CurrentDensity / ADCurrentDensity

Calculates the current density vector field (in A/m^2) when given electrostatic potential (electrostatic = true, default) or electric field.

Overview

CurrentDensity and ADCurrentDensity allow for the calculation of the electric current density given by

$var element = document.getElementById("moose-equation-faf509a6-9df9-4854-a8e8-c495ca519495");katex.render(" \\vec{J} = \\sigma \\vec{E}", element, {displayMode:true,throwOnError:false});$

where

$var element = document.getElementById("moose-equation-2bdf5d92-82bf-4d17-8a76-789738847c2c");katex.render("\\vec{J}", element, {displayMode:false,throwOnError:false});$ is the current density (SI units of A/m $var element = document.getElementById("moose-equation-92f4b29d-5bd1-4ed2-9489-115f5635bb98");katex.render("^2", element, {displayMode:false,throwOnError:false});$ ),
$var element = document.getElementById("moose-equation-19ae8577-adca-4d00-b714-98f45ca5b8c2");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the electrical conductivity (SI units of S/m), and
$var element = document.getElementById("moose-equation-21cd4f1d-6ca0-47de-a216-fb3039d63689");katex.render("\\vec{E}", element, {displayMode:false,throwOnError:false});$ is the electric field (SI units of V/m).

The electric field can be determined either directly via an electromagnetic field calculation (in which case, the "electrostatic" parameter should be set to false), or calculated via the electrostatic potential $var element = document.getElementById("moose-equation-149e81b2-3ef0-4388-bd20-224a858bf0e3");katex.render("V", element, {displayMode:false,throwOnError:false});$ , where

$var element = document.getElementById("moose-equation-5384ca8b-8475-4929-8e3b-4e92479bd0d3");katex.render(" \\vec{E} = -\\nabla V.", element, {displayMode:true,throwOnError:false});$

Note that calculation via the electrostatic potential is the default behavior. MOOSE errors will be thrown if the inappropriate coupled variable is provided, given the setting for the "electrostatic" boolean parameter.

Additionally, note that the electrical conductivity $var element = document.getElementById("moose-equation-afbfd34d-0177-4fa3-8e5b-8a6616efba4b");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ must be provided as a material property for the block(s) this kernel is being applied to. The user can use, e.g., GenericConstantMaterial / ADGenericConstantMaterial, GenericFunctionMaterial, or one of their AD counterparts. The user must also set the "prop_names" parameter of the chosen object to electrical_conductivity.

Example Input File Syntax

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [current_density]
    type = ADCurrentDensity<<<{"description": "Calculates the current density vector field (in A/m^2) when given electrostatic potential (electrostatic = true, default) or electric field.", "href": "CurrentDensity.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = J
    potential<<<{"description": "Electrostatic potential variable"}>>> = potential
  []
[]

Input Parameters

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>
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>
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
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
electric_fieldElectric field variable (electromagnetic)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Electric field variable (electromagnetic)
electrostaticTrueWhether the electric field is based on electrostatic potential or is fully electromagnetic (default = TRUE)
Default:True
C++ Type:bool
Controllable:No
Description:Whether the electric field is based on electrostatic potential or is fully electromagnetic (default = TRUE)
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
Options:NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, 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.
potentialElectrostatic potential variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Electrostatic potential variable

Optional 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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
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

(moose/modules/electromagnetics/test/tests/auxkernels/current_density/current_density.i)

# This test creates a current density field in graphite running from the top left
# corner of the domain (powered with a potential of 1 V) into the bottom right
# corner (a slice has been taken from this corner to provide a grounded surface).
# Current flow should proceed from the powered surfaces to the grounded surface.

[Mesh]
  [box]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
    elem_type = TRI6
  []
  [delete_corner]
    type = PlaneDeletionGenerator
    input = box
    point = '0.9 0.1 0'
    normal = '1 -1 0'
    new_boundary = 'corner'
  []
[]

[Variables]
  [potential]
    family = LAGRANGE
    order = FIRST
  []
[]

[AuxVariables]
  [J]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [poisson]
    type = Diffusion
    variable = potential
  []
[]

[BCs]
  [driven]
    type = DirichletBC
    variable = potential
    value = 1
    boundary = 'top left'
  []
  [grounded]
    type = DirichletBC
    variable = potential
    value = 0
    boundary = 'corner'
  []
[]

[AuxKernels]
  [current_density]
    type = ADCurrentDensity
    variable = J
    potential = potential
  []
[]

[Materials]
  [conductivity]                            # Electrical conductivity for graphite at 293.15 K in S/m
    type = ADGenericConstantMaterial        # perpendicular to basal plane
    prop_names = 'electrical_conductivity'  # Citation: H. Pierson, "Handbook of carbon, graphite,
    prop_values = 3.33e2                    #           diamond, and fullerenes: properties, processing,
  []                                        #           and applications," p. 61, William Andrew, 1993.
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

Overview
Example Input File Syntax
Input Parameters