Example 05 : Automatic Mesh Adaptivity

MOOSE has support for mesh adaptivity that can automatically refine and coarsen the mesh in areas of higher/lower error when solving problems. This can improve the quality of your results in addition to reducing computation time. You don't need to write any C++ code to use mesh adaptivity. Instead, it can easily be enabled by filling out the Adaptivity section in an input file:

[Adaptivity<<<{"href": "../../../syntax/Adaptivity/index.html"}>>>]
  marker<<<{"description": "The name of the Marker to use to actually adapt the mesh."}>>> = errorfrac # this specifies which marker from 'Markers' subsection to use
  steps<<<{"description": "The number of adaptive steps to use when doing a Steady simulation."}>>> = 2 # run adaptivity 2 times, recomputing solution, indicators, and markers each time

  # Use an indicator to compute an error-estimate for each element:
  [./Indicators<<<{"href": "../../../syntax/Adaptivity/Indicators/index.html"}>>>]
    # create an indicator computing an error metric for the convected variable
    [./error]
      # arbitrary, use-chosen name
      type = GradientJumpIndicator<<<{"description": "Compute the jump of the solution gradient across element boundaries.", "href": "../../../source/indicators/GradientJumpIndicator.html"}>>>
      variable<<<{"description": "The name of the variable that this side indicator applies to"}>>> = convected
      outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = none
    [../]
  [../]

  # Create a marker that determines which elements to refine/coarsen based on error estimates
  # from an indicator:
  [./Markers<<<{"href": "../../../syntax/Adaptivity/Markers/index.html"}>>>]
    [./errorfrac]
      # arbitrary, use-chosen name (must match 'marker=...' name above
      type = ErrorFractionMarker<<<{"description": "Marks elements for refinement or coarsening based on the fraction of the min/max error from the supplied indicator.", "href": "../../../source/markers/ErrorFractionMarker.html"}>>>
      indicator<<<{"description": "The name of the Indicator that this Marker uses."}>>> = error # use the 'error' indicator specified above
      refine<<<{"description": "Elements within this percentage of the max error will be refined.  Must be between 0 and 1!"}>>> = 0.5 # split/refine elements in the upper half of the indicator error range
      coarsen<<<{"description": "Elements within this percentage of the min error will be coarsened.  Must be between 0 and 1!"}>>> = 0 # don't do any coarsening
      outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = none
    [../]
  [../]
[]

More details about this functionality are provided on the Adaptivity page. MOOSE includes multiple Indicators you can use to compute different error estimates in addition to a few Markers.

Results

The results shown here are created using 6 refinement steps. However, because it can take a while to run, the ex05.i input file only specifies running 2 mesh refinement steps. Mesh results from each of the 6 refinement steps are shown below:

Initial mesh

Adaptivity Step 1

Adaptivity Step 2

Adaptivity Step 3

Adaptivity Step 4

Adaptivity Step 5

Adaptivity Step 6

And here is the final solution after all refinement steps are complete:

Example 5 Output

Complete Source Files

(examples/ex05_amr/ex05.i)
(examples/ex05_amr/include/kernels/ExampleCoefDiffusion.h)
(examples/ex05_amr/src/kernels/ExampleCoefDiffusion.C)

Example 4 Custom B. . .Example 06 Transie. . .

(examples/ex05_amr/ex05.i)

[Mesh]
  file = cube-hole.e
[]

# This is where mesh adaptivity magic happens:
[Adaptivity]
  marker = errorfrac # this specifies which marker from 'Markers' subsection to use
  steps = 2 # run adaptivity 2 times, recomputing solution, indicators, and markers each time

  # Use an indicator to compute an error-estimate for each element:
  [./Indicators]
    # create an indicator computing an error metric for the convected variable
    [./error] # arbitrary, use-chosen name
      type = GradientJumpIndicator
      variable = convected
      outputs = none
    [../]
  [../]

  # Create a marker that determines which elements to refine/coarsen based on error estimates
  # from an indicator:
  [./Markers]
    [./errorfrac] # arbitrary, use-chosen name (must match 'marker=...' name above
      type = ErrorFractionMarker
      indicator = error # use the 'error' indicator specified above
      refine = 0.5 # split/refine elements in the upper half of the indicator error range
      coarsen = 0 # don't do any coarsening
      outputs = none
    [../]
  [../]
[]

