mfem::RusanovFlux Class Reference

Rusanov flux, also known as local Lax-Friedrichs, F̂ n = ½(F(u⁺,x)n + F(u⁻,x)n) - ½λ(u⁺ - u⁻) where λ is the maximum characteristic speed. More...

#include <hyperbolic.hpp>

Inheritance diagram for mfem::RusanovFlux:

Collaboration diagram for mfem::RusanovFlux:

Public Member Functions
	RusanovFlux (const FluxFunction &fluxFunction)
	Constructor for a flux function.
real_t	Eval (const Vector &state1, const Vector &state2, const Vector &nor, FaceElementTransformations &Tr, Vector &flux) const override
	Normal numerical flux F̂(u⁻,u⁺,x) n.
void	Grad (int side, const Vector &state1, const Vector &state2, const Vector &nor, FaceElementTransformations &Tr, DenseMatrix &grad) const override
	Jacobian of normal numerical flux F̂(u⁻,u⁺,x) n.
real_t	Average (const Vector &state1, const Vector &state2, const Vector &nor, FaceElementTransformations &Tr, Vector &flux) const override
	Average normal numerical flux over the interval [u⁻, u⁺] in the second argument of the flux F̂(u⁻,u,x) n.
void	AverageGrad (int side, const Vector &state1, const Vector &state2, const Vector &nor, FaceElementTransformations &Tr, DenseMatrix &grad) const override
	Jacobian of average normal numerical flux over the interval [u⁻, u⁺] in the second argument of the flux F̂(u⁻,u,x) n.
Public Member Functions inherited from mfem::NumericalFlux
	NumericalFlux (const FluxFunction &fluxFunction)
	Constructor for a flux function.
virtual	~NumericalFlux ()=default
const FluxFunction &	GetFluxFunction () const
	Get flux function F.

Protected Attributes
Vector	fluxN1
Vector	fluxN2
DenseMatrix	JDotN
Protected Attributes inherited from mfem::NumericalFlux
const FluxFunction &	fluxFunction

Detailed Description

Rusanov flux, also known as local Lax-Friedrichs, F̂ n = ½(F(u⁺,x)n + F(u⁻,x)n) - ½λ(u⁺ - u⁻) where λ is the maximum characteristic speed.

Note

The implementation assumes monotonous |dF(u,x)/du⋅n| in u, so the maximum characteristic speed λ for any interval [u⁻, u⁺] is given by max(|dF(u⁺,x)/du⁺⋅n|, |dF(u⁻,x)/du⁻⋅n|).

Definition at line 428 of file hyperbolic.hpp.

Constructor & Destructor Documentation

RusanovFlux()

mfem::RusanovFlux::RusanovFlux

(

const FluxFunction &

fluxFunction

)

Constructor for a flux function.

Parameters

fluxFunction

flux function F(u,x)

Definition at line 441 of file hyperbolic.cpp.

Member Function Documentation

Average()

real_t mfem::RusanovFlux::Average ( const Vector & state1, const Vector & state2, const Vector & nor, FaceElementTransformations & Tr, Vector & flux ) const

overridevirtual

Average normal numerical flux over the interval [u⁻, u⁺] in the second argument of the flux F̂(u⁻,u,x) n.

Note

The average normal flux F̄ n is required to be implemented in FluxFunction::ComputeAvgFluxDotN()

Systems of equations are treated component-wise

Parameters

[in]	state1	state value (u⁻) of the beginning of the interval (num_equations)
[in]	state2	state value (u⁺) of the end of the interval (num_equations)
[in]	nor	normal vector (not a unit vector) (dim)
[in]	Tr	face element transformation
[out]	flux	½(F̄(u⁻,u⁺,x)n + F(u⁻,x)n) - ¼λ(u⁺ - u⁻)

Returns

max(|dF(u⁺,x)/du⁺⋅n|, |dF(u⁻,x)/du⁻⋅n|)

Reimplemented from mfem::NumericalFlux.

Definition at line 506 of file hyperbolic.cpp.

