Sigma

Calculates the surface charge due to a simplified version of the ion flux to a boundary.

Overview

Sigma calculates a simplifed version of the surface charge on a boundary due to the advection flux of an ion species. Sigma assumes a mobility coefficient of unity, the electrostatic approximation for the electric field, and a non-scaled version of the specie's density.

The surface charge is defined as

$var element = document.getElementById("moose-equation-a8d98071-2863-404f-9d82-b1d562636d8d");katex.render("\\sigma = \\int \\Gamma_{i} \\cdot \\textbf{n} \\ \\text{d}t \\\\[10pt] \\Gamma_{i} = \\text{-} \\nabla (V) n_{i}", element, {displayMode:true,throwOnError:false});$

Where $var element = document.getElementById("moose-equation-1d91d6e5-3983-450a-b3c5-740f37f7af42");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the surface charge, $var element = document.getElementById("moose-equation-9bfb6431-97f9-44ca-b8e4-d4d7ceedd3ea");katex.render("\\Gamma_{i}", element, {displayMode:false,throwOnError:false});$ is the advective flux of the ions, $var element = document.getElementById("moose-equation-e34220bd-0b93-4b66-9f37-bc990316af21");katex.render("\\textbf{n}", element, {displayMode:false,throwOnError:false});$ is the outward pointing unit normal on the boundary, $var element = document.getElementById("moose-equation-f9ab4812-ddeb-4e85-9ad2-1b0e8d100ecd");katex.render("V", element, {displayMode:false,throwOnError:false});$ is the potential, and $var element = document.getElementById("moose-equation-e2340818-4201-49d6-934c-d5db67d91f1b");katex.render("n_{i}", element, {displayMode:false,throwOnError:false});$ is the ion density.

Using the midpoint method for integration, the surface charge calculation becomes

$var element = document.getElementById("moose-equation-2b7237dd-3c8b-4548-822b-bb8b5baca879");katex.render("\\sigma_{t} = \\sigma_{t-1} - \\nabla (V) n_{i} \\cdot \\textbf{n} \\ \\text{d}t", element, {displayMode:true,throwOnError:false});$

Where $var element = document.getElementById("moose-equation-cc511a43-c769-4f01-b070-fb55b7b4850e");katex.render("\\sigma_{t}", element, {displayMode:false,throwOnError:false});$ is the surface charge of the current time step, $var element = document.getElementById("moose-equation-d531890b-bc7b-406c-9df3-61b5449428b5");katex.render("\\sigma_{t-1}", element, {displayMode:false,throwOnError:false});$ is the surface of the previous time step, and $var element = document.getElementById("moose-equation-06d5c182-3a61-4a44-ab70-b713f6102afb");katex.render("\\text{d}t", element, {displayMode:false,throwOnError:false});$ is the difference between time steps.

note

When calculating the surface charge for scaled densities, non-unity coefficients, and includes contribution due to electron flux, please refer to ADSurfaceCharge.

warning:Untested Class

The Sigma does not have a formalized test, yet. For this reason, users should be aware of unforeseen bugs when using Sigma. 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


[AuxKernels]
  [Surface_Charge]
    type = Sigma
    variable = charge
    n = ions
    potential =  potential
  []
[]

Input Parameters

nThe density of the ions.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The density of the ions.
potentialThe potential
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The potential
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

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
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
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

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.
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.
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