# LevelSetForcingFunctionSUPG

This kernel adds the Streamline Upwind/Petrov-Galerkin (SUPG) stabilization term (Brooks and Hughes, 1982; Donea and Huerta, 2003) to a forcing or source term of a partial differential equation:

(1) where is the level set velocity, is the forcing term, and as defined below.

(2) where is the element length.

## Example Syntax

The LevelSetForcingFunctionSUPG Kernel should be used in conjunction with a forcing term. For example, if a BodyForce is defined as follows in the [Kernels] block.


[./phi_forcing]
type = BodyForce
variable = phi
function = phi_mms
[../]
(modules/level_set/test/tests/verification/1d_level_set_supg_mms/1d_level_set_supg_mms.i)

Given the forcing term, it is then possible to add the SUPG term to the same forcing function in the [Kernels] block as follows.


[./phi_forcing_supg]
type = LevelSetForcingFunctionSUPG
velocity_x = v_x
variable = phi
function = phi_mms
[../]
(modules/level_set/test/tests/verification/1d_level_set_supg_mms/1d_level_set_supg_mms.i)

## 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

• function1A function that describes the body force

Default:1

C++ Type:FunctionName

Options:

Description:A function that describes the body force

• postprocessor1A postprocessor whose value is multiplied by the body force

Default:1

C++ Type:PostprocessorName

Options:

Description:A postprocessor whose value is multiplied by the body force

• value1Coefficent to multiply by the body force term

Default:1

C++ Type:double

Options:

Description:Coefficent to multiply by the body force term

• velocity_zThe variable containing the z-component of the velocity front.

C++ Type:std::vector

Options:

Description:The variable containing the z-component of the velocity front.

• velocity_xThe variable containing the x-component of the velocity front.

C++ Type:std::vector

Options:

Description:The variable containing the x-component of the velocity front.

• velocity_yThe variable containing the y-component of the velocity front.

C++ Type:std::vector

Options:

Description:The variable containing the y-component of the velocity front.

• 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_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

• 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

• 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

## References

1. A. N. Brooks and T. J. R. Hughes. Streamline Upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32:199–259, 1982.[BibTeX]
2. J. Donea and A. Huerta. Finite element methods for flow problems. John Wiley & Sons, 2003.[BibTeX]