AverageGrad()

void mfem::RusanovFlux::AverageGrad ( int side, const Vector & state1, const Vector & state2, const Vector & nor, FaceElementTransformations & Tr, DenseMatrix & grad ) const

overridevirtual

Jacobian of average normal numerical flux over the interval [u⁻, u⁺] in the second argument of the flux F̂(u⁻,u,x) n.

Note

The average normal flux F̄ n is required to be implemented in FluxFunction::ComputeAvgFluxDotN() and the Jacobian of flux J n in FluxFunction::ComputeFluxJacobianDotN()

Only the diagonal terms of the J n are considered, i.e., systems are treated as a set of independent equations

Parameters

[in]	side	gradient w.r.t the first (u⁻) or second argument (u⁺)
[in]	state1	state value (u⁻) of the beginning of the interval (num_equations)
[in]	state2	state value (u⁺) of the end of the interval (num_equations)
[in]	nor	normal vector (not a unit vector) (dim)
[in]	Tr	face element transformation
[out]	grad	Jacobian of F̄(u⁻,u⁺,x) n side = 1: ½(F̄(u⁻,u⁺,x)n - F(u⁻,x)n) / (u⁺ - u⁻) - ½J(u⁻,x)n + ¼λ side = 2: ½(F(u⁺,x)n - F̄(u⁻,u⁺,x)n) / (u⁺ - u⁻) - ¼λ

Reimplemented from mfem::NumericalFlux.

Definition at line 527 of file hyperbolic.cpp.

Eval()

real_t mfem::RusanovFlux::Eval ( const Vector & state1, const Vector & state2, const Vector & nor, FaceElementTransformations & Tr, Vector & flux ) const

overridevirtual

Normal numerical flux F̂(u⁻,u⁺,x) n.

Note

Systems of equations are treated component-wise

Parameters

[in]	state1	state value (u⁻) at a point from the first element (num_equations)
[in]	state2	state value (u⁺) at a point from the second element (num_equations)
[in]	nor	normal vector (not a unit vector) (dim)
[in]	Tr	face element transformation
[out]	flux	F̂ n = ½(F(u⁺,x)n + F(u⁻,x)n) - ½λ(u⁺ - u⁻)

Returns

max(|dF(u⁺,x)/du⁺⋅n|, |dF(u⁻,x)/du⁻⋅n|)

Implements mfem::NumericalFlux.

Definition at line 450 of file hyperbolic.cpp.

Grad()

void mfem::RusanovFlux::Grad ( int side, const Vector & state1, const Vector & state2, const Vector & nor, FaceElementTransformations & Tr, DenseMatrix & grad ) const

overridevirtual

Jacobian of normal numerical flux F̂(u⁻,u⁺,x) n.

Note

The Jacobian of flux J n is required to be implemented in FluxFunction::ComputeFluxJacobianDotN()

Parameters

[in]	side	gradient w.r.t the first (u⁻) or second argument (u⁺)
[in]	state1	state value (u⁻) of the beginning of the interval (num_equations)
[in]	state2	state value (u⁺) of the end of the interval (num_equations)
[in]	nor	normal vector (not a unit vector) (dim)
[in]	Tr	face element transformation
[out]	grad	Jacobian of F(u⁻,u⁺,x) n side = 1: ½J(u⁻,x)n + ½λ side = 2: ½J(u⁺,x)n - ½λ

Reimplemented from mfem::NumericalFlux.

Definition at line 470 of file hyperbolic.cpp.

Member Data Documentation

fluxN1

Vector mfem::RusanovFlux::fluxN1

mutableprotected

Definition at line 524 of file hyperbolic.hpp.

fluxN2

Vector mfem::RusanovFlux::fluxN2

protected

Definition at line 524 of file hyperbolic.hpp.

JDotN

DenseMatrix mfem::RusanovFlux::JDotN

mutableprotected

Definition at line 525 of file hyperbolic.hpp.

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

• fem/hyperbolic.hpp
• fem/hyperbolic.cpp