GodunovNumericalFlux Gives an implementation for Godunov solver for hyperbolic's flux function. More...

#include <HyperbolicFluxNumerical.hpp>

Inheritance diagram for GodunovNumericalFlux< Mesh, SolverType >:

Collaboration diagram for GodunovNumericalFlux< Mesh, SolverType >:

Protected Attributes
Real	M_brentToll
	Tollerance for the Brent algorithm used for Godunov flux. More...

UInt	M_brentMaxIter
	Maximum of iteration for the Brent algorithm used for Godunov flux. More...

Protected Attributes inherited from AbstractNumericalFlux< Mesh, SolverType >
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 AbstractNumericalFlux< Mesh, SolverType >::vectorFunction_Type	vectorFunction_Type

typedef AbstractNumericalFlux< Mesh, SolverType >::scalarFunction_Type	scalarFunction_Type

typedef AbstractNumericalFlux< Mesh, SolverType >::dataFile_Type	dataFile_Type

typedef AbstractNumericalFlux< Mesh, SolverType >::normal_Type	normal_Type

Constructors and destructor
	GodunovNumericalFlux (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	~GodunovNumericalFlux ()
	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
	Computes the face contribution of the flux. More...

Additional Inherited Members
Public Types inherited from AbstractNumericalFlux< Mesh, SolverType >
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

Public Member Functions inherited from AbstractNumericalFlux< Mesh, SolverType >
	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...

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

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 Member Functions inherited from AbstractNumericalFlux< Mesh, SolverType >
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::GodunovNumericalFlux< Mesh, SolverType >

GodunovNumericalFlux Gives an implementation for Godunov solver 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 an implementation for Godunov solver for hyperbolic's flux functions $\mathbf{F}( u )$ . In particular it implements

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 computed using Godunov solver
$\hat{\mathbf{F}} \cdot \mathbf{n} (a,b)= \left\{ \begin{array}{l l} \displaystyle \min_{a \leq u \leq b} \mathbf{F} \cdot \mathbf{n} ( u ) & \mathrm{if} \quad a \leq b\,, \\ \displaystyle \max_{b \leq u \leq a} \mathbf{F} \cdot \mathbf{n} ( u ) & \mathrm{otherwise}\,. \end{array} \right.$
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 527 of file HyperbolicFluxNumerical.hpp.

Member Typedef Documentation

◆ vectorFunction_Type

typedef AbstractNumericalFlux<Mesh, SolverType>::vectorFunction_Type vectorFunction_Type

Definition at line 535 of file HyperbolicFluxNumerical.hpp.

◆ scalarFunction_Type

typedef AbstractNumericalFlux<Mesh, SolverType>::scalarFunction_Type scalarFunction_Type

Definition at line 536 of file HyperbolicFluxNumerical.hpp.

◆ dataFile_Type

typedef AbstractNumericalFlux<Mesh, SolverType>::dataFile_Type dataFile_Type

Definition at line 537 of file HyperbolicFluxNumerical.hpp.

◆ normal_Type

typedef AbstractNumericalFlux<Mesh, SolverType>::normal_Type normal_Type

Definition at line 538 of file HyperbolicFluxNumerical.hpp.

Constructor & Destructor Documentation

◆ GodunovNumericalFlux()

GodunovNumericalFlux	(	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 614 of file HyperbolicFluxNumerical.hpp.

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◆ ~GodunovNumericalFlux()

~GodunovNumericalFlux ( )

virtual

Virtual destructor.

Definition at line 633 of file HyperbolicFluxNumerical.hpp.

Member Function Documentation

◆ operator()()

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

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, using Godunov flux.

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.