- 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

# 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 instead of the variable to whom's residual the `CoupledTimeDerivative`

kernel contributes. Consequently, the strong form on the the domain is

(1) where the second term on the left hand side corresponds to the strong forms of other kernels. The `CoupledTimeDerivative`

weak form is then

(2) where the are test functions and is the finite element solution of the weak formulation.

The Jacobian contribution is equal to (3) where is a constant that depends on the time stepping scheme; 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

- 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