# TimeDerivative

## Description

The TimeDerivative kernel implements a simple time derivative for the domain given by

(1) where the second term on the left hand side corresponds to the strong forms of other kernels. The corresponding TimeDerivative weak form using inner-product notation is

(2) where is the approximate solution and is a finite element test function.

The Jacobian is given by

(3) where is referred to as du_dot_du in MOOSE syntax. More information about time kernels can be found on the Kernels description page.

## Example Syntax

Time derivative terms are ubiquitous in any transient simulation. The kernel block for a transient advection-diffusion-reaction problem that demonstrates the TimeDerivative syntax is shown below:

[Kernels]

active = 'trans advection diffusion source'

[./trans]
type = TimeDerivative
variable = phi
[../]

variable = phi
Au = 10.
Bu = -6.
Cu = 5.
Av = 10.
Bv = 8.
Cv = -1.
[../]

[./diffusion]
type = Diffusion0
variable = phi
Ak = 10.
Bk = 0.1
Ck = 0.1
[../]

[./source]
type = ForcingFunctionXYZ0
variable = phi
omega0 = 2.
A0 = 1.
B0 = 1.2
C0 = 0.8
Au = 10.
Bu = -6.
Cu = 5.
Av = 10.
Bv = 8.
Cv = -1.
Ak = 10.
Bk = 0.1
Ck = 0.1
[../]

[]


## 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

• lumpingFalseTrue for mass matrix lumping, false otherwise

Default:False

C++ Type:bool

Options:

Description:True for mass matrix lumping, false otherwise

• displacementsThe displacements

C++ Type:std::vector

Options:

Description:The displacements

• 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

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

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

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.)

• 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.

• 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.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Options:

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

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.)

• 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

• 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

• 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

• 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