[Variables]
  [./convected]
    order = FIRST
    family = LAGRANGE
  [../]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./example_diff]
    type = ExampleCoefDiffusion
    variable = convected
    coef = 0.125
  [../]
  [./conv]
    type = ExampleConvection
    variable = convected
    some_variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[BCs]
  # convected=0 on all vertical sides except the right (x-max)
  [./cylinder_convected]
    type = DirichletBC
    variable = convected
    boundary = inside
    value = 1
  [../]
  [./exterior_convected]
    type = DirichletBC
    variable = convected
    boundary = 'left top bottom'
    value = 0
  [../]
  [./left_diffused]
    type = DirichletBC
    variable = diffused
    boundary = left
    value = 0
  [../]
  [./right_diffused]
    type = DirichletBC
    variable = diffused
    boundary = right
    value = 10
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'

  l_tol = 1e-3
  nl_rel_tol = 1e-12
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(examples/ex05_amr/ex05.i)

[Mesh]
  file = cube-hole.e
[]

# This is where mesh adaptivity magic happens:
[Adaptivity]
  marker = errorfrac # this specifies which marker from 'Markers' subsection to use
  steps = 2 # run adaptivity 2 times, recomputing solution, indicators, and markers each time

  # Use an indicator to compute an error-estimate for each element:
  [./Indicators]
    # create an indicator computing an error metric for the convected variable
    [./error] # arbitrary, use-chosen name
      type = GradientJumpIndicator
      variable = convected
      outputs = none
    [../]
  [../]

  # Create a marker that determines which elements to refine/coarsen based on error estimates
  # from an indicator:
  [./Markers]
    [./errorfrac] # arbitrary, use-chosen name (must match 'marker=...' name above
      type = ErrorFractionMarker
      indicator = error # use the 'error' indicator specified above
      refine = 0.5 # split/refine elements in the upper half of the indicator error range
      coarsen = 0 # don't do any coarsening
      outputs = none
    [../]
  [../]
[]

[Variables]
  [./convected]
    order = FIRST
    family = LAGRANGE
  [../]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./example_diff]
    type = ExampleCoefDiffusion
    variable = convected
    coef = 0.125
  [../]
  [./conv]
    type = ExampleConvection
    variable = convected
    some_variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[BCs]
  # convected=0 on all vertical sides except the right (x-max)
  [./cylinder_convected]
    type = DirichletBC
    variable = convected
    boundary = inside
    value = 1
  [../]
  [./exterior_convected]
    type = DirichletBC
    variable = convected
    boundary = 'left top bottom'
    value = 0
  [../]
  [./left_diffused]
    type = DirichletBC
    variable = diffused
    boundary = left
    value = 0
  [../]
  [./right_diffused]
    type = DirichletBC
    variable = diffused
    boundary = right
    value = 10
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'

  l_tol = 1e-3
  nl_rel_tol = 1e-12
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

(examples/ex05_amr/include/kernels/ExampleCoefDiffusion.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "Kernel.h"

class ExampleCoefDiffusion : public Kernel
{
public:
  ExampleCoefDiffusion(const InputParameters & parameters);

  static InputParameters validParams();

protected:
  virtual Real computeQpResidual() override;

  virtual Real computeQpJacobian() override;

private:
  Real _coef;
};

(examples/ex05_amr/src/kernels/ExampleCoefDiffusion.C)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#include "ExampleCoefDiffusion.h"

registerMooseObject("ExampleApp", ExampleCoefDiffusion);

InputParameters
ExampleCoefDiffusion::validParams()
{
  InputParameters params = Kernel::validParams();
  params.set<Real>("coef") = 0.0;
  return params;
}

ExampleCoefDiffusion::ExampleCoefDiffusion(const InputParameters & parameters)
  : Kernel(parameters), _coef(getParam<Real>("coef"))
{
}

Real
ExampleCoefDiffusion::computeQpResidual()
{
  return _coef * _grad_test[_i][_qp] * _grad_u[_qp];
}

Real
ExampleCoefDiffusion::computeQpJacobian()
{
  return _coef * _grad_test[_i][_qp] * _grad_phi[_j][_qp];
}

Results
Complete Source Files