#include <StabilizationSD.hpp>

Collaboration diagram for StabilizationSD< MeshType, DofType >:

typedef MeshType	mesh_Type

typedef DofType	dof_Type

Constructor and Destructor
	StabilizationSD (const GetPot &dataFile, const mesh_Type &mesh, const dof_Type &dof, const ReferenceFE &refFE, const QuadratureRule &quadRule, Real viscosity)
	Constructor. More...

virtual	~StabilizationSD ()
	~Destructor More...

Methods
template<typename MatrixType , typename VectorType >
void	applySUPG (const Real dt, MatrixType &matrix, const VectorType &state)
	compute the SUPG stabilization terms and add them into the monolithic N.S. matrix More...

template<typename MatrixType , typename VectorType >
void	applySD (const Real dt, MatrixType &matrix, const VectorType &state)
	compute the SD stabilization terms and add them into the Momentum matrix More...

template<typename VectorType , typename SourceType >
void	applyRHS (const Real dt, VectorType &vector, const VectorType &state, const SourceType &source, const Real &time)
	compute the SUPG stabilization terms and add them into the right and side 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 $( \beta \nabla \mathbf{u} , \beta \nabla \mathbf{v})$ . More...

void	setGammaDiv (const Real &gammaDiv)
	Set the stabilization parameter $\gamma_d$ for $( div \mathbf{u} , div \nabla \mathbf{v})$ . More...

Private Constructor
	StabilizationSD ()
	Default Constructor. More...

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

Private Methods
template<typename VectorType >
void	computeParameters (const Real dt, const UInt iVol, const VectorType &state, VectorElemental &beta, Real &coeffBeta, Real &coeffDiv) const
	Compute the stabilization coefficients for each element. More...

void	bgradu_bgradv (const Real &coef, VectorElemental &vel, ElemMat &elmat, const CurrentFE &fe, UInt iblock, UInt jblock, UInt nb) const
	Evaluate the varf $(\beta \nabla \mathbf{u}, \beta \nabla \mathbf{v})$ . More...

void	lapu_bgradv (const Real &coef, VectorElemental &vel, MatrixElemental &elmat, const CurrentFE &fe, UInt iblock, UInt jblock, UInt nb) const
	Evaluate the varf $(\Delta \mathbf{u}, \beta \nabla \mathbf{v})$ . More...

void	gradp_bgradv (const Real &coef, VectorElemental &vel, MatrixElemental &elmat, const CurrentFE &fe) const
	Evaluate the varf $(\nabla p, \beta \nabla \mathbf{v})$ . More...

void	lapu_gradq (const Real &coef, MatrixElemental &elmat, const CurrentFE &fe) const
	Evaluate the varf $(\Delta \mathbf{u}, \nabla q)$ . More...

template<typename SourceType >
void	f_bgradv (const Real &coef, SourceType &source, VectorElemental &vel, VectorElemental &elvec, const CurrentFE &fe, UInt iblock, const Real &time) const
	Evaluate the varf $(f, \beta \nabla \mathbf{v})$ . More...

template<typename SourceType >
void	f_gradq (const Real &coef, SourceType &source, VectorElemental &elvec, const CurrentFE &fe, UInt iblock, const Real &time) const
	Evaluate the varf $(f, \nabla q)$ . More...

Private Attributes
const mesh_Type &	M_mesh
	the mesh object More...

const dof_Type &	M_dof
	the dof object More...

CurrentFE	M_fe
	current fe for the assembling of stabilization terms. More...

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

Real	M_gammaBeta
	Stabilization coefficient of $(c(h,dt, \|\beta\|, nu) \beta \nabla \mathbf{u} , \beta \nabla \mathbf{v})$ . More...

Real	M_gammaDiv
	Stabilization coefficient of $(c(h,dt) div \mathbf{u} , div \nabla \mathbf{v})$ . More...

MatrixElemental	M_elMat
	Elementary Matrix for assembling the stabilization terms. More...

VectorElemental	M_elVec
	Elementary Vector for assembling the stabilization terms. More...

Detailed Description

template<typename MeshType, typename DofType>
class LifeV::StabilizationSD< MeshType, DofType >

StabilizationSD Class.

Streamline diffusion and SUPG for Navier-Stokes

Author: M.A. Fernandez

Implementation of streamline diffusion (SD) and SUPG for the Navier-Stokes equations.
SUPG can be used only with equal order finite element for the discretization of velocity and pressure fields.

Definition at line 59 of file StabilizationSD.hpp.

Member Typedef Documentation

◆ mesh_Type

typedef MeshType mesh_Type

Definition at line 65 of file StabilizationSD.hpp.

