AbstractNumericalFlux Gives a common interface for hyperbolic's flux function. More...

#include <HyperbolicFluxNumerical.hpp>

Inheritance diagram for AbstractNumericalFlux< Mesh, SolverType >:

Collaboration diagram for AbstractNumericalFlux< Mesh, SolverType >:

Protected Attributes
vectorFunction_Type	M_physicalFlux
	Physical flux function. More...

vectorFunction_Type	M_firstDerivativePhysicalFlux
	First derivative, respect to unknown, of physical flux function. More...

Real	M_CFLBrentToll
	Tollerance for the Brent algorithm for computing the CFL condition. More...

UInt	M_CFLBrentMaxIter
	Maximum of iterations for the Brent algorithm for computing the CFL condition. More...

const FESpace< Mesh, MapEpetra > &	M_fESpace
	Finite element space of the hyperbolic solver. More...

std::vector< const vectorPtr_Type *>	M_fields
	Vector of pointers for the dependences of the permeability to external vector fields. More...

Public Types
typedef std::function< Vector(const Real &, const Real &, const Real &, const Real &, const std::vector< Real > &) >	vectorFunction_Type

typedef std::function< Real(const Real &) >	scalarFunction_Type

typedef SolverType::vector_type	vector_Type

typedef std::shared_ptr< vector_Type >	vectorPtr_Type

typedef GetPot	dataFile_Type

typedef KN< Real >	normal_Type

Constructors and destructor
	AbstractNumericalFlux (const vectorFunction_Type &physicalFlux, const vectorFunction_Type &firstDerivativePhysicalFlux, const FESpace< Mesh, MapEpetra > &fESpace, const dataFile_Type &data, const std::string &section="numerical_flux/")
	Constructor for the class. More...

virtual	~AbstractNumericalFlux ()
	Virtual destructor. More...

Operators
virtual Real	operator() (const Real &leftState, const Real &rightState, const normal_Type &normal, const UInt &iElem, const Real &t=0, const Real &x=0, const Real &y=0, const Real &z=0) const =0
	Computes the face contribution of the flux. More...

Set Methods
void	setExternalField (const vectorPtr_Type &field)
	Add one external field. More...

Get Methods
vectorFunction_Type	physicalFlux () const
	Return the physical flux. More...

vectorFunction_Type	firstDerivativePhysicalFlux () const
	Return the first derivative, respect to the unknown, of the physical flux. More...

Real	physicalFluxDotNormal (const normal_Type &normal, const UInt &iElem, const Real &t, const Real &x, const Real &y, const Real &z, const Real &unknown) const
	Evaluate the flux dot normal in a given point of a face. More...

Real	firstDerivativePhysicalFluxDotNormal (const normal_Type &normal, const UInt &iElem, const Real &t, const Real &x, const Real &y, const Real &z, const Real &unknown) const
	Evaluate the first derivative of the flux dot normal in a given point of a face. More...

Real	normInfinity (const Real &leftState, const Real &rightState, const normal_Type &normal, const UInt &iElem, const Real &t=0, const Real &x=0, const Real &y=0, const Real &z=0) const
	Computes the local infinity norm of the first derivative of the flux dot normal. More...

Protected Methods
scalarFunction_Type	computeFunctionDotNormal (const vectorFunction_Type &function, const normal_Type &normal, const UInt &iElem, const Real &t, const Real &x, const Real &y, const Real &z, const Real &plusMinus) const
	Return a scalar function from a general vector function dot normal in a given point of a face. More...

scalarFunction_Type	computeAbsFunctionDotNormal (const vectorFunction_Type &function, const normal_Type &normal, const UInt &iElem, const Real &t, const Real &x, const Real &y, const Real &z, const Real &plusMinus) const
	Return a scalar function from the absolute value of a general vector function dot normal in a given point of a face. More...

Detailed Description

template<typename Mesh, typename SolverType = LifeV::SolverAztecOO>
class LifeV::AbstractNumericalFlux< Mesh, SolverType >

AbstractNumericalFlux Gives a common interface for hyperbolic's flux function.

