KKSCHBulk

KKS model kernel for the Bulk Cahn-Hilliard term. This operates on the concentration 'c' as the non-linear variable

Non-split KKS Cahn-Hilliard bulk kernel, which is not fully implemented. The non-linear variable for this Kernel is the concentration .

Residual

In the residual routine we need to calculate the term . We exploit the KKS identity and arbitrarily use the a-phase instead. The gradient can be calculated through the chain rule (note that is potentially a function of many variables).

With being the vector of all arguments to this simplifies to

using as a shorthand for the term (and represented in the code as the array _second_derivatives[i]). We do have access to the gradients of through MOOSE (stored in _grad\_args[i]).

Jacobian

The calculation of the Jacobian involves the derivative of the Residual term w.r.t. the individual coefficients of all parameters of . Here can stand for any variable .

In the code is given by jvar for the off diagonal case, and (not or !) in the on diagonal case.

Off-diagonal

Let's focus on off diagonal first. Here is zero, if jvar is not equal . Allowing us to remove the sum over and replace it with the single non-zero summand

In the first term in the square brackets the derivative is only non-zero if is jvar. We can therefore pull this term out of the sum.

With the rules for derivatives we get

where is _j in the code.

On-diagonal

For the on diagonal terms we look at the derivative w.r.t. the components of the non-linear variable of this kernel. Note, that is only indirectly a function of . We assume the dependence is given through . The chain rule will thus yield terms of this form

which is given as equation (23) in KKS. Following the off-diagonal derivation we get

On-diagonal second approach

Let's get back to the original residual with . Then

Input Parameters

  • caphase concentration corresponding to the non-linear variable of this kernel

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

    Unit:(no unit assumed)

    Controllable:No

    Description:phase concentration corresponding to the non-linear variable of this kernel

  • cbphase concentration corresponding to the non-linear variable of this kernel

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

    Unit:(no unit assumed)

    Controllable:No

    Description:phase concentration corresponding to the non-linear variable of this kernel

  • fa_nameBase name of the free energy function F (f_name in the corresponding derivative function material)

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:Base name of the free energy function F (f_name in the corresponding derivative function material)

  • fb_nameBase name of the free energy function F (f_name in the corresponding derivative function material)

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:Base name of the free energy function F (f_name in the corresponding derivative function material)

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • args_aVector of additional arguments to Fa

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

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of additional arguments to Fa

  • blockThe list of blocks (ids or names) that this object will be applied

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

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • coupled_variablesVector of variable arguments of the mobility

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

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of variable arguments of the mobility

  • displacementsThe displacements

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

    Unit:(no unit assumed)

    Controllable:No

    Description:The displacements

  • h_namehBase name for the switching function h(eta)

    Default:h

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

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

  • mob_nameMThe mobility used with the kernel

    Default:M

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The mobility used with the kernel

  • 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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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.

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>

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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