#include <StabilizationIP.hpp>

Collaboration diagram for StabilizationIP< MeshType, DofType >:

Public Types
typedef std::shared_ptr< MeshType >	mesh_type

typedef MeshType	mesh_Type

typedef DofType	dof_Type

typedef std::shared_ptr< mesh_Type >	meshPtr_Type

typedef std::shared_ptr< dof_Type >	dofPtr_Type

Constructor and Destructor
	StabilizationIP ()
	Default Constructor. More...

virtual	~StabilizationIP ()

Methods
template<typename MatrixType , typename VectorType >
void	apply (MatrixType &matrix, const VectorType &state, bool verbose=true)
	compute IP stabilization terms and add them into matrix More...

void	showMe (std::ostream &output=std::cout) const
	Display class informations. More...

Set Methods
void	setGammaBeta (const Real &gammaBeta)
	Set the stabilization parameter $\gamma_\beta$ for $\Sigma_{f\in\mathcal{F}}\int_{f} [\beta \cdot \nabla \mathbf{u}] [\beta \cdot \nabla \mathbf{v}]$ . More...

void	setGammaDiv (const Real &gammaDiv)
	Set the stabilization parameter $\gamma_d$ for $\Sigma_{f\in\mathcal{F}}\int_{f} [div \mathbf{u}] [div \mathbf{v}]$ . More...

void	setGammaPress (const Real &gammaPress)
	Set the stabilization parameter $\gamma_p$ for $\Sigma_{f\in\mathcal{F}}\int_{f} [\nabla p] \cdot [\nabla q]$ . More...

void	setViscosity (const Real &viscosity)
	Set the fluid viscosity $\nu$ . More...

void	setMesh (const meshPtr_Type mesh)
	Set the mesh file. More...

void	setDiscretization (const dofPtr_Type &dof, const ReferenceFE &refFE, CurrentFEManifold &feBd, const QuadratureRule &quadRule)
	Set Discretization. More...

template<typename MapType >
void	setFeSpaceVelocity (FESpace< mesh_Type, MapType > &feSpaceVelocity)
	Set the fespace. More...

Private Types
typedef ID(*	FTOP) (ID const &localFacet, ID const &point)
	facetToPoint(i,j) = localId of jth point on ith local facet More...

Private Constructor
	StabilizationIP (const StabilizationIP< mesh_Type, dof_Type > &original)
	Copy Constructor. More...

Private Attributes
meshPtr_Type	M_mesh
	Pointer to the mesh object. More...

dofPtr_Type	M_dof
	reference to the DofType data structure More...

std::shared_ptr< CurrentFE >	M_feOnSide1
	current Fe on side 1 of the current facet More...

std::shared_ptr< CurrentFE >	M_feOnSide2
	current Fe on side 2 of the current facet More...

CurrentFEManifold *	M_feBd
	current boundary FE More...

Real	M_gammaBeta
	Stabilization parameter $\gamma_\beta$ for $\int_{facet} [\beta \cdot \nabla \mathbf{u}] [\beta \cdot \nabla \mathbf{v}]$ . More...

Real	M_gammaDiv
	Stabilization parameter $\gamma_d$ for $\int_{facet} [div \mathbf{u}] [div \mathbf{v}]$ . More...

Real	M_gammaPress
	Stabilization parameter $\gamma_p$ for $\int_{facet} [\nabla p] \cdot [\nabla q]$ . More...

Real	M_viscosity
	Fluid viscosity $\nu$ . More...

FTOP	M_facetToPoint
	facetToPoint(i,j) = localId of jth point on ith local facet More...

Detailed Description

template<typename MeshType, typename DofType>
class LifeV::details::StabilizationIP< MeshType, DofType >

StabilizationIP Class.

Interior Penality Stabilization

Author: C. Winkelmann chris.nosp@m.toph.nosp@m..wink.nosp@m.elma.nosp@m.nn@ep.nosp@m.fl.c.nosp@m.h

Implementation of I.P. stabilization for inf-sup incompatible finite elements for the Navier-Stokes equations.