Author: Alessio Fumagalli aless.nosp@m.io.f.nosp@m.umaga.nosp@m.lli@.nosp@m.mail..nosp@m.poli.nosp@m.mi.it; Michel Kern miche.nosp@m.l.ke.nosp@m.rn@in.nosp@m.ria..nosp@m.fr

This class gives a common interface for hyperbolic's flux functions $\mathbf{F}( u )$ , in particoular it computes

the flux function dot product the outward unit normal $\mathbf{n}$ ;
the first derivative of the flux function, respect to , dot product the outward unit normal;
the maximum value of $\hat{\mathbf{F}} \cdot \mathbf{n}$ between to adjacent elements;
the value of $\Vert \mathbf{F}^\prime \cdot \mathbf{n}_{e, K} \Vert_{L^\infty(a_0, b_0) }$ between to adjacent elements.

The class can handle the dependeces of the flux function $\mathbf{F}$ of external vector or scalar fields.

Note: In the implementation of the physical flux $\mathbf{F}$ we suppose that the first parameter of the vector is the unknown. See the test case for an example.

Definition at line 137 of file HyperbolicFluxNumerical.hpp.

Member Typedef Documentation

◆ vectorFunction_Type

typedef std::function< Vector ( const Real&, const Real&, const Real&, const Real&, const std::vector<Real>& ) > vectorFunction_Type

Definition at line 148 of file HyperbolicFluxNumerical.hpp.

◆ scalarFunction_Type

typedef std::function< Real ( const Real& ) > scalarFunction_Type

Definition at line 150 of file HyperbolicFluxNumerical.hpp.

◆ vector_Type

typedef SolverType::vector_type vector_Type

Definition at line 152 of file HyperbolicFluxNumerical.hpp.

◆ vectorPtr_Type

typedef std::shared_ptr< vector_Type > vectorPtr_Type

Definition at line 153 of file HyperbolicFluxNumerical.hpp.

◆ dataFile_Type

typedef GetPot dataFile_Type

Definition at line 155 of file HyperbolicFluxNumerical.hpp.

◆ normal_Type

typedef KN< Real > normal_Type

Definition at line 156 of file HyperbolicFluxNumerical.hpp.

Constructor & Destructor Documentation

◆ AbstractNumericalFlux()

AbstractNumericalFlux	(	const vectorFunction_Type &	physicalFlux,
		const vectorFunction_Type &	firstDerivativePhysicalFlux,
		const FESpace< Mesh, MapEpetra > &	fESpace,
		const dataFile_Type &	data,
		const std::string &	section = `"numerical_flux/"`
	)

Constructor for the class.

Parameters

physicalFlux	Physical flux for the problem.
firstDerivativePhysicalFlux	First derivative, respect the the unknown, of the physical flux.
fESpace	Finite element space of the hyperbolic problem.
data	Data for the problem.
section	Section for read the data from GetPot file.

Definition at line 400 of file HyperbolicFluxNumerical.hpp.

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◆ ~AbstractNumericalFlux()

~AbstractNumericalFlux ( )

virtual

Virtual destructor.

Definition at line 418 of file HyperbolicFluxNumerical.hpp.

Member Function Documentation

◆ operator()()

virtual Real operator()	(	const Real &	leftState,
		const Real &	rightState,
		const normal_Type &	normal,
		const UInt &	iElem,
		const Real &	t = `0`,
		const Real &	x = `0`,
		const Real &	y = `0`,
		const Real &	z = `0`
	)		const

pure virtual

Computes the face contribution of the flux.

Given a face $e \in \partial K$ it evaluates

$\max \hat{\mathbf{F}} \cdot \mathbf{n}$

between to elements sharing the face.

Parameters

leftState	Left value of the unknown respect to the face.
rightValue	Right value of the unknown respect to the face.
normal	Normal of the face.
iElem	The ID of the current element in the mesh.
t	Current time.
x	Abscissa.
y	Ordinate.
z	Quota.

