Abstract class for hyperbolic flux for a system of hyperbolic conservation laws. More...

#include <hyperbolic.hpp>

Inheritance diagram for mfem::FluxFunction:

Public Member Functions
	FluxFunction (const int num_equations, const int dim)

virtual	~FluxFunction ()

virtual real_t	ComputeFlux (const Vector &state, ElementTransformation &Tr, DenseMatrix &flux) const =0
	Compute flux F(u, x). Must be implemented in a derived class.

virtual real_t	ComputeFluxDotN (const Vector &state, const Vector &normal, FaceElementTransformations &Tr, Vector &fluxDotN) const
	Compute normal flux F(u, x)⋅n. Optionally overloaded in a derived class to avoid creating a full dense matrix for flux.

virtual real_t	ComputeAvgFlux (const Vector &state1, const Vector &state2, ElementTransformation &Tr, DenseMatrix &flux_) const
	Compute average flux over the given interval of states. Optionally overloaded in a derived class.

virtual real_t	ComputeAvgFluxDotN (const Vector &state1, const Vector &state2, const Vector &normal, FaceElementTransformations &Tr, Vector &fluxDotN) const
	Compute average normal flux over the given interval of states. Optionally overloaded in a derived class.

virtual void	ComputeFluxJacobian (const Vector &state, ElementTransformation &Tr, DenseTensor &J_) const
	Compute flux Jacobian J(u, x). Optionally overloaded in a derived class when Jacobian is necessary (e.g. Newton iteration, flux limiter)

virtual void	ComputeFluxJacobianDotN (const Vector &state, const Vector &normal, ElementTransformation &Tr, DenseMatrix &JDotN) const
	Compute normal flux Jacobian J(u, x)⋅n. Optionally overloaded in a derived class to avoid creating a full dense tensor for Jacobian.

Public Attributes
const int	num_equations

const int	dim

Detailed Description

Abstract class for hyperbolic flux for a system of hyperbolic conservation laws.

Definition at line 57 of file hyperbolic.hpp.

Constructor & Destructor Documentation

◆ FluxFunction()

mfem::FluxFunction::FluxFunction	(	const int	num_equations,
		const int	dim )

inline

Definition at line 63 of file hyperbolic.hpp.

◆ ~FluxFunction()

virtual mfem::FluxFunction::~FluxFunction ( )

inlinevirtual

Definition at line 66 of file hyperbolic.hpp.

Member Function Documentation

◆ ComputeAvgFlux()

virtual real_t mfem::FluxFunction::ComputeAvgFlux	(	const Vector &	state1,
		const Vector &	state2,
		ElementTransformation &	Tr,
		DenseMatrix &	flux_ ) const

inlinevirtual

Compute average flux over the given interval of states. Optionally overloaded in a derived class.

The average flux is defined as F̄(u1,u2) = ∫ F(u) du / (u2 - u1) for u ∈ [u1,u2], where u1 is the first state (state1) and the u2 the second state (state2), while F(u) is the flux as defined in ComputeFlux().

Used in the default implementation of ComputeAvgFluxDotN().

Parameters

[in]	state1	state of the beginning of the interval (num_equations)
[in]	state2	state of the end of the interval (num_equations)
[in]	Tr	element transformation
[out]	flux_	average flux from the given element at the current integration point (num_equations, dim)

Returns: real_t maximum characteristic speed |dF(u,x)/du| over the interval [u1,u2]

Reimplemented in mfem::AdvectionFlux, and mfem::BurgersFlux.

Definition at line 118 of file hyperbolic.hpp.

◆ ComputeAvgFluxDotN()

real_t mfem::FluxFunction::ComputeAvgFluxDotN	(	const Vector &	state1,
		const Vector &	state2,
		const Vector &	normal,
		FaceElementTransformations &	Tr,
		Vector &	fluxDotN ) const

virtual

Compute average normal flux over the given interval of states. Optionally overloaded in a derived class.

The average normal flux is defined as F̄(u1,u2)n = ∫ F(u)n du / (u2 - u1) for u ∈ [u1,u2], where u1 is the first state (state1) and the u2 the second state (state2), while n is the normal and F(u) is the flux as defined in ComputeFlux().

Used in NumericalFlux::Average() and NumericalFlux::AverageGrad() for evaluation of the average normal flux on a face.

Parameters

[in]	state1	state of the beginning of the interval (num_equations)
[in]	state2	state of the end of the interval (num_equations)
[in]	normal	normal vector, see mfem::CalcOrtho() (dim)
[in]	Tr	face transformation
[out]	fluxDotN	average normal flux from the given element at the current integration point (num_equations)

Returns: real_t maximum (normal) characteristic speed |dF(u,x)/du⋅n| over the interval [u1,u2]

Reimplemented in mfem::AdvectionFlux, and mfem::BurgersFlux.

