Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder > Class Template Reference

This file contains different higher order methods for approximating the velocity. More...

#include <dumux/freeflow/staggeredupwindmethods.hh>

Description

template<class Scalar, int upwindSchemeOrder>
class Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >

This file contains different higher order methods for approximating the velocity.

Public Member Functions
	StaggeredUpwindMethods (const std::string &paramGroup="")
TvdApproach	tvdApproachFromString (const std::string &tvd)
	Convenience function to convert user input given as std::string to the corresponding enum class used for choosing the TVD Approach. More...
std::string	tvdApproachToString (TvdApproach tvd)
	return the name of the TVD approach More...
DifferencingScheme	differencingSchemeFromString (const std::string &differencingScheme)
	Convenience function to convert user input given as std::string to the corresponding enum class used for choosing the Discretization Method. More...
std::string	differencingSchemeToString (DifferencingScheme differencingScheme)
	return the name of the Discretization Method More...
Scalar	upwind (const Scalar downstreamMomentum, const Scalar upstreamMomentum) const
	Upwind Method. More...
Scalar	tvd (const std::array< Scalar, 3 > &momenta, const std::array< Scalar, 3 > &distances, const bool selfIsUpstream, const TvdApproach tvdApproach) const
	Tvd Scheme: Total Variation Diminishing. More...
Scalar	tvdUniform (const std::array< Scalar, 3 > &momenta, const std::array< Scalar, 3 > &distances, const bool selfIsUpstream) const
	Tvd Scheme: Total Variation Diminishing. More...
Scalar	tvdLi (const std::array< Scalar, 3 > &momenta, const std::array< Scalar, 3 > &distances, const bool selfIsUpstream) const
	Tvd Scheme: Total Variation Diminishing. More...
Scalar	tvdHou (const std::array< Scalar, 3 > &momenta, const std::array< Scalar, 3 > &distances, const bool selfIsUpstream) const
	Tvd Scheme: Total Variation Diminishing. More...
const TvdApproach &	tvdApproach () const
	Returns the Tvd approach. More...
const DifferencingScheme &	differencingScheme () const
	Returns the differencing scheme. More...

Static Public Member Functions
static Scalar	vanleer (const Scalar r, const Scalar R)
	Van Leer flux limiter function [Van Leer 1974]. More...
static Scalar	vanalbada (const Scalar r, const Scalar R)
	Van Albada flux limiter function [Van Albada et al. 1982]. More...
static Scalar	minmod (const Scalar r, const Scalar R)
	MinMod flux limiter function [Roe 1985]. More...
static Scalar	superbee (const Scalar r, const Scalar R)
	SUPERBEE flux limiter function [Roe 1985]. More...
static Scalar	umist (const Scalar r, const Scalar R)
	UMIST flux limiter function [Lien and Leschziner 1993]. More...
static Scalar	mclimiter (const Scalar r, const Scalar R)
static Scalar	wahyd (const Scalar r, const Scalar R)
	WAHYD Scheme [Hou, Simons, Hinkelmann 2007];. More...

Constructor & Destructor Documentation

StaggeredUpwindMethods()

template<class Scalar , int upwindSchemeOrder>

Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::StaggeredUpwindMethods ( const std::string &  paramGroup = "" )

inline

Member Function Documentation

differencingScheme()

template<class Scalar , int upwindSchemeOrder>

const DifferencingScheme & Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::differencingScheme ( ) const

inline

Returns the differencing scheme.

differencingSchemeFromString()

template<class Scalar , int upwindSchemeOrder>

DifferencingScheme Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::differencingSchemeFromString ( const std::string &  differencingScheme )

inline

Convenience function to convert user input given as std::string to the corresponding enum class used for choosing the Discretization Method.

differencingSchemeToString()

template<class Scalar , int upwindSchemeOrder>

std::string Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::differencingSchemeToString ( DifferencingScheme  differencingScheme )

inline

return the name of the Discretization Method

mclimiter()

template<class Scalar , int upwindSchemeOrder>

static Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::mclimiter ( const Scalar  r, const Scalar  R  )

inlinestatic

minmod()

template<class Scalar , int upwindSchemeOrder>

static Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::minmod ( const Scalar  r, const Scalar  R  )

inlinestatic

MinMod flux limiter function [Roe 1985].

superbee()

template<class Scalar , int upwindSchemeOrder>

static Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::superbee ( const Scalar  r, const Scalar  R  )

inlinestatic

SUPERBEE flux limiter function [Roe 1985].

