ArrayTimeDerivative

Description

This array kernel implements the following piece of a weak form: $var element = document.getElementById("moose-equation-eb1488b4-1bc4-44c8-ae63-fbc3329c34d9");katex.render("(\\vec{u}^\\ast, \\mathbf{T} \\dot{\\vec{u}}),", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-cd8d56b3-f3e5-494a-8bb0-0dd60d51de33");katex.render("\\vec{u}^\\ast", element, {displayMode:false,throwOnError:false});$ is the test function, $var element = document.getElementById("moose-equation-ff520af1-a3e9-4d96-8e7d-3f6047e9a56f");katex.render("\\dot{\\vec{u}}", element, {displayMode:false,throwOnError:false});$ is time derivative of the array of finite element solutions ( $var element = document.getElementById("moose-equation-6ec59fb0-f6ad-4e2f-85e3-f309f671a51a");katex.render("\\dot{\\vec{u}} = \\left[\\frac{\\partial u_1}{\\partial t},\\frac{\\partial u_2}{\\partial t},...\\right]^T", element, {displayMode:false,throwOnError:false});$ ), and $var element = document.getElementById("moose-equation-d79bc58b-6b22-4162-a321-93cec3b231ec");katex.render("\\mathbf{T}", element, {displayMode:false,throwOnError:false});$ is a matrix of the time derivative coefficients ( $var element = document.getElementById("moose-equation-1974e4ce-16e0-49e4-bc1b-7221ce4b56a4");katex.render("(\\mathbf{T})_{n,m} = T_{n,m}", element, {displayMode:false,throwOnError:false});$ ).

Similarly as showed in ArrayDiffusion, we can rearrange it into $var element = document.getElementById("moose-equation-0ddbbf57-9780-45a4-827e-fefb4b3e2bb0");katex.render("(\\vec{u}^\\ast, \\mathbf{T} \\dot{\\vec{u}}) = \\sum_{e} \\sum_{i=1}^{N_{\\text{dof}}} \\sum_{\\text{qp}=1}^{N_{qp}} (|J|w)_{\\text{qp}} \\vec{w}_p\\vec{u}_i^\\ast \\underline{\\mathbf{T}_{\\text{qp}} \\dot{\\vec{u}}_{\\text{qp}} b_{i,\\text{qp}}},", element, {displayMode:true,throwOnError:false});$ where the underlined term is the vector provided by ArrayTimeDerivative::computeQpResidual. Detailed explanations on the notations can be found in ArrayDiffusion.

In general, the reaction coefficient $var element = document.getElementById("moose-equation-12c0912c-32e2-4312-b900-dc7ea50e1e1d");katex.render("\\mathbf{T}", element, {displayMode:false,throwOnError:false});$ is a square matrix with the size of the number of components. When it is a diagonal matrix, it can be represented by a vector. In such a case, the components are not coupled with this array time derivative kernel. If all elements of the time derivative coefficient vector are the same, we can use a scalar reaction coefficient. Thus this kernel gives users an option to set the coefficient to a scalar, vector, or matrix material property, corresponding to scalar, diagonal matrix, and full matrix, respectively.

The local Jacobian can be found in the following equation: $var element = document.getElementById("moose-equation-d1b04e8a-7a03-40a0-bb7e-7b9f4bd391ed");katex.render("J_{n,m,i,j} = \\sum_{e} \\sum_{i=1}^{N_{\\text{dof}}} \\sum_{j=1}^{N_{\\text{dof}}} \\sum_{\\text{qp}=1}^{N_{qp}} (|J|w)_{\\text{qp}} \\vec{w}_p u_{n,i}^\\ast \\underline{T_{n,m,\\text{qp}} b_{j,\\text{qp}} b_{i,\\text{qp}} \\frac{\\partial \\dot{u}_{m,j}}{\\partial u_{m,j}}},", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-4fbeac07-9a61-4d75-ad85-39b27f2715f7");katex.render("n", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-0f8739e1-5128-4c84-8287-76850d16c139");katex.render("m", element, {displayMode:false,throwOnError:false});$ are the component row and column, respectively. The underlined part is the local Jacobian evaluated by ArrayTimeDerivative::computeQpJacobian and ArrayTimeDerivative::computeQpOffDiagJacobian.