Definition at line 408 of file hyperbolic.cpp.

◆ ComputeFlux()

virtual real_t mfem::FluxFunction::ComputeFlux	(	const Vector &	state,
		ElementTransformation &	Tr,
		DenseMatrix &	flux ) const

pure virtual

Compute flux F(u, x). Must be implemented in a derived class.

Used in HyperbolicFormIntegrator::AssembleElementVector() for evaluation of (F(u), ∇v) and in the default implementation of ComputeFluxDotN() for evaluation of F(u)⋅n.

Parameters

[in]	state	state at the current integration point (num_equations)
[in]	Tr	element transformation
[out]	flux	flux from the given element at the current integration point (num_equations, dim)

Returns: real_t maximum characteristic speed |dF(u,x)/du|

Note: One can put assertion in here to detect non-physical solution

Implemented in mfem::AdvectionFlux, mfem::BurgersFlux, mfem::EulerFlux, and mfem::ShallowWaterFlux.

◆ ComputeFluxDotN()

real_t mfem::FluxFunction::ComputeFluxDotN	(	const Vector &	state,
		const Vector &	normal,
		FaceElementTransformations &	Tr,
		Vector &	fluxDotN ) const

virtual

Compute normal flux F(u, x)⋅n. Optionally overloaded in a derived class to avoid creating a full dense matrix for flux.

Used in NumericalFlux for evaluation of the normal flux on a face.

Parameters

[in]	state	state at the current integration point (num_equations)
[in]	normal	normal vector, see mfem::CalcOrtho() (dim)
[in]	Tr	face transformation
[out]	fluxDotN	normal flux from the given element at the current integration point (num_equations)

Returns: real_t maximum (normal) characteristic speed |dF(u,x)/du⋅n|

Reimplemented in mfem::AdvectionFlux, mfem::BurgersFlux, mfem::EulerFlux, and mfem::ShallowWaterFlux.

Definition at line 393 of file hyperbolic.cpp.

◆ ComputeFluxJacobian()

virtual void mfem::FluxFunction::ComputeFluxJacobian	(	const Vector &	state,
		ElementTransformation &	Tr,
		DenseTensor &	J_ ) const

inlinevirtual

Compute flux Jacobian J(u, x). Optionally overloaded in a derived class when Jacobian is necessary (e.g. Newton iteration, flux limiter)

Used in HyperbolicFormIntegrator::AssembleElementGrad() for evaluation of Jacobian of the flux in an element and in the default implementation of ComputeFluxJacobianDotN().

Parameters

[in]	state	state at the current integration point (num_equations)
[in]	Tr	element transformation
[out]	J_	flux Jacobian, \( J(i,j,d) = dF_{id} / du_j \)

Reimplemented in mfem::AdvectionFlux, and mfem::BurgersFlux.

Definition at line 159 of file hyperbolic.hpp.

◆ ComputeFluxJacobianDotN()

void mfem::FluxFunction::ComputeFluxJacobianDotN	(	const Vector &	state,
		const Vector &	normal,
		ElementTransformation &	Tr,
		DenseMatrix &	JDotN ) const

virtual

Compute normal flux Jacobian J(u, x)⋅n. Optionally overloaded in a derived class to avoid creating a full dense tensor for Jacobian.

Used in NumericalFlux for evaluation of Jacobian of the normal flux on a face.

Parameters

[in]	state	state at the current integration point (num_equations)
[in]	normal	normal vector, see mfem::CalcOrtho() (dim)
[in]	Tr	element transformation
[out]	JDotN	normal flux Jacobian, \( JDotN(i,j) = d(F_{id} n_d) / du_j \)

Reimplemented in mfem::AdvectionFlux, and mfem::BurgersFlux.

Definition at line 423 of file hyperbolic.cpp.

Member Data Documentation

◆ dim

const int mfem::FluxFunction::dim

Definition at line 61 of file hyperbolic.hpp.

◆ num_equations

const int mfem::FluxFunction::num_equations

Definition at line 60 of file hyperbolic.hpp.

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

fem/hyperbolic.hpp
fem/hyperbolic.cpp

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FluxFunction()

◆ ~FluxFunction()

Member Function Documentation

◆ ComputeAvgFlux()

◆ ComputeAvgFluxDotN()

◆ ComputeFlux()

◆ ComputeFluxDotN()

◆ ComputeFluxJacobian()

◆ ComputeFluxJacobianDotN()

Member Data Documentation

◆ dim

◆ num_equations