With R != 2 is the modified SUPERBEE flux limiter function [Hou, Simons, Hinkelmann 2007]

tvd()

template<class Scalar , int upwindSchemeOrder>

Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::tvd ( const std::array< Scalar, 3 > &  momenta, const std::array< Scalar, 3 > &  distances, const bool  selfIsUpstream, const TvdApproach  tvdApproach  ) const

inline

Tvd Scheme: Total Variation Diminishing.

tvdApproach()

template<class Scalar , int upwindSchemeOrder>

const TvdApproach & Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::tvdApproach ( ) const

inline

Returns the Tvd approach.

tvdApproachFromString()

template<class Scalar , int upwindSchemeOrder>

TvdApproach Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::tvdApproachFromString ( const std::string &  tvd )

inline

Convenience function to convert user input given as std::string to the corresponding enum class used for choosing the TVD Approach.

tvdApproachToString()

template<class Scalar , int upwindSchemeOrder>

std::string Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::tvdApproachToString ( TvdApproach  tvd )

inline

return the name of the TVD approach

tvdHou()

template<class Scalar , int upwindSchemeOrder>

Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::tvdHou ( const std::array< Scalar, 3 > &  momenta, const std::array< Scalar, 3 > &  distances, const bool  selfIsUpstream  ) const

inline

Tvd Scheme: Total Variation Diminishing.

This function manages the non uniformities of the grid according to [Hou, Simons, Hinkelmann 2007]. It should behave better then the Li's version in very stretched grids.

tvdLi()

template<class Scalar , int upwindSchemeOrder>

Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::tvdLi ( const std::array< Scalar, 3 > &  momenta, const std::array< Scalar, 3 > &  distances, const bool  selfIsUpstream  ) const

inline

Tvd Scheme: Total Variation Diminishing.

This function manages the non uniformities of the grid according to [Li, Liao 2007]. It tries to reconstruct the value for the velocity at the upstream-upstream point if the grid was uniform.

tvdUniform()

template<class Scalar , int upwindSchemeOrder>

Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::tvdUniform ( const std::array< Scalar, 3 > &  momenta, const std::array< Scalar, 3 > &  distances, const bool  selfIsUpstream  ) const

inline

Tvd Scheme: Total Variation Diminishing.

This function assumes the cell size distribution to be uniform.

umist()

template<class Scalar , int upwindSchemeOrder>

static Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::umist ( const Scalar  r, const Scalar  R  )

inlinestatic

UMIST flux limiter function [Lien and Leschziner 1993].

upwind()

template<class Scalar , int upwindSchemeOrder>

Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::upwind ( const Scalar  downstreamMomentum, const Scalar  upstreamMomentum  ) const

inline

Upwind Method.

vanalbada()

template<class Scalar , int upwindSchemeOrder>

static Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::vanalbada ( const Scalar  r, const Scalar  R  )

inlinestatic

Van Albada flux limiter function [Van Albada et al. 1982].

vanleer()

template<class Scalar , int upwindSchemeOrder>

static Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::vanleer ( const Scalar  r, const Scalar  R  )

inlinestatic

Van Leer flux limiter function [Van Leer 1974].

With R != 2 is the modified Van Leer flux limiter function [Hou, Simons, Hinkelmann 2007]

wahyd()

template<class Scalar , int upwindSchemeOrder>

static Scalar Dumux::StaggeredUpwindMethods< Scalar, upwindSchemeOrder >::wahyd ( const Scalar  r, const Scalar  R  )

inlinestatic

WAHYD Scheme [Hou, Simons, Hinkelmann 2007];.

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

• staggeredupwindmethods.hh