Example Input Syntax

[Kernels]
  [dudt]
    type = ArrayTimeDerivative
    variable = u
    time_derivative_coefficient = tc
  []
  [diff]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = dc
  []
  [reaction]
    type = ArrayReaction
    variable = u
    reaction_coefficient = rc
  []
[]

Input Parameters

variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

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
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
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.
time_derivative_coefficientThe name of the time derivative coefficient. Can be scalar, vector, or matrix material property.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The name of the time derivative coefficient. Can be scalar, vector, or matrix material property.
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

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, system, time
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging 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.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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

(moose/framework/src/kernels/ArrayTimeDerivative.C)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// 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 "ArrayTimeDerivative.h"

registerMooseObject("MooseApp", ArrayTimeDerivative);

InputParameters
ArrayTimeDerivative::validParams()
{
  InputParameters params = ArrayTimeKernel::validParams();
  params.addClassDescription("Array time derivative operator with the weak form of $(\\psi_i, "
                             "\\frac{\\partial u_h}{\\partial t})$.");
  params.addParam<MaterialPropertyName>("time_derivative_coefficient",
                                        "The name of the time derivative coefficient. "
                                        "Can be scalar, vector, or matrix material property.");
  return params;
}

ArrayTimeDerivative::ArrayTimeDerivative(const InputParameters & parameters)
  : ArrayTimeKernel(parameters),
    _has_coefficient(isParamValid("time_derivative_coefficient")),
    _coeff(_has_coefficient && hasMaterialProperty<Real>("time_derivative_coefficient")
               ? &getMaterialProperty<Real>("time_derivative_coefficient")
               : nullptr),
    _coeff_array(_has_coefficient &&
                         hasMaterialProperty<RealEigenVector>("time_derivative_coefficient")
                     ? &getMaterialProperty<RealEigenVector>("time_derivative_coefficient")
                     : nullptr),
    _coeff_2d_array(_has_coefficient &&
                            hasMaterialProperty<RealEigenMatrix>("time_derivative_coefficient")
                        ? &getMaterialProperty<RealEigenMatrix>("time_derivative_coefficient")
                        : nullptr)
{
  if (!_coeff && !_coeff_array && !_coeff_2d_array && _has_coefficient)
  {
    MaterialPropertyName mat = getParam<MaterialPropertyName>("time_derivative_coefficient");
    mooseError("Property " + mat + " is of unsupported type for ArrayTimeDerivative");
  }
}

void
ArrayTimeDerivative::computeQpResidual(RealEigenVector & residual)
{
  if (!_has_coefficient)
    residual = _u_dot[_qp] * _test[_i][_qp];
  else if (_coeff)
    residual = (*_coeff)[_qp] * _u_dot[_qp] * _test[_i][_qp];
  else if (_coeff_array)
  {
    mooseAssert((*_coeff_array)[_qp].size() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    // WARNING: use noalias() syntax with caution. See ArrayDiffusion.C for more details.
    residual.noalias() = (*_coeff_array)[_qp].asDiagonal() * _u_dot[_qp] * _test[_i][_qp];
  }
  else
  {
    mooseAssert((*_coeff_2d_array)[_qp].cols() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    mooseAssert((*_coeff_2d_array)[_qp].rows() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    // WARNING: use noalias() syntax with caution. See ArrayDiffusion.C for more details.
    residual.noalias() = (*_coeff_2d_array)[_qp] * _u_dot[_qp] * _test[_i][_qp];
  }
}

RealEigenVector
ArrayTimeDerivative::computeQpJacobian()
{
  Real tmp = _test[_i][_qp] * _phi[_j][_qp] * _du_dot_du[_qp];
  if (!_has_coefficient)
    return RealEigenVector::Constant(_var.count(), tmp);
  else if (_coeff)
    return RealEigenVector::Constant(_var.count(), tmp * (*_coeff)[_qp]);
  else if (_coeff_array)
    return tmp * (*_coeff_array)[_qp];
  else
    return tmp * (*_coeff_2d_array)[_qp].diagonal();
}

RealEigenMatrix
ArrayTimeDerivative::computeQpOffDiagJacobian(const MooseVariableFEBase & jvar)
{
  if (jvar.number() == _var.number() && _coeff_2d_array)
    return _phi[_j][_qp] * _test[_i][_qp] * _du_dot_du[_qp] * (*_coeff_2d_array)[_qp];
  else
    return ArrayKernel::computeQpOffDiagJacobian(jvar);
}

(moose/framework/src/kernels/ArrayTimeDerivative.C)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// 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 "ArrayTimeDerivative.h"

registerMooseObject("MooseApp", ArrayTimeDerivative);

