CoupledTimeDerivative

Description

The CoupledTimeDerivative kernel is very similar to the TimeDerivative kernel with the exception that the time derivative operator is applied to a coupled variable $var element = document.getElementById("moose-equation-1843fe78-2ff1-48b9-8197-14c7950ce314");katex.render("v", element, {displayMode:false,throwOnError:false});$ instead of the variable $var element = document.getElementById("moose-equation-c1fdec72-7bb6-49ff-8f60-f23acdc57c41");katex.render("u", element, {displayMode:false,throwOnError:false});$ to whom's residual the CoupledTimeDerivative kernel contributes. Consequently, the strong form on the domain $var element = document.getElementById("moose-equation-54cb8fc7-0042-4520-ac08-c6fb0e50cda3");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ is

$(1)var element = document.getElementById("moose-equation-bd21abb8-abef-48ab-b0c1-4ee80a22fd8c");katex.render("\\underbrace{\\frac{\\partial v}{\\partial t}}_{\\textrm{CoupledTimeDerivative}} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega ", element, {displayMode:true,throwOnError:false});$ where the second term on the left hand side corresponds to the strong forms of other kernels. The CoupledTimeDerivative weak form is then

$(2)var element = document.getElementById("moose-equation-6b37cad4-b274-49d8-bcd5-33a7e7bbcd42");katex.render("R_i(u_h) = \\bigg(\\psi_i, \\frac{\\partial v_h}{\\partial t}\\bigg) \\quad \\forall \\psi_i, ", element, {displayMode:true,throwOnError:false});$ where the $var element = document.getElementById("moose-equation-51300feb-adb8-4633-a9cd-37142ea846d6");katex.render("\\psi_i", element, {displayMode:false,throwOnError:false});$ are test functions and $var element = document.getElementById("moose-equation-e473ddc7-0167-48fb-adeb-4141c3797b1c");katex.render("u_h \\in \\mathcal{S}^h", element, {displayMode:false,throwOnError:false});$ is the finite element solution of the weak formulation.

The Jacobian contribution is equal to $var element = document.getElementById("moose-equation-57601ec9-447e-4fcb-86f2-cf96c13e16e4");katex.render("\\frac{\\partial R_i(u_h)}{\\partial u_j} = (\\psi_i, a_v\\phi_j).", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-9c8574eb-a802-4e68-8e1a-579c92552a88");katex.render("a_v", element, {displayMode:false,throwOnError:false});$ is a constant that depends on the time stepping scheme; $var element = document.getElementById("moose-equation-4b28b67a-e8ce-46a9-b8cb-a5ca81908ff3");katex.render("a_v", element, {displayMode:false,throwOnError:false});$ is denoted by _dv_dot in the CoupledTimeDerivative class.

Example Syntax

CoupledTimeDerivative is used for example in the split Cahn Hilliard equations for phase field calculations. The syntax is simple, taking its type (CoupledTimeDerivative), the variable to that the residual the CoupledTimeDerivative contributes, and the coupled variable v that the time derivative operator acts upon. Example syntax can be found in the kernel block below:

[Kernels]
  [./time_u]
    type = TimeDerivative
    variable = u
  [../]
  [./fn_u]
    type = BodyForce
    variable = u
    function = 1
  [../]
  [./time_v]
    type = CoupledTimeDerivative
    variable = v
    v = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

Input Parameters

vCoupled variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled variable
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.
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_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, system
Controllable:No
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
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/test/tests/kernels/coupled_time_derivative/coupled_time_derivative_test.i)

###########################################################
# This is a simple test of the CoupledTimeDerivative kernel.
# The expected solution for the variable v is
# v(x) = 1/2 * (x^2 + x)
###########################################################

[Mesh]
  type = GeneratedMesh
  nx = 5
  ny = 5
  dim = 2
[]

[Variables]
  [./u]
  [../]
  [./v]
  [../]
[]

[Kernels]
  [./time_u]
    type = TimeDerivative
    variable = u
  [../]
  [./fn_u]
    type = BodyForce
    variable = u
    function = 1
  [../]
  [./time_v]
    type = CoupledTimeDerivative
    variable = v
    v = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = v
    boundary = 'left'
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = v
    boundary = 'right'
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

Description
Example Syntax
Input Parameters