This function adds the following stabilization terms to the Navier-Stokes monolithic matrix:

Block(1,1): $\Sigma_{f\in\mathcal{F}}\int_{f} c_\beta [\beta \cdot \nabla \mathbf{u}] [\beta \cdot \nabla \mathbf{v}] + \Sigma_{f\in\mathcal{F}}\int_{f} c_d [div \mathbf{u}] [div \mathbf{v}]$
Block(1,2): 0
Block(2,1): 0
Block(2,2): $\Sigma_{f\in\mathcal{F}}\int_{f} c_p [\nabla p] \cdot [\nabla q]$

where

$\mathcal{F}$ is the set of all the internal facets in the mesh;
$[\cdot]$ is the jump operator: .

and the parameter $c_\beta$ , $c_d$ , $c_p$ , are defined as follows:

$\displaystyle c_\beta = \frac{\gamma_\beta h} {\|\beta\|_\infty}$ , being the facet measure;
$\displaystyle c_d = \gamma_d h \|\beta\|_\infty$ ;
$\displaystyle c_p = \frac{\gamma_p h}{\max(\|\beta\|_\infty, \nu/h^2)}$ .

Both high Pechlet numbers and inf-sup incompatible FEM are stabilized.

Definition at line 91 of file StabilizationIP.hpp.

Member Typedef Documentation

◆ mesh_type

typedef std::shared_ptr<MeshType> mesh_type

Definition at line 97 of file StabilizationIP.hpp.

◆ mesh_Type

typedef MeshType mesh_Type

Definition at line 98 of file StabilizationIP.hpp.

◆ dof_Type

typedef DofType dof_Type

Definition at line 99 of file StabilizationIP.hpp.

◆ meshPtr_Type

typedef std::shared_ptr<mesh_Type> meshPtr_Type

Definition at line 100 of file StabilizationIP.hpp.

◆ dofPtr_Type

typedef std::shared_ptr<dof_Type> dofPtr_Type

Definition at line 101 of file StabilizationIP.hpp.

◆ FTOP

typedef ID( * FTOP) (ID const &localFacet, ID const &point)

private

facetToPoint(i,j) = localId of jth point on ith local facet

Definition at line 189 of file StabilizationIP.hpp.

Constructor & Destructor Documentation

◆ StabilizationIP() [1/2]

StabilizationIP ( )

Default Constructor.

Definition at line 229 of file StabilizationIP.hpp.

◆ ~StabilizationIP()

virtual ~StabilizationIP ( )

inlinevirtual

Definition at line 110 of file StabilizationIP.hpp.

◆ StabilizationIP() [2/2]

StabilizationIP ( const StabilizationIP< mesh_Type, dof_Type > & original )

private

Copy Constructor.

Member Function Documentation

◆ apply()

void apply	(	MatrixType &	matrix,
		const VectorType &	state,
		bool	verbose = `true`
	)

compute IP stabilization terms and add them into matrix

This function adds the following stabilization terms to the Navier-Stokes monolithic matrix:

Block(1,1): $\Sigma_{f\in\mathcal{F}}\int_{f} c_\beta [\beta \cdot \nabla \mathbf{u}] [\beta \cdot \nabla \mathbf{v}] + \Sigma_{f\in\mathcal{F}}\int_{f} c_d [div \mathbf{u}] [div \mathbf{v}]$
Block(1,2): 0
Block(2,1): 0
Block(2,2): $\Sigma_{f\in\mathcal{F}}\int_{f} c_p [\nabla p] \cdot [\nabla q]$

where

$\displaystyle c_\beta = \frac{\gamma_\beta h} {\|\beta\|_\infty}$ , being the facet measure;
$\displaystyle c_d = \gamma_\beta h \|\beta\|_\infty$ ;
$\displaystyle c_p = \frac{\gamma_p h}{\max(\|\beta\|_\infty, \nu/h^2)}$ .

Both high Pechlet numbers and inf-sup incompatible FEM are stabilized.

PREREQUISITE: The velocity and the pressure field should belong to the same finite element space

Parameters are the followings:

Parameters

dt	Real timestep (INPUT)
matrix	MatrixType where the stabilization terms are added into. (OUTPUT)
state	VectorType velocity field for the linearization of the stabilization (INPUT)
verbose	bool whenever of not to print on screen

Definition at line 242 of file StabilizationIP.hpp.

◆ showMe()

void showMe ( std::ostream & output = std::cout ) const

Display class informations.

Write information relative to the class on output

Parameters

output ostream ostream were to write (Default cout)

Definition at line 572 of file StabilizationIP.hpp.

◆ setGammaBeta()

void setGammaBeta ( const Real & gammaBeta )

inline

Set the stabilization parameter $\gamma_\beta$ for $\Sigma_{f\in\mathcal{F}}\int_{f} [\beta \cdot \nabla \mathbf{u}] [\beta \cdot \nabla \mathbf{v}]$ .

Definition at line 154 of file StabilizationIP.hpp.

◆ setGammaDiv()

void setGammaDiv ( const Real & gammaDiv )

inline

Set the stabilization parameter $\gamma_d$ for $\Sigma_{f\in\mathcal{F}}\int_{f} [div \mathbf{u}] [div \mathbf{v}]$ .

