MFEMScalarTimeAverageAux

Overview

AuxKernel for calculating the running time average of a scalar coefficient during a transient simulation using the rectangle rule.

var element = document.getElementById("moose-equation-96ebacb5-3f70-4efb-bb86-d7f5efb2e4aa");katex.render("v(t) = (1 - \\omega) v(t - \\Delta t) + \\omega u(t), \\,\\,\\, \\omega = \\Delta t / (t - s), \\,\\,\\, t > s", 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 $var element = document.getElementById("moose-equation-a77c48be-f7b6-47ba-9eff-8fed99245f02");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the scalar coefficient to take the average of, $var element = document.getElementById("moose-equation-3ef17700-cb5e-4261-ac3c-bf1dda854e71");katex.render("v \\in H^1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ or $var element = document.getElementById("moose-equation-ed19b988-2cf6-4f95-9211-1e4443d93654");katex.render("L^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the scalar variable holding the time average of $var element = document.getElementById("moose-equation-cb15045f-367e-4f07-8ef1-1db03e24c280");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and $var element = document.getElementById("moose-equation-8069193b-ee52-4947-8dc0-564bef1fdb78");katex.render("s", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a timeskip, i.e. a timespan at the beginning of the simulation, prescribed by the user, during which no time averaging occurs.

Example Input File Syntax

[AuxKernels<<<{"href": "../../../syntax/AuxKernels/index.html"}>>>]
  inactive<<<{"description": "If specified blocks matching these identifiers will be skipped."}>>> = average_field
  [average_field]
    type = MFEMScalarTimeAverageAux<<<{"description": "Calculates a running time average of a scalar coefficient projected onto an auxvariable", "href": "MFEMScalarTimeAverageAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = average_temperature
    source<<<{"description": "Scalar coefficient to average. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = temperature
  []
[]

Input Parameters

sourceScalar coefficient to average. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
C++ Type:MFEMScalarCoefficientName
Controllable:No
Description:Scalar coefficient to average. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
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, 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.
time_skip0Time to skip before beginning the average
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Time to skip before beginning the average

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/kernels/heattransfer.i)
(test/tests/mfem/kernels/nl_heatconduction.i)

(test/tests/mfem/kernels/heattransfer.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/mug.e
  dim = 3
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

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

[AuxVariables]
  inactive = average_temperature
  [average_temperature]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxKernels]
  inactive = average_field
  [average_field]
    type = MFEMScalarTimeAverageAux
    variable = average_temperature
    source = temperature
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
[]

[BCs]
  active = 'bottom top_convective'
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    coefficient = 1.0
  []
  [top_convective]
    type = MFEMConvectiveHeatFluxBC
    variable = temperature
    boundary = '2'
    T_infinity = .5
    heat_transfer_coefficient = 5
  []
  [top_dirichlet]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '2'
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
  l_max_its = 1000
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 2.0
  start_time = 0.0
  end_time = 6.0
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/HeatTransfer
    vtk_format = ASCII
  []
[]

(test/tests/mfem/kernels/heattransfer.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/mug.e
  dim = 3
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

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

[AuxVariables]
  inactive = average_temperature
  [average_temperature]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxKernels]
  inactive = average_field
  [average_field]
    type = MFEMScalarTimeAverageAux
    variable = average_temperature
    source = temperature
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
[]

[BCs]
  active = 'bottom top_convective'
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    coefficient = 1.0
  []
  [top_convective]
    type = MFEMConvectiveHeatFluxBC
    variable = temperature
    boundary = '2'
    T_infinity = .5
    heat_transfer_coefficient = 5
  []
  [top_dirichlet]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '2'
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
  l_max_its = 1000
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 2.0
  start_time = 0.0
  end_time = 6.0
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/HeatTransfer
    vtk_format = ASCII
  []
[]

(test/tests/mfem/kernels/nl_heatconduction.i)

# Implementation of MFEM Example 16, for a time dependent nonlinear heat equation problem of the
# form
# dT/dt = \nabla \cdot (\kappa + \alpha T) \nabla T

kappa = 0.5
alpha = 1e-2

[Mesh]
  type = MFEMMesh
  file = ../mesh/star.mesh
  uniform_refine = 1
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = SECOND
  []
[]

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

[AuxVariables]
  inactive = average_temperature
  [average_temperature]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxKernels]
  inactive = average_field
  [average_field]
    type = MFEMScalarTimeAverageAux
    variable = average_temperature
    source = temperature
  []
[]

[Functions]
  [initial]
    type = ParsedFunction
    expression = 'if((x*x + y*y > 0.251), 1.0, 2.0)'
  []
  [diffusivity_temperature_dependence]
    type = MFEMParsedFunction
    expression = 'alpha * temperature'
    symbol_names = 'alpha temperature'
    symbol_values = '${alpha} temperature'
  []
[]

[ICs]
  [diffused_ic]
    type = MFEMScalarIC
    coefficient = initial
    variable = temperature
  []
[]

[Kernels]
  [nl_diffusion]
    type = MFEMNLDiffusionKernel
    variable = temperature
    k_coefficient = diffusivity_temperature_dependence
    dk_du_coefficient = ${alpha}
  []
  [linear_diffusion]
    type = MFEMDiffusionKernel
    variable = temperature
    coefficient = ${kappa}
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
[]

[Solver]
  type = MFEMMUMPS
  print_level = 0
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 1e-2
  start_time = 0.0
  end_time = 0.5

  nl_max_its = 30
  nl_abs_tol = 1.0e-5
  nl_rel_tol = 1.0e-5
  print_level = 1
[]

[VectorPostprocessors]
  [centre_temperature]
    type = MFEMPointValueSampler
    variable = 'temperature'
    points = '0.0 0.0 0.0'
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  file_base = OutputData/NLHeatConduction
  csv = true
  time_step_interval = 10

  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/NLHeatConduction
    vtk_format = ASCII
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files