◆ dof_Type

typedef DofType dof_Type

Definition at line 66 of file StabilizationSD.hpp.

Constructor & Destructor Documentation

◆ StabilizationSD() [1/3]

StabilizationSD	(	const GetPot &	dataFile,
		const mesh_Type &	mesh,
		const dof_Type &	dof,
		const ReferenceFE &	refFE,
		const QuadratureRule &	quadRule,
		Real	viscosity
	)

Constructor.

Parameters

dataFile	GetPot dataFile where to read the stabilization parameter
mesh	mesh_Type mesh
dof	dof_Type velocity field degree of freedom
refFE	refFE velocity field reference finite element
quadRule	QuadratureRule quadrature rule for the integration of the stabilization variational forms
viscosity	viscosity fluid viscosity $\nu$

Definition at line 236 of file StabilizationSD.hpp.

Here is the caller graph for this function:

◆ ~StabilizationSD()

virtual ~StabilizationSD ( )

inlinevirtual

~Destructor

Definition at line 87 of file StabilizationSD.hpp.

◆ StabilizationSD() [2/3]

StabilizationSD ( )

private

Default Constructor.

◆ StabilizationSD() [3/3]

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

private

Copy Constructor.

Member Function Documentation

◆ applySUPG()

void applySUPG	(	const Real	dt,
		MatrixType &	matrix,
		const VectorType &	state
	)

compute the SUPG stabilization terms and add them into the monolithic N.S. matrix

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

Block(1,1): $c_\beta(\beta \nabla \mathbf{u} , \beta \nabla \mathbf{v}) + c_\beta( - \mu L \mathbf{u} , \beta \nabla \mathbf{v} )+ c_d( div \mathbf{u} , div \nabla \mathbf{v})$
Block(1,2): $c_\beta(\nabla p , \beta \nabla \mathbf{v})$
Block(2,1): $c_\beta(\beta \nabla \mathbf{u} , \nabla q) + c_\beta( - \mu L \mathbf{u} , \nabla q )$
Block(2,2): $c_\beta(\nabla p , \nabla q)$

where $(\cdot, \cdot)$ represents the $L^2$ scalar product, and

$\displaystyle c_\beta = \frac{\gamma_\beta}{\sqrt{ 4/( dt^2) + 4\|\beta\|_\infty/h^2 + 16*\nu/h^4 }}$ , where is the diameter of the element;
$\displaystyle c_d = \gamma_d h \|\beta\|_\infty$ .

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)

Definition at line 257 of file StabilizationSD.hpp.

◆ applySD()

void applySD	(	const Real	dt,
		MatrixType &	matrix,
		const VectorType &	state
	)

compute the SD stabilization terms and add them into the Momentum matrix

The following stabilization term is added: $c_\beta(\beta \nabla \mathbf{u} , \beta \nabla \mathbf{v})$

Parameters

dt	Real timestep
matrix	MatrixType where the stabilization terms are added into
state	VectorType velocity field for the linearization of the stabilization

Definition at line 344 of file StabilizationSD.hpp.

◆ applyRHS()

void applyRHS	(	const Real	dt,
		VectorType &	vector,
		const VectorType &	state,
		const SourceType &	source,
		const Real &	time
	)

compute the SUPG stabilization terms and add them into the right and side

Add the following stabilization terms to rhs

Block(1,1): $(c_\beta f , \beta \nabla \mathbf{v})$ ;
Block(1,2): $(c_\beta f , \nabla q )$ .

Parameters

dt	Real timestep
vector	VectorType where the stabilization terms are added into
state	VectorType velocity field for the linearization of the stabilization
source	SourceType a functor f(time, x, y, z, ic) which represents the forcing term
time	REAL the actual time in which source should be evaluated

Definition at line 417 of file StabilizationSD.hpp.

◆ showMe()

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

Display class informations.

Definition at line 487 of file StabilizationSD.hpp.

◆ setGammaBeta()

void setGammaBeta ( const Real & gammaBeta )

inline

Set the stabilization parameter $\gamma_\beta$ for $( \beta \nabla \mathbf{u} , \beta \nabla \mathbf{v})$ .

Definition at line 156 of file StabilizationSD.hpp.

◆ setGammaDiv()

void setGammaDiv ( const Real & gammaDiv )

inline

Set the stabilization parameter $\gamma_d$ for $( div \mathbf{u} , div \nabla \mathbf{v})$ .

Definition at line 161 of file StabilizationSD.hpp.

◆ computeParameters()

void computeParameters	(	const Real	dt,
		const UInt	iVol,
		const VectorType &	state,
		VectorElemental &	beta,
		Real &	coeffBeta,
		Real &	coeffDiv
	)		const

private

Compute the stabilization coefficients for each element.

