DriftDiffusion

Generic drift-diffusion equation that contains both an electric field driven advection term and a diffusion term (Densities must be in logarithmic form)

Overview

DriftDiffusion is a flux term containing an electric field driven advection and diffusion term used for variables in logarithmic form. DriftDiffusion assumes the electrostatic approximation for the electric field in multiple dimensions and can assume a uniform electric field for 1D.

The strong form for an electric field driven advection and diffusion flux is usually defined as

$var element = document.getElementById("moose-equation-8b0884b2-bbd9-44b6-9aec-e95c9c16bb82");katex.render("\\nabla \\cdot \\Gamma = \\nabla \\cdot \\left[ \\text{sign}_{j} \\mu_{j} n_{j} \\ E - D_{j} \\nabla (n_{j}) \\right] \\\\[10pt] E = \\text{-} \\nabla (V)", element, {displayMode:true,throwOnError:false});$

Where $var element = document.getElementById("moose-equation-ac40858b-57e6-4501-bbab-ef96c326388a");katex.render("\\Gamma", element, {displayMode:false,throwOnError:false});$ is the species' flux, $var element = document.getElementById("moose-equation-7db73a00-93b0-41b5-a9de-85cd970681c4");katex.render("\\text{sign}_{j}", element, {displayMode:false,throwOnError:false});$ indicates the advection behavior ( $var element = document.getElementById("moose-equation-1fc44bcf-f97f-4a37-8ef5-df0880a7ec7e");katex.render("\\text{+}1", element, {displayMode:false,throwOnError:false});$ for positively charged species and $var element = document.getElementById("moose-equation-901b7d91-b5b4-410c-be46-beec2867a9a1");katex.render("\\text{-}1", element, {displayMode:false,throwOnError:false});$ for negatively charged species), $var element = document.getElementById("moose-equation-d85d0a57-3be3-451c-b33b-97c066ff958d");katex.render("\\mu_{j}", element, {displayMode:false,throwOnError:false});$ is the mobility coefficient, $var element = document.getElementById("moose-equation-71c73c71-85af-42a9-9e02-4390c5343f62");katex.render("n_{j}", element, {displayMode:false,throwOnError:false});$ is the density, $var element = document.getElementById("moose-equation-25b3ec68-136d-4a7b-9eeb-1c495da1b951");katex.render("D_{j}", element, {displayMode:false,throwOnError:false});$ is the diffusion coefficient, $var element = document.getElementById("moose-equation-4c2d8a43-d05d-4ab6-ae40-4f7196c18db5");katex.render("E", element, {displayMode:false,throwOnError:false});$ is the electric field and $var element = document.getElementById("moose-equation-bb0e6253-653e-492f-b3f3-c86256a38d38");katex.render("V", element, {displayMode:false,throwOnError:false});$ is the potential. When converting the density to logarithmic form and applying a scaling factor of the mesh, the strong form for DriftDiffusion is defined as

$var element = document.getElementById("moose-equation-9fe16eed-130c-4193-bbe0-b4b7904e5190");katex.render("\\nabla \\cdot \\Gamma = \\nabla \\cdot \\left[ \\text{sign}_{j} \\mu_{j} \\exp(N_{j}) \\ \\text{-} \\nabla (V / l_{c}) - D_{j} \\exp(N_{j}) \\nabla (N_{j} / l_{c}) \\right]", element, {displayMode:true,throwOnError:false});$

Where $var element = document.getElementById("moose-equation-b9b7457b-d727-40dc-805c-c5ff13bbe5ff");katex.render("N_{j}", element, {displayMode:false,throwOnError:false});$ is the molar density of the species in logarithmic form and $var element = document.getElementById("moose-equation-b6b9fefd-d563-4e82-ae3a-6e2da969e100");katex.render("l_{c}", element, {displayMode:false,throwOnError:false});$ is the scaling factor of the mesh.

warning:Untested Class

The DriftDiffusion does not have a formalized test, yet. For this reason, users should be aware of unforeseen bugs when using DriftDiffusion. To report a bug or discuss future contributions to Zapdos, please refer to the Zapdos GitHub Discussions page. For standards of how to contribute to Zapdos and the MOOSE framework, please refer to the MOOSE Contributing page.

Example Input File Syntax


[Kernels]
  [Electrons_DriftDiffusion]
    type = DriftDiffusion
    variable = electrons
    potential = potential
    position_units = 1.0
  []
[]

Input Parameters

position_unitsUnits of position.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Units of position.
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

EFieldOptionally can use a specified electric field for 1D simulations in place of a potential variable
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Optionally can use a specified electric field for 1D simulations in place of a potential variable
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
diffThe user-defined diffusivity.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The user-defined diffusivity.
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
muThe user-defined mobility.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The user-defined mobility.
potentialThe gradient of the potential will be used to compute the advection velocity.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The gradient of the potential will be used to compute the advection velocity.
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.
signThe user-defined sign of the charged particle.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The user-defined sign of the charged particle.
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.
use_material_propsTrueWhether to use a material for properties.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to use a material for properties.

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

Overview
Example Input File Syntax
Input Parameters