PotentialToFieldAux

An AuxKernel that calculates the electrostatic electric field given the electrostatic potential.

Overview

This AuxKernel object uses the following equation for electric field:

$var element = document.getElementById("moose-equation-bc5ff77b-e953-466d-9f94-91ce1c73ad78");katex.render(" \\mathbf{E} = s \\nabla V", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where

$var element = document.getElementById("moose-equation-a1d08f23-ecee-4f50-a02b-5659d1ed0e63");katex.render("\\mathbf{E}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the electric field in units of Volts per meter,
$var element = document.getElementById("moose-equation-6e960b21-f5bc-477c-a972-18b264eefc7c");katex.render("V", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the electrostatic potential in units of Volts, and
$var element = document.getElementById("moose-equation-0bd38f52-52bf-4798-a579-a0ffd4cd35c7");katex.render("s", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a coefficient set via the "sign" parameter, and defaults to $var element = document.getElementById("moose-equation-a4b64e07-bfaf-4d1e-a1ed-542ab353fba9");katex.render("-1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

The sign of the resulting calculation can be changed from the default, if needed, by setting "sign" to positive. This option is the result of the desire to keep the object code as general as possible for use in other scenarios where the positive gradient of a solution variable is desired, while still retaining the traditional and expected electrostatic field result from various electrodynamics texts by default.

Example Input File Syntax

[AuxKernels]
  [Ex_aux]
    type = PotentialToFieldAux
    variable = Ex
    gradient_variable = potential
    sign = negative
    component = x
  []
[]

Input Parameters

gradient_variableThe variable from which to compute the gradient component
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The variable from which to compute the gradient component
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
componentThe gradient component to compute
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:x, y, z
Controllable:No
Description:The gradient component to compute
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:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, 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.
signnegativeSign of potential gradient.
Default:negative
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:negative, positive
Controllable:No
Description:Sign of potential gradient.
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

Input Files

(modules/electromagnetics/test/tests/benchmarks/eigenvalue_problems/eigen_base.i)

(modules/electromagnetics/test/tests/benchmarks/eigenvalue_problems/eigen_base.i)

# Base input file for eigenvalue example tests for multiple waveguide geometries
# RECTANGULAR (Default)
#     Mesh file rectangular.e based on Mesh block:
#         [Mesh]
#           [gmg]
#             type = GeneratedMeshGenerator
#             dim = 2
#             nx = 50
#             ny = 25
#             xmin = 0
#             xmax = 2
#             ymin = 0
#             ymax = 1
#             elem_type = TRI3
#           []
#         []
#     Expected analytic eigenvalue = 12.337005
#     EM Module calculated eigenvalue = 12.363806
# CIRCULAR (Mesh/file=circle.msh, BCs/active='circle eigen_circle')
#     Mesh generated using gmsh
#       radius = 1
#       center = (0, 0)
#     Expected analytic eigenvalue = 5.784025
#     EM Module calculated eigenvalue = 5.824152
# COAXIAL (Mesh/file=coaxial.msh, BCs/active='coaxial eigen_coaxial')
#     Mesh generated using gmsh with coaxial.geo
#       inner_radius = 0.125
#       outer_radius = 0.5
#       center = (0, 0)
#     Expected analytic eigenvalue = 67.108864
#     EM Module calculated eigenvalue = 68.007802


[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = rectangular.e
  []
[]

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

[AuxVariables]
  [Ex]
    order = CONSTANT
    family = MONOMIAL
  []
  [Ey]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = potential
  []
  [coeff]
    type = CoefReaction
    coefficient = -1
    variable = potential
    extra_vector_tags = 'eigen'
  []
[]

[AuxKernels]
  [Ex_aux]
    type = PotentialToFieldAux
    variable = Ex
    gradient_variable = potential
    sign = negative
    component = x
  []
  [Ey_aux]
    type = PotentialToFieldAux
    variable = Ey
    gradient_variable = potential
    sign = negative
    component = y
  []
[]

