ArrayTimeDerivative

Description

This array kernel implements the following piece of a weak form: $var element = document.getElementById("moose-equation-dab4346a-a656-4e8e-a7e0-c129ad0585d1");katex.render("(\\vec{u}^\\ast, \\mathbf{T} \\dot{\\vec{u}}),", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-d40cf468-547e-4110-b201-f03e65137fd6");katex.render("\\vec{u}^\\ast", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the test function, $var element = document.getElementById("moose-equation-2c847cbd-aedb-4fff-a029-25fa1a15fd39");katex.render("\\dot{\\vec{u}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is time derivative of the array of finite element solutions ( $var element = document.getElementById("moose-equation-a3ae5d7e-de08-4ceb-9848-e9d0803be2f3");katex.render("\\dot{\\vec{u}} = \\left[\\frac{\\partial u_1}{\\partial t},\\frac{\\partial u_2}{\\partial t},...\\right]^T", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ ), and $var element = document.getElementById("moose-equation-c5d0e598-58bd-4212-b16c-b3743272838d");katex.render("\\mathbf{T}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a matrix of the time derivative coefficients ( $var element = document.getElementById("moose-equation-fe403212-445d-4a83-a787-6407adedcd87");katex.render("(\\mathbf{T})_{n,m} = T_{n,m}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ ).

Similarly as showed in ArrayDiffusion, we can rearrange it into $var element = document.getElementById("moose-equation-ae60880c-cff5-45ec-a59c-04e22019dda7");katex.render("(\\vec{u}^\\ast, \\mathbf{T} \\dot{\\vec{u}}) = \\sum_{e} \\sum_{i=1}^{N_{\\text{dof}}} \\sum_{\\text{qp}=1}^{N_{qp}} (|J|w)_{\\text{qp}} \\vec{w}_p\\vec{u}_i^\\ast \\underline{\\mathbf{T}_{\\text{qp}} \\dot{\\vec{u}}_{\\text{qp}} b_{i,\\text{qp}}},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where the underlined term is the vector provided by ArrayTimeDerivative::computeQpResidual. Detailed explanations on the notations can be found in ArrayDiffusion.

/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);

defineLegacyParams(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");
  return params;
}

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

RealEigenVector
ArrayTimeDerivative::computeQpResidual()
{
  if (_coeff)
    return (*_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");
    return ((*_coeff_array)[_qp].array() * _u_dot[_qp].array()) * _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");
    return (*_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 (_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(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);
}

In general, the reaction coefficient $var element = document.getElementById("moose-equation-37402f34-20ac-4f31-92ff-82dbbbfa65d2");katex.render("\\mathbf{T}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ 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: $var element = document.getElementById("moose-equation-7914e6a7-2099-4737-a689-8e58c104a2cb");katex.render("J_{n,m,i,j} = \\sum_{e} \\sum_{i=1}^{N_{\\text{dof}}} \\sum_{j=1}^{N_{\\text{dof}}} \\sum_{\\text{qp}=1}^{N_{qp}} (|J|w)_{\\text{qp}} \\vec{w}_p u_{n,i}^\\ast \\underline{T_{n,m,\\text{qp}} b_{j,\\text{qp}} b_{i,\\text{qp}} \\frac{\\partial \\dot{u}_{m,j}}{\\partial u_{m,j}}},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-df9973ef-23cf-4c9e-87ec-3e343af0eb67");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-e84d9fef-82c0-4666-b1f0-95b053a877a7");katex.render("m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are the component row and column, respectively. The underlined part is the local Jacobian evaluated by ArrayTimeDerivative::computeQpJacobian and ArrayTimeDerivative::computeQpOffDiagJacobian.

/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);

defineLegacyParams(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");
  return params;
}

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

RealEigenVector
ArrayTimeDerivative::computeQpResidual()
{
  if (_coeff)
    return (*_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");
    return ((*_coeff_array)[_qp].array() * _u_dot[_qp].array()) * _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");
    return (*_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 (_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(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);
}

/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);

defineLegacyParams(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");
  return params;
}

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

RealEigenVector
ArrayTimeDerivative::computeQpResidual()
{
  if (_coeff)
    return (*_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");
    return ((*_coeff_array)[_qp].array() * _u_dot[_qp].array()) * _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");
    return (*_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 (_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(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);
}

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
  []
[]

/opt/civet/build_0/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
[]

Input Parameters

variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements
time_derivative_coefficientThe name of the time derivative coefficient. Can be scalar, vector, or matrix
C++ Type:MaterialPropertyName
Options:
Description:The name of the time derivative coefficient. Can be scalar, vector, or matrix

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
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
Options:
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
Options:
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
Options:
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
Options:
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
Options:
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
Options:
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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
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
Options:
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
Options:nontime system time
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
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

test/tests/kernels/array_kernels/array_diffusion_reaction_transient.i

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
Input Files

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ArrayTimeDerivative

Description

Example Input Syntax

Input Parameters

Required Parameters

Optional Parameters

Advanced Parameters

Tagging Parameters

Input Files