Note: We assume left and right side of is given by: the normal direction goes from the left side to the right side.

Implemented in GodunovNumericalFlux< Mesh, SolverType >.

◆ setExternalField()

void setExternalField ( const vectorPtr_Type & field )

inline

Add one external field.

Add one extra field for the dependece from $\mathbf{F}$ .

Parameters

field The filed to be added.

Definition at line 223 of file HyperbolicFluxNumerical.hpp.

◆ physicalFlux()

vectorFunction_Type physicalFlux ( ) const

inline

Return the physical flux.

Returns: The physical flux.

Definition at line 237 of file HyperbolicFluxNumerical.hpp.

◆ firstDerivativePhysicalFlux()

vectorFunction_Type firstDerivativePhysicalFlux ( ) const

inline

Return the first derivative, respect to the unknown, of the physical flux.

Returns: The first derivative of the physical flux.

Definition at line 246 of file HyperbolicFluxNumerical.hpp.

◆ physicalFluxDotNormal()

Real physicalFluxDotNormal	(	const normal_Type &	normal,
		const UInt &	iElem,
		const Real &	t,
		const Real &	x,
		const Real &	y,
		const Real &	z,
		const Real &	unknown
	)		const

inline

Evaluate the flux dot normal in a given point of a face.

Parameters

normal	The normal of the face.
iElem	The ID of the current element in the mesh.
t	Current time.
x	Abscissa.
y	Ordinate.
z	Quota.
unknown	The value of the unknown.

Returns: The value of $\mathbf{ \hat{ F } } \cdot \mathbf{ n }$ in the point .

Definition at line 262 of file HyperbolicFluxNumerical.hpp.

◆ firstDerivativePhysicalFluxDotNormal()

Real firstDerivativePhysicalFluxDotNormal	(	const normal_Type &	normal,
		const UInt &	iElem,
		const Real &	t,
		const Real &	x,
		const Real &	y,
		const Real &	z,
		const Real &	unknown
	)		const

inline

Evaluate the first derivative of the flux dot normal in a given point of a face.

Parameters

normal	The normal of the face.
iElem	The ID of the current element in the mesh.
t	Current time.
x	Abscissa.
y	Ordinate.
z	Quota.
unknown	The value of the unknown.

Returns: The value of $\mathbf{ \hat{ F^\prime } } \cdot \mathbf{ n }$ in the point .

Definition at line 284 of file HyperbolicFluxNumerical.hpp.

◆ normInfinity()

Real normInfinity	(	const Real &	leftState,
		const Real &	rightState,
		const normal_Type &	normal,
		const UInt &	iElem,
		const Real &	t = `0`,
		const Real &	x = `0`,
		const Real &	y = `0`,
		const Real &	z = `0`
	)		const

Computes the local infinity norm of the first derivative of the flux dot normal.

Given a face $e \in \partial K$ it evaluates

$\displaystyle \max_{e \in \partial K^- \cap \partial K^+} \vert \hat{\mathbf{F^\prime}} \cdot \mathbf{n} \vert$

between to elements sharing the face.

Parameters

leftState	Left value of the unknown respect to the face.
rightValue	Right value of the unknown respect to the face.
normal	Normal of the face.
iElem	The ID of the current element in the mesh.
t	Current time.
x	Abscissa.
y	Ordinate.
z	Quota.

Note: We assume left and right side of is given by: the normal direction goes from the left side to the right side.

Definition at line 431 of file HyperbolicFluxNumerical.hpp.

◆ computeFunctionDotNormal()

std::function< Real(const Real &) > computeFunctionDotNormal	(	const vectorFunction_Type &	function,
		const normal_Type &	normal,
		const UInt &	iElem,
		const Real &	t,
		const Real &	x,
		const Real &	y,
		const Real &	z,
		const Real &	plusMinus
	)		const

protected

Return a scalar function from a general vector function dot normal in a given point of a face.

