KKSPhaseChemicalPotential

KKS model kernel to enforce the pointwise equality of phase chemical potentials dFa/dca=dFb/dcbdF_a/dc_a = dF_b/dc_b. The non-linear variable of this kernel is cac_a.

Enforces the point wise equality of the phase chemical potentials

dFadca=dFbdcb.\frac{dF_a}{dc_a}=\frac{dF_b}{dc_b}.

The non-linear variable of this Kernel is cac_a.

Residual

R=dFadcadFbdcbR=\frac{dF_a}{dc_a} - \frac{dF_b}{dc_b}

Jacobian

For the Jacobian we need to calculate

J=uj(dFadcadFbdcb).J=\frac \partial{\partial u_j}\left( \frac{dF_a}{dc_a} - \frac{dF_b}{dc_b} \right).

On-Diagonal

J=ϕj(2Faca22Fbcacb)J = \phi_j \left( \frac{\partial^2 F_a}{\partial c_a^2} - \frac{\partial^2 F_b}{\partial c_a \partial c_b} \right)

Off-Diagonal

With qq the union of the argument vectors of FaF_a and FbF_b (represented in the code by _coupled_moose_vars[]) we get

i(2Facaqiqiuj2Fbcbqiqiuj).\sum_i \left( \frac{\partial^2 F_a}{\partial c_a \partial q_i}\frac{\partial q_i}{\partial u_j} - \frac{\partial^2 F_b}{\partial c_b \partial q_i}\frac{\partial q_i}{\partial u_j} \right).

Again the qiuj\frac{\partial q_i}{\partial u_j} is non-zero only if uqiu\equiv q_i, which is the case if qiq_i is the argument selected through jvar.

J=2Facaqjvarϕj2Fbcbqjvarϕj.J = \frac{\partial^2 F_a}{\partial c_a \partial q_\text{jvar}}\phi_j - \frac{\partial^2 F_b}{\partial c_b \partial q_\text{jvar}}\phi_j.

Note that in the code jvar is not an index into _coupled_moose_vars[] but has to be resolved through the _jvar_map.

Input Parameters

  • cbPhase b concentration

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

    Unit:(no unit assumed)

    Controllable:No

    Description:Phase b concentration

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

  • fb_nameBase name of the free energy function Fb (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 Fb (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 further parameters to Fa (optional, to add in second cross derivatives of Fa)

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

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of further parameters to Fa (optional, to add in second cross derivatives of Fa)

  • args_bVector of further parameters to Fb (optional, to add in second cross derivatives of Fb)

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

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of further parameters to Fb (optional, to add in second cross derivatives of Fb)

  • 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>

    Unit:(no unit assumed)

    Controllable:No

    Description:The displacements

  • ka1Site fraction for the ca variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Site fraction for the ca variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)

  • kb1Site fraction for the cb variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Site fraction for the cb variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)

  • matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Whether this object is only doing assembly to matrices (no vectors)

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

Contribution To Tagged Field Data 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>

    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

    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>

    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

    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

  • 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

    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.

Material Property Retrieval Parameters

Input Files