PolycrystalMatDiffusion

Diffusion equation Kernel that takes an isotropic Diffusivity from a material property

This kernel implements the same term as MatDiffusion (residual contribution is the same). However, this kernel can account for explicit dependence of $var element = document.getElementById("moose-equation-02470936-bace-448d-814c-d2cc99157f0a");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ on order parameters and the gradients of the order parameters in calculating the Jacobian contributions. This is in contrast to MatDiffusion, where only explicit dependence of $var element = document.getElementById("moose-equation-1afd511c-0075-4124-b634-93e7e35597e7");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ on the order parameters themselves is accounted for. Accounting for the Jacobian contribution can accelerate convergence when $var element = document.getElementById("moose-equation-12a92004-7a14-4b52-945c-bd65d71edcc1");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ explicitly depends on gradients of the order parameters.

The off-diagonal Jacobian contribution is calculated as $var element = document.getElementById("moose-equation-521fd720-c22e-4ced-bed2-e2dbaefd03a0");katex.render("\\frac{\\partial R_i}{\\partial u_j} = \\nabla \\psi \\cdot \\left(\\frac{\\partial D}{\\partial u_h} \\frac{\\partial u_h}{\\partial u_j} + \\frac{\\partial D}{\\partial \\nabla u_h} \\frac{\\partial \\nabla u_h}{\\partial u_j} \\right) \\nabla v", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ $var element = document.getElementById("moose-equation-707ab50c-f6ed-40d3-978a-5757de617434");katex.render("\\frac{\\partial R_i}{\\partial u_j} = \\nabla \\psi \\cdot \\left(\\frac{\\partial D}{\\partial u} \\phi_j + \\frac{\\partial D}{\\partial \\nabla u} \\nabla \\phi_j \\right) \\nabla v", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-faf61b87-8d2d-4d70-92a0-1c0445645a63");katex.render("R_i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the residual contribution from this kernel, $var element = document.getElementById("moose-equation-e49feb66-236c-47bc-8f01-23f741c63379");katex.render("u_j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the basis function coefficient, $var element = document.getElementById("moose-equation-06012b1b-47af-4e88-b3f8-9cbe52ad29fb");katex.render("\\psi", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the test function, $var element = document.getElementById("moose-equation-d328b2a1-ffd4-4801-9438-559a1b1a9feb");katex.render("u_h", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the trial function, $var element = document.getElementById("moose-equation-5b21051e-61b9-40c6-95aa-d2eb387f75c8");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the variable that $var element = document.getElementById("moose-equation-d463deea-64c3-4b21-9c25-db020465162d");katex.render("u_h", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a discrete approximation of, $var element = document.getElementById("moose-equation-b2cfc517-77e8-42ef-a6c3-afdc192473ef");katex.render("\\phi_j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the basis or shape function, and $var element = document.getElementById("moose-equation-b96c7598-b33c-4abb-bc6d-2ecbce1f3810");katex.render("v", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the non-linear variable for this kernel. The first term in the above equation is accounted for in MatDiffusion. The second term is accounted for in this kernel.

Input Parameters

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

add_grain_op_gradientsTrueWhether grain order parameter gradient contributions are added to Jacobian.
Default:True
C++ Type:bool
Controllable:No
Description:Whether grain order parameter gradient contributions are added to Jacobian.
argsOptional vector of arguments for the diffusivity. If provided and diffusivity is a derivative parsed material, Jacobian contributions from the diffusivity will be automatically computed
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Optional vector of arguments for the diffusivity. If provided and diffusivity is a derivative parsed material, Jacobian contributions from the diffusivity will be automatically computed
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
concDeprecated! Use 'v' instead
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Deprecated! Use 'v' instead
diffusivityDThe diffusivity value or material property
Default:D
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The diffusivity value or material property
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
grain_op_varsArray of grain order parameter variables
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Array of grain order parameter variables
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)
op_numArray of grain order parameter variables (num_name)
C++ Type:unsigned int
Controllable:No
Description:Array of grain order parameter variables (num_name)
surface_op_varName of the order parameter for solid-pore surface. For use when diffusivity depends on these OP gradients, leave this parameter un-set otherwise.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Name of the order parameter for solid-pore surface. For use when diffusivity depends on these OP gradients, leave this parameter un-set otherwise.
vCoupled concentration variable for kernel to operate on; if this is not specified, the kernel's nonlinear variable will be used as usual
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled concentration variable for kernel to operate on; if this is not specified, the kernel's nonlinear variable will be used as usual
var_name_baseArray of grain order parameter variables (base_name)
C++ Type:std::string
Controllable:No
Description:Array of grain order parameter variables (base_name)

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 Parameters