Steady State Diffusion

Summary

Solves a steady state diffusion problem for the temperature profile across a mug with fixed temperatures on two boundaries.

Description

This problem solves the steady state heat equation with strong form:

where , on the base of the mug and at the top of the mug.

In this example, we solve this using the weak form

where

Example File

[Mesh<<<{"href": "../Mesh/index.html"}>>>]
  type = MFEMFileMesh
  file = ../mesh/mug.e
[]

[Problem<<<{"href": "../Problem/index.html"}>>>]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
[]

[Variables<<<{"href": "../Variables/index.html"}>>>]
  [concentration]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables<<<{"href": "../AuxVariables/index.html"}>>>]
  [concentration_gradient]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxKernels<<<{"href": "../AuxKernels/index.html"}>>>]
  [grad]
    type = MFEMGradAux
    variable = concentration_gradient
    source = concentration
    execute_on = TIMESTEP_END
  []
[]

[BCs<<<{"href": "../BCs/index.html"}>>>]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'bottom'
    coefficient = 1.0
  []
  [top]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'top'
  []
[]

[Kernels<<<{"href": "../Kernels/index.html"}>>>]
  [diff]
    type = MFEMDiffusionKernel
    variable = concentration
  []
[]

[Solvers]
  inactive = 'jacobi'
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
  [main]
    type = MFEMHypreGMRES
    preconditioner = boomeramg
    l_tol = 1e-16
    l_max_its = 1000
  []
[]

[Executioner<<<{"href": "../Executioner/index.html"}>>>]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors<<<{"href": "../Postprocessors/index.html"}>>>]
  [solution_l2_norm]
    type = MFEML2Error
    variable = concentration
    function = 0
  []
[]

[VectorPostprocessors<<<{"href": "../VectorPostprocessors/index.html"}>>>]
  [line_sample]
    type = MFEMVariableLineValueSampler
    variable = 'concentration'
    start_point = '2.125 0 -2.375'
    end_point = '2.125 0 2.625'
    num_points = 101
  []
[]

[Outputs<<<{"href": "../Outputs/index.html"}>>>]
  active<<<{"description": "If specified only the blocks named will be visited and made active"}>>> = CSV
  [CSV]
    type = CSV<<<{"description": "Output for postprocessors, vector postprocessors, and scalar variables using comma seperated values (CSV).", "href": "../../source/outputs/CSV.html"}>>>
    file_base<<<{"description": "The desired solution output name without an extension. If not provided, MOOSE sets it with Outputs/file_base when available. Otherwise, MOOSE uses input file name and this object name for a master input or uses master file_base, the subapp name and this object name for a subapp input to set it."}>>> = OutputData/diffusion
  []
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/ParaViewDataCollection
    vtk_format = ASCII
  []
  [VisItDataCollection]
    type = MFEMVisItDataCollection
    file_base = OutputData/VisItDataCollection
  []
  [ConduitDataCollection]
    type = MFEMConduitDataCollection
    file_base = OutputData/ConduitDataCollection/Run
    protocol = conduit_bin
  []
[]
(moose/test/tests/mfem/kernels/diffusion.i)