[BCs]
  active = 'rectangle eigen_rectangle'
  [rectangle]
    type = DirichletBC
    variable = potential
    boundary = 'left right top bottom'
    value = 0
  []
  [eigen_rectangle]
    type = EigenDirichletBC
    variable = potential
    boundary = 'left right top bottom'
  []
  # alternative BCs for circle case
  [circle]
    type = DirichletBC
    variable = potential
    boundary = 'wall'
    value = 0
  []
  [eigen_circle]
    type = EigenDirichletBC
    variable = potential
    boundary = 'wall'
  []
  # alternative BCs for coaxial case
  [coaxial]
    type = DirichletBC
    variable = potential
    boundary = 'outer inner'
    value = 0
  []
  [eigen_coaxial]
    type = EigenDirichletBC
    variable = potential
    boundary = 'outer inner'
  []
[]

[VectorPostprocessors]
  [eigenvalues]
    type = Eigenvalues
  []
[]

[Executioner]
  type = Eigenvalue
[]

[Outputs]
  csv = true
  exodus = false
  execute_on = FINAL
[]

(modules/electromagnetics/test/tests/benchmarks/eigenvalue_problems/eigen_base.i)

# Base input file for eigenvalue example tests for multiple waveguide geometries
# RECTANGULAR (Default)
#     Mesh file rectangular.e based on Mesh block:
#         [Mesh]
#           [gmg]
#             type = GeneratedMeshGenerator
#             dim = 2
#             nx = 50
#             ny = 25
#             xmin = 0
#             xmax = 2
#             ymin = 0
#             ymax = 1
#             elem_type = TRI3
#           []
#         []
#     Expected analytic eigenvalue = 12.337005
#     EM Module calculated eigenvalue = 12.363806
# CIRCULAR (Mesh/file=circle.msh, BCs/active='circle eigen_circle')
#     Mesh generated using gmsh
#       radius = 1
#       center = (0, 0)
#     Expected analytic eigenvalue = 5.784025
#     EM Module calculated eigenvalue = 5.824152
# COAXIAL (Mesh/file=coaxial.msh, BCs/active='coaxial eigen_coaxial')
#     Mesh generated using gmsh with coaxial.geo
#       inner_radius = 0.125
#       outer_radius = 0.5
#       center = (0, 0)
#     Expected analytic eigenvalue = 67.108864
#     EM Module calculated eigenvalue = 68.007802


[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = rectangular.e
  []
[]

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

[AuxVariables]
  [Ex]
    order = CONSTANT
    family = MONOMIAL
  []
  [Ey]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = potential
  []
  [coeff]
    type = CoefReaction
    coefficient = -1
    variable = potential
    extra_vector_tags = 'eigen'
  []
[]

[AuxKernels]
  [Ex_aux]
    type = PotentialToFieldAux
    variable = Ex
    gradient_variable = potential
    sign = negative
    component = x
  []
  [Ey_aux]
    type = PotentialToFieldAux
    variable = Ey
    gradient_variable = potential
    sign = negative
    component = y
  []
[]

[BCs]
  active = 'rectangle eigen_rectangle'
  [rectangle]
    type = DirichletBC
    variable = potential
    boundary = 'left right top bottom'
    value = 0
  []
  [eigen_rectangle]
    type = EigenDirichletBC
    variable = potential
    boundary = 'left right top bottom'
  []
  # alternative BCs for circle case
  [circle]
    type = DirichletBC
    variable = potential
    boundary = 'wall'
    value = 0
  []
  [eigen_circle]
    type = EigenDirichletBC
    variable = potential
    boundary = 'wall'
  []
  # alternative BCs for coaxial case
  [coaxial]
    type = DirichletBC
    variable = potential
    boundary = 'outer inner'
    value = 0
  []
  [eigen_coaxial]
    type = EigenDirichletBC
    variable = potential
    boundary = 'outer inner'
  []
[]

[VectorPostprocessors]
  [eigenvalues]
    type = Eigenvalues
  []
[]

[Executioner]
  type = Eigenvalue
[]

[Outputs]
  csv = true
  exodus = false
  execute_on = FINAL
[]

Overview
Example Input File Syntax
Input Parameters
Input Files