives are taken with respect to
- hj_namesSwitching Function Materials that provide h. Place in same order as Fj_names!
C++ Type:std::vector
Description:Switching Function Materials that provide h. Place in same order as Fj_names!
- variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Description:The name of the variable that this Kernel operates on
KKSMultiACBulkC
Multi-phase KKS model kernel (part 2 of 2) for the Bulk Allen-Cahn. This includes all terms dependent on chemical potential.
Residual
For the 3-phase KKS model, if the non-linear variable is ,
where is the phase concentration for phase 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). Since in the KKS model, chemical potentials are constrained to be equal at each position, .
Jacobian
On-diagonal
If the non-linear variable is , the on-diagonal Jacobian is
Off-diagonal: Phase Concentrations
Since appears in the residual, the off-diagonal Jacobian for is a little more complicated than for or . For , and similarly for . then , and are handled first in the code. For the off-diagonal Jacobians we also need to multiply by , the Allen-Cahn mobility.
Off-diagonal: Other Coupled Variables
If the non-linear variable is , the off-diagonal Jacobian for is and similar for .
For any other coupled variables, for example temperature
What's implemented in the code for the off-diagonal Jacobian for , and any other coupled variables such as is the generalization for the above two equations for non-linear variable : (This handles everything except for , , , which are handled separately first). For the off-diagonal Jacobians we also need to multiply by , the Allen-Cahn mobility.
Input Parameters
- argsVector of arguments of the mobility
C++ Type:std::vector
Description:Vector of arguments of the mobility
- blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied
- displacementsThe displacements
C++ Type:std::vector
Description:The displacements
- mob_nameLThe mobility used with the kernel
Default:L
C++ Type:MaterialPropertyName
Description:The mobility used with the kernel
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
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
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
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
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
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
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
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
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
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
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
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
Description:The tag for the vectors this Kernel should fill
Tagging Parameters
Input Files
- R. Folch and M. Plapp.
Quantitative phase-field modeling of two-phase growth.
Phys. Rev. E, 72:011602, Jul 2005.
URL: https://link.aps.org/doi/10.1103/PhysRevE.72.011602, doi:10.1103/PhysRevE.72.011602.[BibTeX]