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 $var element = document.getElementById("moose-equation-20d7fca2-6b8c-41dd-aec2-9cd1f0616929");katex.render("v", element, {displayMode:false,throwOnError:false});$ instead of the variable $var element = document.getElementById("moose-equation-f7ea448c-77a5-49d5-969d-edaa03e5dafe");katex.render("u", element, {displayMode:false,throwOnError:false});$ to whom's residual the CoupledTimeDerivative kernel contributes. Consequently, the strong form on the the domain $var element = document.getElementById("moose-equation-4a51e504-657f-47d8-84d5-67d62766bdbe");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ is

$(1)var element = document.getElementById("moose-equation-d97d1b63-470f-4cf3-87e1-105277b43b38");katex.render("\\underbrace{\\frac{\\partial v}{\\partial t}}_{\\textrm{CoupledTimeDerivative}} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega \", element, {displayMode:true,throwOnError:false});$ where the second term on the left hand side corresponds to the strong forms of other kernels. The CoupledTimeDerivative weak form is then

$(2)var element = document.getElementById("moose-equation-e6b7b38a-2aa3-4811-988a-affa32b88140");katex.render("R_i(u_h) = \\bigg(\\psi_i, \\frac{\\partial v_h}{\\partial t}\\bigg) \\quad \\forall \\psi_i, \", element, {displayMode:true,throwOnError:false});$ where the $var element = document.getElementById("moose-equation-060914be-b0ed-4dc3-b03e-9015706a4f57");katex.render("\\psi_i", element, {displayMode:false,throwOnError:false});$ are test functions and $var element = document.getElementById("moose-equation-56addabb-4551-4960-915e-1a307d608fed");katex.render("u_h \\in \\mathcal{S}^h", element, {displayMode:false,throwOnError:false});$ is the finite element solution of the weak formulation.

The Jacobian contribution is equal to $(3)var element = document.getElementById("moose-equation-544ce0fd-4362-4193-92c0-7627d668313d");katex.render("\\frac{\\partial R_i(u_h)}{\\partial u_j} = (\\psi_i, a_v\\phi_j).", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-a5bc1e8e-1c32-4dc9-b9e6-d7a7ea7569c3");katex.render("a_v", element, {displayMode:false,throwOnError:false});$ is a constant that depends on the time stepping scheme; $var element = document.getElementById("moose-equation-2f68aa43-28e2-4af5-b950-be10df6f06b4");katex.render("a_v", element, {displayMode:false,throwOnError:false});$ 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:

test/tests/kernels/coupled_time_derivative/coupled_time_derivative_test.i
block=Kernels label=false

Input Parameters

variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Description:The name of the variable that this Kernel operates on
vCoupled variable
C++ Type:std::vector
Description:Coupled variable

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied

Optional Parameters

enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
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
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.)
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
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.
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Description:The seed for the master random number generator
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
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.)
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Description:Determines whether this object is calculated using an implicit or explicit form

Advanced Parameters

vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Description:The tag for the vectors this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
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
Description:The tag for the matrices this Kernel should fill
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Description:The extra tags for the matrices this Kernel should fill

Tagging Parameters

Description
Example Syntax
Input Parameters