Definition at line 159 of file StabilizationIP.hpp.

◆ setGammaPress()

void setGammaPress ( const Real & gammaPress )

inline

Set the stabilization parameter $\gamma_p$ for $\Sigma_{f\in\mathcal{F}}\int_{f} [\nabla p] \cdot [\nabla q]$ .

Definition at line 164 of file StabilizationIP.hpp.

◆ setViscosity()

void setViscosity ( const Real & viscosity )

inline

Set the fluid viscosity $\nu$ .

Definition at line 169 of file StabilizationIP.hpp.

◆ setMesh()

void setMesh ( const meshPtr_Type mesh )

inline

Set the mesh file.

Definition at line 174 of file StabilizationIP.hpp.

◆ setDiscretization()

void setDiscretization	(	const dofPtr_Type &	dof,
		const ReferenceFE &	refFE,
		CurrentFEManifold &	feBd,
		const QuadratureRule &	quadRule
	)

Set Discretization.

Definition at line 587 of file StabilizationIP.hpp.

◆ setFeSpaceVelocity()

void setFeSpaceVelocity ( FESpace< mesh_Type, MapType > & feSpaceVelocity )

Set the fespace.

Definition at line 599 of file StabilizationIP.hpp.

Field Documentation

◆ M_mesh

meshPtr_Type M_mesh

private

Pointer to the mesh object.

Definition at line 201 of file StabilizationIP.hpp.

◆ M_dof

dofPtr_Type M_dof

private

reference to the DofType data structure

Definition at line 203 of file StabilizationIP.hpp.

◆ M_feOnSide1

std::shared_ptr<CurrentFE> M_feOnSide1

private

current Fe on side 1 of the current facet

Definition at line 205 of file StabilizationIP.hpp.

◆ M_feOnSide2

std::shared_ptr<CurrentFE> M_feOnSide2

private

current Fe on side 2 of the current facet

Definition at line 207 of file StabilizationIP.hpp.

◆ M_feBd

CurrentFEManifold* M_feBd

private

current boundary FE

Definition at line 209 of file StabilizationIP.hpp.

◆ M_gammaBeta

Real M_gammaBeta

private

Stabilization parameter $\gamma_\beta$ for $\int_{facet} [\beta \cdot \nabla \mathbf{u}] [\beta \cdot \nabla \mathbf{v}]$ .

Definition at line 211 of file StabilizationIP.hpp.

◆ M_gammaDiv

Real M_gammaDiv

private

Stabilization parameter $\gamma_d$ for $\int_{facet} [div \mathbf{u}] [div \mathbf{v}]$ .

Definition at line 213 of file StabilizationIP.hpp.

◆ M_gammaPress

Real M_gammaPress

private

Stabilization parameter $\gamma_p$ for $\int_{facet} [\nabla p] \cdot [\nabla q]$ .

Definition at line 215 of file StabilizationIP.hpp.

◆ M_viscosity

Real M_viscosity

private

Fluid viscosity $\nu$ .

Definition at line 217 of file StabilizationIP.hpp.

◆ M_facetToPoint

FTOP M_facetToPoint

private

facetToPoint(i,j) = localId of jth point on ith local facet

Definition at line 219 of file StabilizationIP.hpp.

The documentation for this class was generated from the following file:

StabilizationIP.hpp

Public Types

Constructor and Destructor

Methods

Set Methods

Private Types

Private Constructor

Private Attributes

Detailed Description

template<typename MeshType, typename DofType> class LifeV::details::StabilizationIP< MeshType, DofType >

Member Typedef Documentation

◆ mesh_type

◆ mesh_Type

◆ dof_Type

◆ meshPtr_Type

◆ dofPtr_Type

◆ FTOP

Constructor & Destructor Documentation

◆ StabilizationIP() [1/2]

◆ ~StabilizationIP()

◆ StabilizationIP() [2/2]

Member Function Documentation

◆ apply()

◆ showMe()

◆ setGammaBeta()

◆ setGammaDiv()

◆ setGammaPress()

◆ setViscosity()

◆ setMesh()

◆ setDiscretization()

◆ setFeSpaceVelocity()

Field Documentation

◆ M_mesh

◆ M_dof

◆ M_feOnSide1

◆ M_feOnSide2

◆ M_feBd

◆ M_gammaBeta

◆ M_gammaDiv

◆ M_gammaPress

◆ M_viscosity

◆ M_facetToPoint

template<typename MeshType, typename DofType>
class LifeV::details::StabilizationIP< MeshType, DofType >