KKSACBulkF

KKS model kernel (part 1 of 2) for the Bulk Allen-Cahn. This includes all terms NOT dependent on chemical potential.

KKS Allen-Cahn kernel for the terms without a direct composition dependence.

(1)

Jacobian

On-diagonal

We are looking for the derivative of , where . We need to apply the chain rule and will again only keep terms with the derivative.

(2)

(The implicit dependence of and on through and does not contribute to the Jacobian, so .

Off-Diagonal

The off-diagonal components are calculated for any other variables that and depend on. For example, for :

(3)

in the KKS formulation, so this term would not need to be included if was the only variable depended on. However, the code calculates derivatives with respect to all variables that and depend on in a general way so that the Jacobian entries for other dependencies are correctly computed using the same piece of code. For example, both and could depend on temperature , in which case

(4)

which is computed using the same code. The off-diagonal Jacobian contribution is also multiplied by the Allen-Cahn mobility at each point for consistency with the other terms in the Allen-Cahn equation.

Input Parameters

• variableThe name of the variable that this Kernel operates on

C++ Type:NonlinearVariableName

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

• fa_nameBase name of the free energy function F (f_base in the corresponding KKSBaseMaterial)

C++ Type:MaterialPropertyName

Description:Base name of the free energy function F (f_base in the corresponding KKSBaseMaterial)

• fb_nameBase name of the free energy function F (f_base in the corresponding KKSBaseMaterial)

C++ Type:MaterialPropertyName

Description:Base name of the free energy function F (f_base in the corresponding KKSBaseMaterial)

• wDouble well height parameter

C++ Type:double

Description:Double well height parameter

Required Parameters

• mob_nameLThe mobility used with the kernel

Default:L

C++ Type:MaterialPropertyName

Description:The mobility used with the kernel

• g_namegBase name for the double well function g(eta)

Default:g

C++ Type:MaterialPropertyName

Description:Base name for the double well function g(eta)

• argsVector of arguments of the mobility

C++ Type:std::vector

Description:Vector of arguments of the mobility

• h_namehBase name for the switching function h(eta)

Default:h

C++ Type:MaterialPropertyName

Description:Base name for the switching function h(eta)

• 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

Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

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

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

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

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

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

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

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

• 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

• 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

• 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