CoupledSusceptibilityTimeDerivative

A modified coupled time derivative Kernel that multiplies the time derivative of a coupled variable by a generalized susceptibility

Implements

$var element = document.getElementById("moose-equation-d82d46df-0275-46bb-bb08-01b8fa260766");katex.render("F(u,v,a,b,\\dots)\\cdot\\frac{\\partial v}{\\partial t},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

where $var element = document.getElementById("moose-equation-f67147fa-52e0-482c-8af8-094929fe63ed");katex.render("F", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (f_name) is a FunctionMaterial providing derivatives (for example defined using the DerivativeParsedMaterial), $var element = document.getElementById("moose-equation-0e3c173f-8c55-4fc2-8aab-0bbb91304946");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the variable the kernel is acting on, $var element = document.getElementById("moose-equation-07f95cee-cb36-48a5-a971-9db066774ae9");katex.render("v", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (v) is the coupled variable the time derivative is taken of, and $var element = document.getElementById("moose-equation-3ba81bba-f152-4f58-b8c3-0beba2f80a05");katex.render("a, b, \\dots", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (args) are further arguments of the susceptibility function $var element = document.getElementById("moose-equation-00d6644c-8799-4075-a0ae-ebf353095b1d");katex.render("F", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ which should contribute to off-diagonal Jacobian entries.

Input Parameters

f_nameSusceptibility function F defined in a FunctionMaterial
C++ Type:MaterialPropertyName
Options:
Description:Susceptibility function F defined in a FunctionMaterial
vCoupled variable
C++ Type:std::vector
Options:
Description:Coupled variable
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

argsVector of arguments of the susceptibility
C++ Type:std::vector
Options:
Description:Vector of arguments of the susceptibility
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

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_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialPFM.i

modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialPFM.i

# this input file test the implementation of the grand-potential phase-field model based on M.Plapp PRE 84,031601(2011)
# in this simple example, the liquid and solid free energies are parabola with the same curvature and the material properties are constant
# Note that this example also test The SusceptibilityTimeDerivative kernels
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 16
  ny = 16
  xmax = 32
  ymax = 32
[]

[GlobalParams]
  radius = 20.0
  int_width = 4.0
  x1 = 0
  y1 = 0
[]

[Variables]
  [./w]
  [../]
  [./eta]
  [../]
[]

[ICs]
  [./w]
    type = SmoothCircleIC
    variable = w
    # note w = A*(c-cleq), A = 1.0, cleq = 0.0 ,i.e., w = c (in the matrix/liquid phase)
    outvalue = -0.2
    invalue = 0.2
  [../]
  [./eta]
    type = SmoothCircleIC
    variable = eta
    outvalue = 0.0
    invalue = 1.0
  [../]
[]

[Kernels]
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
    args = '' # in this case chi (the susceptibility) is simply a constant
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = D
    args = ''
  [../]
  [./coupled_etadot]
    type = CoupledSusceptibilityTimeDerivative
    variable = w
    v = eta
    f_name = ft
    args = 'eta'
  [../]
  [./AC_bulk]
    type = AllenCahn
    variable = eta
    f_name = F
    args = 'w'
  [../]
  [./AC_int]
    type = ACInterface
    variable = eta
  [../]
  [./e_dot]
    type = TimeDerivative
    variable = eta
  [../]
[]

[Materials]
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'kappa_op  D    L    chi  cs   cl   A'
    prop_values = '4.0       1.0  1.0  1.0  0.0  1.0  1.0'
  [../]

  [./liquid_GrandPotential]
    type = DerivativeParsedMaterial
    function = '-0.5 * w^2/A - cl * w'
    args = 'w'
    f_name = f1
    material_property_names = 'cl A'
  [../]
  [./solid_GrandPotential]
    type = DerivativeParsedMaterial
    function = '-0.5 * w^2/A - cs * w'
    args = 'w'
    f_name = f2
    material_property_names = 'cs A'
  [../]
  [./switching_function]
    type = SwitchingFunctionMaterial
    eta = eta
    h_order = HIGH
  [../]
  [./barrier_function]
    type = BarrierFunctionMaterial
    eta = eta
  [../]
  [./total_GrandPotential]
    type = DerivativeTwoPhaseMaterial
    args = 'w'
    eta = eta
    fa_name = f1
    fb_name = f2
    derivative_order = 2
    W = 1.0
  [../]
  [./coupled_eta_function]
    type = DerivativeParsedMaterial
    function = '(cs - cl) * dh'
    args = 'eta'
    f_name = ft
    material_property_names = 'cs cl dh:=D[h,eta]'
    derivative_order = 1
    outputs = exodus
  [../]

  [./concentration]
    type = ParsedMaterial
    f_name = c
    material_property_names = 'dF:=D[F,w]'
    function = '-dF'
    outputs = exodus
  [../]
[]

[Postprocessors]
  [./C]
    type = ElementIntegralMaterialProperty
    mat_prop = c
    execute_on = 'initial timestep_end'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON

  l_max_its = 15
  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  num_steps = 5
  dt = 10.0
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = 'TIMESTEP_END'
[]

Child Objects

modules/phase_field/include/kernels/AntitrappingCurrent.h

modules/phase_field/include/kernels/AntitrappingCurrent.h

// 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

#pragma once

#include "CoupledSusceptibilityTimeDerivative.h"

// Forward Declaration
class AntitrappingCurrent;

template <>
InputParameters validParams<AntitrappingCurrent>();

/**
 * This calculates a modified coupled time derivative that multiplies the time derivative of a
 * coupled variable by a function of the variables and interface normal
 */
class AntitrappingCurrent : public CoupledSusceptibilityTimeDerivative
{
public:
  AntitrappingCurrent(const InputParameters & parameters);

protected:
  virtual Real computeQpResidual();
  virtual Real computeQpJacobian();
  virtual Real computeQpOffDiagJacobian(unsigned int jvar);

  const VariableGradient & _grad_v;
};

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