Definition at line 502 of file StabilizationSD.hpp.

◆ bgradu_bgradv()

void bgradu_bgradv	(	const Real &	coef,
		VectorElemental &	vel,
		ElemMat &	elmat,
		const CurrentFE &	fe,
		UInt	iblock,
		UInt	jblock,
		UInt	nb
	)		const

private

Evaluate the varf $(\beta \nabla \mathbf{u}, \beta \nabla \mathbf{v})$ .

Definition at line 592 of file StabilizationSD.hpp.

◆ lapu_bgradv()

void lapu_bgradv	(	const Real &	coef,
		VectorElemental &	vel,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		UInt	iblock,
		UInt	jblock,
		UInt	nb
	)		const

private

Evaluate the varf $(\Delta \mathbf{u}, \beta \nabla \mathbf{v})$ .

Definition at line 651 of file StabilizationSD.hpp.

◆ gradp_bgradv()

void gradp_bgradv	(	const Real &	coef,
		VectorElemental &	vel,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)		const

private

Evaluate the varf $(\nabla p, \beta \nabla \mathbf{v})$ .

Definition at line 545 of file StabilizationSD.hpp.

◆ lapu_gradq()

void lapu_gradq	(	const Real &	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)		const

private

Evaluate the varf $(\Delta \mathbf{u}, \nabla q)$ .

Definition at line 714 of file StabilizationSD.hpp.

◆ f_bgradv()

void f_bgradv	(	const Real &	coef,
		SourceType &	source,
		VectorElemental &	vel,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		UInt	iblock,
		const Real &	time
	)		const

private

Evaluate the varf $(f, \beta \nabla \mathbf{v})$ .

Definition at line 748 of file StabilizationSD.hpp.

◆ f_gradq()

void f_gradq	(	const Real &	coef,
		SourceType &	source,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		UInt	iblock,
		const Real &	time
	)		const

private

Evaluate the varf $(f, \nabla q)$ .

Definition at line 793 of file StabilizationSD.hpp.

Field Documentation

◆ M_mesh

const mesh_Type& M_mesh

private

the mesh object

Definition at line 213 of file StabilizationSD.hpp.

◆ M_dof

const dof_Type& M_dof

private

the dof object

Definition at line 215 of file StabilizationSD.hpp.

◆ M_fe

CurrentFE M_fe

private

current fe for the assembling of stabilization terms.

Definition at line 217 of file StabilizationSD.hpp.

◆ M_viscosity

Real M_viscosity

private

fluid viscosity $\nu$

Definition at line 219 of file StabilizationSD.hpp.

◆ M_gammaBeta

Real M_gammaBeta

private

Stabilization coefficient of $(c(h,dt, |\beta|, nu) \beta \nabla \mathbf{u} , \beta \nabla \mathbf{v})$ .

Definition at line 221 of file StabilizationSD.hpp.

◆ M_gammaDiv

Real M_gammaDiv

private

Stabilization coefficient of $(c(h,dt) div \mathbf{u} , div \nabla \mathbf{v})$ .

Definition at line 223 of file StabilizationSD.hpp.

◆ M_elMat

MatrixElemental M_elMat

private

Elementary Matrix for assembling the stabilization terms.

Definition at line 225 of file StabilizationSD.hpp.

◆ M_elVec

VectorElemental M_elVec

private

Elementary Vector for assembling the stabilization terms.

Definition at line 227 of file StabilizationSD.hpp.

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

StabilizationSD.hpp

Constructor and Destructor

Methods

Set Methods

Private Constructor

Private Methods

Private Attributes

Detailed Description

template<typename MeshType, typename DofType> class LifeV::StabilizationSD< MeshType, DofType >

Member Typedef Documentation

◆ mesh_Type

◆ dof_Type

Constructor & Destructor Documentation

◆ StabilizationSD() [1/3]

◆ ~StabilizationSD()

◆ StabilizationSD() [2/3]

◆ StabilizationSD() [3/3]

Member Function Documentation

◆ applySUPG()

◆ applySD()

◆ applyRHS()

◆ showMe()

◆ setGammaBeta()

◆ setGammaDiv()

◆ computeParameters()

◆ bgradu_bgradv()

◆ lapu_bgradv()

◆ gradp_bgradv()

◆ lapu_gradq()

◆ f_bgradv()

◆ f_gradq()

Field Documentation

◆ M_mesh

◆ M_dof

◆ M_fe

◆ M_viscosity

◆ M_gammaBeta

◆ M_gammaDiv

◆ M_elMat

◆ M_elVec

template<typename MeshType, typename DofType>
class LifeV::StabilizationSD< MeshType, DofType >