InputParameters
ArrayTimeDerivative::validParams()
{
  InputParameters params = ArrayTimeKernel::validParams();
  params.addClassDescription("Array time derivative operator with the weak form of $(\\psi_i, "
                             "\\frac{\\partial u_h}{\\partial t})$.");
  params.addParam<MaterialPropertyName>("time_derivative_coefficient",
                                        "The name of the time derivative coefficient. "
                                        "Can be scalar, vector, or matrix material property.");
  return params;
}

ArrayTimeDerivative::ArrayTimeDerivative(const InputParameters & parameters)
  : ArrayTimeKernel(parameters),
    _has_coefficient(isParamValid("time_derivative_coefficient")),
    _coeff(_has_coefficient && hasMaterialProperty<Real>("time_derivative_coefficient")
               ? &getMaterialProperty<Real>("time_derivative_coefficient")
               : nullptr),
    _coeff_array(_has_coefficient &&
                         hasMaterialProperty<RealEigenVector>("time_derivative_coefficient")
                     ? &getMaterialProperty<RealEigenVector>("time_derivative_coefficient")
                     : nullptr),
    _coeff_2d_array(_has_coefficient &&
                            hasMaterialProperty<RealEigenMatrix>("time_derivative_coefficient")
                        ? &getMaterialProperty<RealEigenMatrix>("time_derivative_coefficient")
                        : nullptr)
{
  if (!_coeff && !_coeff_array && !_coeff_2d_array && _has_coefficient)
  {
    MaterialPropertyName mat = getParam<MaterialPropertyName>("time_derivative_coefficient");
    mooseError("Property " + mat + " is of unsupported type for ArrayTimeDerivative");
  }
}

void
ArrayTimeDerivative::computeQpResidual(RealEigenVector & residual)
{
  if (!_has_coefficient)
    residual = _u_dot[_qp] * _test[_i][_qp];
  else if (_coeff)
    residual = (*_coeff)[_qp] * _u_dot[_qp] * _test[_i][_qp];
  else if (_coeff_array)
  {
    mooseAssert((*_coeff_array)[_qp].size() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    // WARNING: use noalias() syntax with caution. See ArrayDiffusion.C for more details.
    residual.noalias() = (*_coeff_array)[_qp].asDiagonal() * _u_dot[_qp] * _test[_i][_qp];
  }
  else
  {
    mooseAssert((*_coeff_2d_array)[_qp].cols() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    mooseAssert((*_coeff_2d_array)[_qp].rows() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    // WARNING: use noalias() syntax with caution. See ArrayDiffusion.C for more details.
    residual.noalias() = (*_coeff_2d_array)[_qp] * _u_dot[_qp] * _test[_i][_qp];
  }
}

RealEigenVector
ArrayTimeDerivative::computeQpJacobian()
{
  Real tmp = _test[_i][_qp] * _phi[_j][_qp] * _du_dot_du[_qp];
  if (!_has_coefficient)
    return RealEigenVector::Constant(_var.count(), tmp);
  else if (_coeff)
    return RealEigenVector::Constant(_var.count(), tmp * (*_coeff)[_qp]);
  else if (_coeff_array)
    return tmp * (*_coeff_array)[_qp];
  else
    return tmp * (*_coeff_2d_array)[_qp].diagonal();
}

RealEigenMatrix
ArrayTimeDerivative::computeQpOffDiagJacobian(const MooseVariableFEBase & jvar)
{
  if (jvar.number() == _var.number() && _coeff_2d_array)
    return _phi[_j][_qp] * _test[_i][_qp] * _du_dot_du[_qp] * (*_coeff_2d_array)[_qp];
  else
    return ArrayKernel::computeQpOffDiagJacobian(jvar);
}

(moose/framework/src/kernels/ArrayTimeDerivative.C)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// 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 "ArrayTimeDerivative.h"

registerMooseObject("MooseApp", ArrayTimeDerivative);

InputParameters
ArrayTimeDerivative::validParams()
{
  InputParameters params = ArrayTimeKernel::validParams();
  params.addClassDescription("Array time derivative operator with the weak form of $(\\psi_i, "
                             "\\frac{\\partial u_h}{\\partial t})$.");
  params.addParam<MaterialPropertyName>("time_derivative_coefficient",
                                        "The name of the time derivative coefficient. "
                                        "Can be scalar, vector, or matrix material property.");
  return params;
}

