MFEMMeridionalCurlAux

Overview

In cylindrical coordinates $var element = document.getElementById("moose-equation-9357468a-5262-48e4-b336-f261b8904df5");katex.render("(r,\\theta,z)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , the curl of a purely azimuthal and axisymmetric field, $var element = document.getElementById("moose-equation-61368051-133b-4f32-9578-95accd00b4fc");katex.render("\\mathbf{A} = A_\\theta(r,z)\\mathbf{e}_\\theta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , is

var element = document.getElementById("moose-equation-178162d2-78e8-4c14-84c1-736b4026f514");katex.render("\\nabla \\times \\mathbf{A} = -\\frac{\\partial A_\\theta}{\\partial z}\\mathbf{e}_r + \\left( \\frac{\\partial A_\\theta}{\\partial r}+\\frac{A_\\theta}{r} \\right)\\mathbf{e}_z", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

This auxkernel computes this quantity for a 2D meridional $var element = document.getElementById("moose-equation-ca66f20e-9830-44e5-b575-c29dd8e6a0d4");katex.render("(r,z)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ formulation represented on a Cartesian mesh with coordinate convention $var element = document.getElementById("moose-equation-0b08da20-977c-43e1-9e1e-c8cd97a649e7");katex.render("(r=x, z=y)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and projects the resulting field in a vector MFEM auxiliary variable.

This auxkernel is useful, e.g., in axisymmetric electromagnetic calculations to compute the magnetic flux density $var element = document.getElementById("moose-equation-96f19f19-413a-4da8-83dc-76e31838a299");katex.render("\\mathbf{B} = \\nabla \\times \\mathbf{A}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ from $var element = document.getElementById("moose-equation-2e4cbec3-8b65-4791-86d0-160b946609d9");katex.render("A_\\theta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , representing the azimuthal component of the magnetic vector potential $var element = document.getElementById("moose-equation-fbdc2837-7800-40c1-9a81-8906e50c525f");katex.render("\\mathbf{A}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

Example Input File Syntax

[AuxKernels<<<{"href": "../../../syntax/AuxKernels/index.html"}>>>]
  [B_from_Atheta]
    type = MFEMMeridionalCurlAux<<<{"description": "Calculates the meridional curl associated with an azimuthal scalar variable A_theta on a 2D meridional mesh with x = r and y = z, and stores the result in a vector MFEM auxvariable.", "href": "MFEMMeridionalCurlAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = B
    source<<<{"description": "Scalar H1 MFEMVariable storing A_theta."}>>> = Atheta
  []
  [J]
    type = MFEMScalarProjectionAux<<<{"description": "Projects a scalar coefficient onto a scalar MFEM auxvariable", "href": "MFEMScalarProjectionAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = J
    coefficient<<<{"description": "Name of the scalar coefficient to project. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = Jtheta
  []
[]

Input Parameters

sourceScalar H1 MFEMVariable storing A_theta.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Scalar H1 MFEMVariable storing A_theta.
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

execute_onTIMESTEP_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:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, 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, MULTISYSTEM_FIXED_POINT_ITERATION_END, FINAL, CUSTOM
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.

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:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/mfem/auxkernels/axisymmetric_magnetostatic.i)

(test/tests/mfem/auxkernels/axisymmetric_magnetostatic.i)

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/hinomaru_offset.e
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [RTFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
  [Atheta]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Functions]
  # Meridional radius r = x
  [r]
    type = MFEMParsedFunction
    expression = 'x'
  []
  [inv_r]
    type = MFEMParsedFunction
    expression = '1.0/x'
  []
  # Weighted source coefficient r * J_theta = x * 8
  [Jtheta_r_wire]
    type = MFEMParsedFunction
    expression = '8.0*x'
  []
[]

[FunctorMaterials]
  [cyl_coeffs]
    type = MFEMGenericFunctorMaterial
    prop_names = 'diffCoef massCoef'
    prop_values = 'r inv_r'
  []
  [J_wire]
    type = MFEMGenericFunctorMaterial
    prop_names = 'Jtheta sourceCoef'
    prop_values = '8.0 Jtheta_r_wire'
    block = wire
  []
[]

[AuxVariables]
  [B]
    type = MFEMVariable
    fespace = RTFESpace
  []

  [J]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = Atheta
    coefficient = diffCoef
  []

  [mass]
    type = MFEMMassKernel
    variable = Atheta
    coefficient = massCoef
  []

  [source_wire]
    type = MFEMDomainLFKernel
    variable = Atheta
    coefficient = sourceCoef
  []
[]

[AuxKernels]
  [B_from_Atheta]
    type = MFEMMeridionalCurlAux
    variable = B
    source = Atheta
  []
  [J]
    type = MFEMScalarProjectionAux
    variable = J
    coefficient = Jtheta
  []
[]

[BCs]
  [essential]
    type = MFEMScalarDirichletBC
    variable = Atheta
    boundary = skin
  []
[]

[Solvers]
  [BoomerAMG]
    type = MFEMHypreBoomerAMG
  []
  [PCG]
    type = MFEMHyprePCG
    l_tol = 1e-8
    preconditioner = BoomerAMG
  []
[]

[Postprocessors]
  [norm] # should be sqrt(8*pi)
    type = MFEMVectorL2Error
    variable = B
    function = '0. 0.'
  []
[]

[Executioner]
  type = MFEMSteady
[]

[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = AxisymmetricMagnetostatic
  []
[]

(test/tests/mfem/auxkernels/axisymmetric_magnetostatic.i)

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/hinomaru_offset.e
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [RTFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
  [Atheta]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Functions]
  # Meridional radius r = x
  [r]
    type = MFEMParsedFunction
    expression = 'x'
  []
  [inv_r]
    type = MFEMParsedFunction
    expression = '1.0/x'
  []
  # Weighted source coefficient r * J_theta = x * 8
  [Jtheta_r_wire]
    type = MFEMParsedFunction
    expression = '8.0*x'
  []
[]

[FunctorMaterials]
  [cyl_coeffs]
    type = MFEMGenericFunctorMaterial
    prop_names = 'diffCoef massCoef'
    prop_values = 'r inv_r'
  []
  [J_wire]
    type = MFEMGenericFunctorMaterial
    prop_names = 'Jtheta sourceCoef'
    prop_values = '8.0 Jtheta_r_wire'
    block = wire
  []
[]

[AuxVariables]
  [B]
    type = MFEMVariable
    fespace = RTFESpace
  []

  [J]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = Atheta
    coefficient = diffCoef
  []

  [mass]
    type = MFEMMassKernel
    variable = Atheta
    coefficient = massCoef
  []

  [source_wire]
    type = MFEMDomainLFKernel
    variable = Atheta
    coefficient = sourceCoef
  []
[]

[AuxKernels]
  [B_from_Atheta]
    type = MFEMMeridionalCurlAux
    variable = B
    source = Atheta
  []
  [J]
    type = MFEMScalarProjectionAux
    variable = J
    coefficient = Jtheta
  []
[]

[BCs]
  [essential]
    type = MFEMScalarDirichletBC
    variable = Atheta
    boundary = skin
  []
[]

[Solvers]
  [BoomerAMG]
    type = MFEMHypreBoomerAMG
  []
  [PCG]
    type = MFEMHyprePCG
    l_tol = 1e-8
    preconditioner = BoomerAMG
  []
[]

[Postprocessors]
  [norm] # should be sqrt(8*pi)
    type = MFEMVectorL2Error
    variable = B
    function = '0. 0.'
  []
[]

[Executioner]
  type = MFEMSteady
[]

[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = AxisymmetricMagnetostatic
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files