Parameters

function	Function to be reduced.
normal	The normal of the face.
iElem	The ID of the current element in the mesh.
t	Current time.
x	Abscissa.
y	Ordinate.
z	Quota.
plusMinus

Returns: The function $g(u) = \pm \mathbf{f}(x,y,z,t,u) \cdot \mathbf{n}$ .

Definition at line 469 of file HyperbolicFluxNumerical.hpp.

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◆ computeAbsFunctionDotNormal()

scalarFunction_Type computeAbsFunctionDotNormal	(	const vectorFunction_Type &	function,
		const normal_Type &	normal,
		const UInt &	iElem,
		const Real &	t,
		const Real &	x,
		const Real &	y,
		const Real &	z,
		const Real &	plusMinus
	)		const

protected

Return a scalar function from the absolute value of a general vector function dot normal in a given point of a face.

Parameters

function	Function to be reduced.
normal	The normal of the face.
iElem	The ID of the current element in the mesh.
t	Current time.
x	Abscissa.
y	Ordinate.
z	Quota.
plusMinus

Returns: The function $g(u) = \pm \vert \mathbf{f}(x,y,z,t,u) \cdot \mathbf{n} \vert$ .

Field Documentation

◆ M_physicalFlux

vectorFunction_Type M_physicalFlux

protected

Physical flux function.

Definition at line 374 of file HyperbolicFluxNumerical.hpp.

◆ M_firstDerivativePhysicalFlux

vectorFunction_Type M_firstDerivativePhysicalFlux

protected

First derivative, respect to unknown, of physical flux function.

Definition at line 377 of file HyperbolicFluxNumerical.hpp.

◆ M_CFLBrentToll

Real M_CFLBrentToll

protected

Tollerance for the Brent algorithm for computing the CFL condition.

Definition at line 380 of file HyperbolicFluxNumerical.hpp.

◆ M_CFLBrentMaxIter

UInt M_CFLBrentMaxIter

protected

Maximum of iterations for the Brent algorithm for computing the CFL condition.

Definition at line 383 of file HyperbolicFluxNumerical.hpp.

◆ M_fESpace

const FESpace<Mesh, MapEpetra>& M_fESpace

protected

Finite element space of the hyperbolic solver.

Definition at line 386 of file HyperbolicFluxNumerical.hpp.

◆ M_fields

std::vector< const vectorPtr_Type* > M_fields

protected

Vector of pointers for the dependences of the permeability to external vector fields.

Definition at line 389 of file HyperbolicFluxNumerical.hpp.

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

HyperbolicFluxNumerical.hpp

Protected Attributes

Public Types

Constructors and destructor

Operators

Set Methods

Get Methods

Protected Methods

Detailed Description

template<typename Mesh, typename SolverType = LifeV::SolverAztecOO> class LifeV::AbstractNumericalFlux< Mesh, SolverType >

Member Typedef Documentation

◆ vectorFunction_Type

◆ scalarFunction_Type

◆ vector_Type

◆ vectorPtr_Type

◆ dataFile_Type

◆ normal_Type

Constructor & Destructor Documentation

◆ AbstractNumericalFlux()

◆ ~AbstractNumericalFlux()

Member Function Documentation

◆ operator()()

◆ setExternalField()

◆ physicalFlux()

◆ firstDerivativePhysicalFlux()

◆ physicalFluxDotNormal()

◆ firstDerivativePhysicalFluxDotNormal()

◆ normInfinity()

◆ computeFunctionDotNormal()

◆ computeAbsFunctionDotNormal()

Field Documentation

◆ M_physicalFlux

◆ M_firstDerivativePhysicalFlux

◆ M_CFLBrentToll

◆ M_CFLBrentMaxIter

◆ M_fESpace

◆ M_fields

template<typename Mesh, typename SolverType = LifeV::SolverAztecOO>
class LifeV::AbstractNumericalFlux< Mesh, SolverType >