ArrayTimeDerivative::ArrayTimeDerivative(const InputParameters & parameters)
  : ArrayTimeKernel(parameters),
    _has_coefficient(isParamValid("time_derivative_coefficient")),
    _coeff(_has_coefficient && hasMaterialProperty<Real>("time_derivative_coefficient")
               ? &getMaterialProperty<Real>("time_derivative_coefficient")
               : nullptr),
    _coeff_array(_has_coefficient &&
                         hasMaterialProperty<RealEigenVector>("time_derivative_coefficient")
                     ? &getMaterialProperty<RealEigenVector>("time_derivative_coefficient")
                     : nullptr),
    _coeff_2d_array(_has_coefficient &&
                            hasMaterialProperty<RealEigenMatrix>("time_derivative_coefficient")
                        ? &getMaterialProperty<RealEigenMatrix>("time_derivative_coefficient")
                        : nullptr)
{
  if (!_coeff && !_coeff_array && !_coeff_2d_array && _has_coefficient)
  {
    MaterialPropertyName mat = getParam<MaterialPropertyName>("time_derivative_coefficient");
    mooseError("Property " + mat + " is of unsupported type for ArrayTimeDerivative");
  }
}

void
ArrayTimeDerivative::computeQpResidual(RealEigenVector & residual)
{
  if (!_has_coefficient)
    residual = _u_dot[_qp] * _test[_i][_qp];
  else if (_coeff)
    residual = (*_coeff)[_qp] * _u_dot[_qp] * _test[_i][_qp];
  else if (_coeff_array)
  {
    mooseAssert((*_coeff_array)[_qp].size() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    // WARNING: use noalias() syntax with caution. See ArrayDiffusion.C for more details.
    residual.noalias() = (*_coeff_array)[_qp].asDiagonal() * _u_dot[_qp] * _test[_i][_qp];
  }
  else
  {
    mooseAssert((*_coeff_2d_array)[_qp].cols() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    mooseAssert((*_coeff_2d_array)[_qp].rows() == _var.count(),
                "time_derivative_coefficient size is inconsistent with the number of components "
                "in array variable");
    // WARNING: use noalias() syntax with caution. See ArrayDiffusion.C for more details.
    residual.noalias() = (*_coeff_2d_array)[_qp] * _u_dot[_qp] * _test[_i][_qp];
  }
}

RealEigenVector
ArrayTimeDerivative::computeQpJacobian()
{
  Real tmp = _test[_i][_qp] * _phi[_j][_qp] * _du_dot_du[_qp];
  if (!_has_coefficient)
    return RealEigenVector::Constant(_var.count(), tmp);
  else if (_coeff)
    return RealEigenVector::Constant(_var.count(), tmp * (*_coeff)[_qp]);
  else if (_coeff_array)
    return tmp * (*_coeff_array)[_qp];
  else
    return tmp * (*_coeff_2d_array)[_qp].diagonal();
}

RealEigenMatrix
ArrayTimeDerivative::computeQpOffDiagJacobian(const MooseVariableFEBase & jvar)
{
  if (jvar.number() == _var.number() && _coeff_2d_array)
    return _phi[_j][_qp] * _test[_i][_qp] * _du_dot_du[_qp] * (*_coeff_2d_array)[_qp];
  else
    return ArrayKernel::computeQpOffDiagJacobian(jvar);
}

(moose/test/tests/kernels/array_kernels/array_diffusion_reaction_transient.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 4
  ny = 4
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
    components = 2
  []
[]

[Kernels]
  [dudt]
    type = ArrayTimeDerivative
    variable = u
    time_derivative_coefficient = tc
  []
  [diff]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = dc
  []
  [reaction]
    type = ArrayReaction
    variable = u
    reaction_coefficient = rc
  []
[]

[BCs]
  [left]
    type = ArrayDirichletBC
    variable = u
    boundary = 1
    values = '0 0'
  []

  [right]
    type = ArrayDirichletBC
    variable = u
    boundary = 2
    values = '1 2'
  []
[]

[Materials]
  [tc]
    type = GenericConstantArray
    prop_name = tc
    prop_value = '1 1'
  []
  [dc]
    type = GenericConstantArray
    prop_name = dc
    prop_value = '1 1'
  []
  [rc]
    type = GenericConstant2DArray
    prop_name = rc
    prop_value = '1 0; -0.1 1'
  []
[]

[Postprocessors]
  [intu0]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 0
  []
  [intu1]
    type = ElementIntegralArrayVariablePostprocessor
    variable = u
    component = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  dt = 0.1
  num_steps = 10
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters