Multi-point flux approximation (Mpfa)

A cell-centered finite volume scheme with multi-point flux approximation. More...

Description

A cell-centered finite volume scheme with multi-point flux approximation.

Files
file	mpfa/computetransmissibility.hh
	This file contains free functions to evaluate the transmissibilities associated with flux evaluations across sub-control volume faces in the context of cell-centered Mpfa schemes.
file	cellcentered/mpfa/connectivitymap.hh
	Stores the face indices corresponding to the neighbors of an element that contribute to the derivative calculation. Depending on if an mpfa scheme leads to a symmetric/unsymmetric sparsity pattern, the adequate implementation of the connectivity map is chosen.
file	dualgridindexset.hh
	Class for the index sets of the dual grid in mpfa schemes.
file	discretization/cellcentered/mpfa/elementfluxvariablescache.hh
	The element-local object of flux variables caches.
file	cellcentered/mpfa/elementvolumevariables.hh
	The local (stencil) volume variables class for cell centered mpfa models.
file	discretization/cellcentered/mpfa/fvelementgeometry.hh
	Stencil-local finite volume geometry (scvs and scvfs) for cell-centered mpfa models This builds up the sub control volumes and sub control volume faces for each element in the local scope we are restricting to, e.g. stencil or element.
file	discretization/cellcentered/mpfa/fvgridgeometry.hh
	The finite volume geometry (scvs and scvfs) for cell-centered mpfa models on a grid view This builds up the sub control volumes and sub control volume faces for each element of the grid partition.
file	cellcentered/mpfa/fvgridgeometrytraits.hh
	Traits class to be used in conjunction with the CCMpfaFVGridGeometry.
file	discretization/cellcentered/mpfa/gridfluxvariablescache.hh
	Flux variable caches on a gridview.
file	gridinteractionvolumeindexsets.hh
	Class for the grid interaction volume index sets of mpfa schemes.
file	cellcentered/mpfa/gridvolumevariables.hh
	The grid volume variables class for cell centered mpfa models.
file	helper.hh
	Helper class to get data required for mpfa scheme.
file	interactionvolumebase.hh
	Base class for interaction volumes of mpfa methods.
file	interactionvolumedatahandle.hh
	Data handle class for interaction volumes of mpfa methods. This class is passed to interaction volumes to store the necessary data in it.
file	localassemblerbase.hh
	Defines the general interface of classes used for the assembly of the local systems of equations involved in the transmissibility computation in mpfa schemes.
file	localassemblerhelper.hh
	A class that contains helper functions as well as functionality which is common to different mpfa schemes and which solely operate on the interaction volume.
file	localfacedata.hh
	Data structure holding interaction volume-local information for a grid subb-control volume face embedded in it.
file	methods.hh
	The available mpfa schemes in Dumux.
file	discretization/cellcentered/mpfa/omethod/interactionvolume.hh
	Class for the interaction volume of the mpfa-o scheme.
file	interactionvolumeindexset.hh
	Class for the index set within an interaction volume of the mpfa-o scheme.
file	discretization/cellcentered/mpfa/omethod/localassembler.hh
	Class for the assembly of the local systems of equations involved in the transmissibility computation in an mpfa-o type manner.
file	discretization/cellcentered/mpfa/omethod/localsubcontrolentities.hh
	Classes for sub control entities of the mpfa-o method.
file	scvgeometryhelper.hh
	Helper class providing functionality to compute the geometry of the interaction-volume local sub-control volumes involved in the mpfa-o scheme.
file	staticinteractionvolume.hh
	Class for the interaction volume of the mpfa-o scheme to be used when the sizes are known at compile time, e.g. for non-boundary interaction volumes on structured grids.
file	scvgradients.hh
	Class providing functionality for the reconstruction of the gradients in the sub-control volumes involved in mpfa schemes.
file	discretization/cellcentered/mpfa/subcontrolvolumeface.hh
	The sub control volume face.

Classes
struct	Dumux::NodalIndexSetDefaultTraits< GV >
	Default traits to be used in conjunction with the dual grid nodal index set. More...
class	Dumux::CCMpfaDualGridNodalIndexSet< T >
	Nodal index set for mpfa schemes, constructed around grid vertices. More...
class	Dumux::CCMpfaDualGridIndexSet< NI >
	Class for the index sets of the dual grid in mpfa schemes. More...
struct	Dumux::InteractionVolumeDataStorage< PrimaryIV, PrimaryIVDataHandle, SecondaryIV, SecondaryIVDataHandle >
	Structure to store interaction volumes and data handles. More...
class	Dumux::CCMpfaElementFluxVariablesCache< GFVC, cachingEnabled >
	The flux variables caches for an element. More...
class	Dumux::CCMpfaElementFluxVariablesCache< GFVC, true >
	The flux variables caches for an element with caching enabled. More...
class	Dumux::CCMpfaElementFluxVariablesCache< GFVC, false >
	The flux variables caches for an element with caching disabled. More...
class	Dumux::CCMpfaElementVolumeVariables< GVV, cachingEnabled >
	The local (stencil) volume variables class for cell centered mpfa models. More...
class	Dumux::CCMpfaElementVolumeVariables< GVV, true >
	The local (stencil) volume variables class for cell centered mpfa models with caching. More...
class	Dumux::CCMpfaElementVolumeVariables< GVV, false >
	The local (stencil) volume variables class for cell centered tpfa models with caching. More...
class	Dumux::CCMpfaFVElementGeometry< GG, enableGridGeometryCache >
	Stencil-local finite volume geometry (scvs and scvfs) for cell-centered mpfa models This builds up the sub control volumes and sub control volume faces for each element in the local scope we are restricting to, e.g. stencil or element. More...
class	Dumux::CCMpfaFVElementGeometry< GG, true >
	Stencil-local finite volume geometry (scvs and scvfs) for cell-centered mpfa models Specialization for grid caching enabled. More...
class	Dumux::CCMpfaFVElementGeometry< GG, false >
	Stencil-local finite volume geometry (scvs and scvfs) for cell-centered TPFA models Specialization for grid caching disabled. More...
class	Dumux::CCMpfaFVGridGeometry< GridView, Traits, enableCache >
	The finite volume geometry (scvs and scvfs) for cell-centered mpfa models on a grid view This builds up the sub control volumes and sub control volume faces. More...
class	Dumux::CCMpfaFVGridGeometry< GV, Traits, true >
	The finite volume geometry (scvs and scvfs) for cell-centered mpfa models on a grid view This builds up the sub control volumes and sub control volume faces. More...
class	Dumux::CCMpfaFVGridGeometry< GV, Traits, false >
	The finite volume geometry (scvs and scvfs) for cell-centered mpfa models on a grid view This builds up the sub control volumes and sub control volume faces. More...
struct	Dumux::CCMpfaFVGridGeometryTraits< GV, NI, PIV, SIV >
	Traits class to be used for the CCMpfaFVGridGeometry. More...
struct	Dumux::IvDataHandlePhysicsTraits< ModelTraits >
	Data handle physics traits. More...
struct	Dumux::CCMpfaDefaultGridFluxVariablesCacheTraits< P, FVC, FVCF, PIV, SIV, PDH, SDH >
	Data handle physics traits. More...
class	Dumux::CCMpfaGridFluxVariablesCache< Traits, cachingEnabled >
	Flux variable caches on a gridview. More...
class	Dumux::CCMpfaGridFluxVariablesCache< TheTraits, true >
	Flux variable caches on a gridview with grid caching enabled. More...
class	Dumux::CCMpfaGridFluxVariablesCache< TheTraits, false >
	Flux variable caches on a gridview with grid caching disabled. More...
class	Dumux::CCMpfaGridInteractionVolumeIndexSets< FVG, NI, PI, SI >
	Class that holds all interaction volume index sets on a grid view. More...
struct	Dumux::CCMpfaDefaultGridVolumeVariablesTraits< P, VV >
	Traits for the base class for the grid volume variables. More...
class	Dumux::CCMpfaGridVolumeVariables< Problem, VolumeVariables, cachingEnabled, Traits >
	Base class for the grid volume variables. More...
class	Dumux::MpfaDimensionHelper< GridGeometry, dim, dimWorld >
	Dimension-specific helper class to get data required for mpfa scheme. More...
class	Dumux::MpfaDimensionHelper< GridGeometry, 2, 2 >
	Dimension-specific mpfa helper class for dim == 2 & dimWorld == 2. More...
class	Dumux::MpfaDimensionHelper< GridGeometry, 2, 3 >
	Dimension-specific mpfa helper class for dim == 2 & dimWorld == 3. Reuses some functionality of the specialization for dim = dimWorld = 2. More...
class	Dumux::MpfaDimensionHelper< GridGeometry, 3, 3 >
	Dimension-specific mpfa helper class for dim == 3 & dimWorld == 3. More...
class	Dumux::CCMpfaHelper< GridGeometry >
	Helper class to get the required information on an interaction volume. More...
class	Dumux::CCMpfaInteractionVolumeBase< T >
	Base class for the interaction volumes of mpfa methods. It defines the interface and actual implementations should derive from this class. More...
class	Dumux::CCMpfaDataHandleBases::SystemMatricesHandle< MVT, size1, size2 >
	Common base class to all handles. Stores arrays of the matrices involved in the interaction volume-local systems of equations. Apart from the transmissibility matrix we store those matrices that are needed e.g. for later face pressure reconstruction. The fluxes as well as the local systems of equations can be expressed as functions of the intermediate unknown face face values \(\bar{\mathbf{u}}\) and the known cell/Dirichlet values \(\mathbf{u}\) using the matrices \(\mathbf{A}\), \(\mathbf{B}\), \(\mathbf{C}\), \(\mathbf{D}\) and the vector of Neumann fluxes \(\mathbf{N}\) as follows: More...
class	Dumux::CCMpfaDataHandleBases::SystemVectorsHandle< MVT, size1, size2 >
	Common base class to all handles. Stores arrays of the vectors involved in the interaction volume-local systems of equations. More...
class	Dumux::InteractionVolumeDataHandle< MVT, PT >
	Class for the interaction volume data handle. More...
class	Dumux::InteractionVolumeAssemblerBase< P, EG, EV >
	Defines the general interface of the local assembler classes for the assembly of the interaction volume-local transmissibility matrix. Specializations have to be provided for the available interaction volume implementations. these should derive from this base class. More...
class	Dumux::InteractionVolumeAssemblerHelper
	A class that contains helper functions as well as functionality which is common to different mpfa schemes and which solely operate on the interaction volume. More...
class	Dumux::InteractionVolumeLocalFaceData< GridIndexType, LocalIndexType >
	General implementation of a data structure holding interaction volume-local information for a grid sub-control volume face embedded in it. More...
struct	Dumux::CCMpfaODefaultInteractionVolumeTraits< NodalIndexSet, Scalar >
	The default interaction volume traits class for the mpfa-o method. This uses dynamic types types for matrices/vectors in order to work on general grids. For interaction volumes known at compile time use the static interaction volume implementation. More...
class	Dumux::CCMpfaOInteractionVolume< Traits >
	Forward declaration of the o-method's interaction volume. More...
class	Dumux::CCMpfaOInteractionVolumeIndexSet< DualGridNodalIndexSet >
	The interaction volume index set class for the mpfa-o scheme. More...
class	Dumux::MpfaOInteractionVolumeAssembler< P, EG, EV >
	Specialization of the interaction volume-local assembler class for the schemes using an mpfa-o type assembly. More...
class	Dumux::CCMpfaOInteractionVolumeLocalScv< IvIndexSet, Scalar, dim, dimWorld >
	Class for the interaction volume-local sub-control volume used in the mpfa-o scheme. More...
struct	Dumux::CCMpfaOInteractionVolumeLocalScvf< IvIndexSet >
	Class for the interaction volume-local sub-control volume face used in the mpfa-o scheme. More...
class	Dumux::CCMpfaOScvGeometryHelper< LocalScvType >
	Helper class providing functionality to compute the geometry of the interaction-volume local sub-control volumes of mpfa-o type. More...
struct	Dumux::CCMpfaODefaultStaticInteractionVolumeTraits< NI, S, C, F >
	The default interaction volume traits class for the mpfa-o method with known size of the interaction volumes at compile time. It uses statically sized containers for the iv-local data structures and static matrices and vectors. More...
class	Dumux::CCMpfaOStaticInteractionVolume< Traits >
	Forward declaration of the o-method's static interaction volume. More...
class	Dumux::CCMpfaScvGradients
	Class providing functionality for the reconstruction of the gradients in the sub-control volumes involved in mpfa schemes. More...
struct	Dumux::CCMpfaDefaultScvfGeometryTraits< GridView >
	Default traits class to be used for the sub-control volume faces for the cell-centered finite volume scheme using MPFA. More...
class	Dumux::CCMpfaSubControlVolumeFace< GV, T >
	Class for a sub control volume face in mpfa methods, i.e a part of the boundary of a control volume we compute fluxes on. More...

Enumerations
enum class	Dumux::MpfaMethods : unsigned int { Dumux::MpfaMethods::oMethod }
	The available mpfa schemes in Dumux. More...

Functions
template<class EG , class IVSubControlVolume , class Tensor >
Dune::FieldVector< typename Tensor::field_type, IVSubControlVolume::myDimension >	Dumux::computeMpfaTransmissibility (const IVSubControlVolume &scv, const typename EG::SubControlVolumeFace &scvf, const Tensor &t, typename IVSubControlVolume::ctype extrusionFactor)
	Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t. More...
template<class EG , class IVSubControlVolume , class Tensor >
Dune::FieldVector< typename Tensor::field_type, IVSubControlVolume::myDimension >	Dumux::computeMpfaTransmissibility (const EG &fvGeometry, const IVSubControlVolume &scv, const typename EG::SubControlVolumeFace &scvf, const Tensor &t, typename IVSubControlVolume::ctype extrusionFactor)
	Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t. More...
template<class EG , class IVSubControlVolume , class Tensor , std::enable_if_t< Dune::IsNumber< Tensor >::value, int > = 1>
Dune::FieldVector< Tensor, IVSubControlVolume::myDimension >	Dumux::computeMpfaTransmissibility (const IVSubControlVolume &scv, const typename EG::SubControlVolumeFace &scvf, const Tensor &t, typename IVSubControlVolume::ctype extrusionFactor)
	Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t, where t is a scalar. More...
template<class EG , class IVSubControlVolume , class Tensor , std::enable_if_t< Dune::IsNumber< Tensor >::value, int > = 1>
Dune::FieldVector< Tensor, IVSubControlVolume::myDimension >	Dumux::computeMpfaTransmissibility (const EG &fvGeometry, const IVSubControlVolume &scv, const typename EG::SubControlVolumeFace &scvf, const Tensor &t, typename IVSubControlVolume::ctype extrusionFactor)
	Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t, where t is a scalar. More...
template<class FVElementGeometry >
std::size_t	Dumux::CCMpfa::maxNumBoundaryVolVars (const FVElementGeometry &fvGeometry)
	Computes how many boundary vol vars come into play for flux calculations on an element (for a given element finite volume geometry). This number here is probably always higher than the actually needed number of volume variables. However, we want to make sure it is high enough so that enough memory is reserved in the element volume variables below. More...
template<class VolumeVariables , class IndexType , class Problem , class FVElemGeom , class NodalIndexSet >
void	Dumux::CCMpfa::addBoundaryVolVarsAtNode (std::vector< VolumeVariables > &volVars, std::vector< IndexType > &volVarIndices, const Problem &problem, const typename FVElemGeom::GridGeometry::GridView::template Codim< 0 >::Entity &element, const FVElemGeom &fvGeometry, const NodalIndexSet &nodalIndexSet)
	Adds the boundary volume variables found within a given nodal index set into the provided containers and stores the indices associated with them. More...
template<class VolumeVariables , class IndexType , class Problem , class FVElemGeom >
void	Dumux::CCMpfa::addBoundaryVolVars (std::vector< VolumeVariables > &volVars, std::vector< IndexType > &volVarIndices, const Problem &problem, const typename FVElemGeom::GridGeometry::GridView::template Codim< 0 >::Entity &element, const FVElemGeom &fvGeometry)
	Adds the boundary volume variables found within the stencil to the provided containers and stores the indices associated with them. More...

Enumeration Type Documentation

MpfaMethods

enum class Dumux::MpfaMethods : unsigned int

strong

The available mpfa schemes in Dumux.

Enumerator
oMethod

Function Documentation

addBoundaryVolVars()

template<class VolumeVariables , class IndexType , class Problem , class FVElemGeom >

void Dumux::CCMpfa::addBoundaryVolVars	(	std::vector< VolumeVariables > &	volVars,
		std::vector< IndexType > &	volVarIndices,
		const Problem &	problem,
		const typename FVElemGeom::GridGeometry::GridView::template Codim< 0 >::Entity &	element,
		const FVElemGeom &	fvGeometry
	)

Adds the boundary volume variables found within the stencil to the provided containers and stores the indices associated with them.

Parameters

volVars	The container where the volume variables are stored
volVarIndices	The container where the volume variable indices are stored
problem	The problem containing the Dirichlet boundary conditions
element	The element to which the finite volume geometry was bound
fvGeometry	The element finite volume geometry

addBoundaryVolVarsAtNode()

template<class VolumeVariables , class IndexType , class Problem , class FVElemGeom , class NodalIndexSet >

void Dumux::CCMpfa::addBoundaryVolVarsAtNode	(	std::vector< VolumeVariables > &	volVars,
		std::vector< IndexType > &	volVarIndices,
		const Problem &	problem,
		const typename FVElemGeom::GridGeometry::GridView::template Codim< 0 >::Entity &	element,
		const FVElemGeom &	fvGeometry,
		const NodalIndexSet &	nodalIndexSet
	)

Adds the boundary volume variables found within a given nodal index set into the provided containers and stores the indices associated with them.

Note

It only adds those boundary vol vars that do not live on scvfs that are inside the bound element. These have to be added separately

Parameters

volVars	The container where the volume variables are stored
volVarIndices	The container where the volume variable indices are stored
problem	The problem containing the Dirichlet boundary conditions
element	The element to which the finite volume geometry is bound
fvGeometry	The element finite volume geometry
nodalIndexSet	The dual grid index set around a node

computeMpfaTransmissibility() [1/4]

template<class EG , class IVSubControlVolume , class Tensor >

Dune::FieldVector< typename Tensor::field_type, IVSubControlVolume::myDimension > Dumux::computeMpfaTransmissibility	(	const EG &	fvGeometry,
		const IVSubControlVolume &	scv,
		const typename EG::SubControlVolumeFace &	scvf,
		const Tensor &	t,
		typename IVSubControlVolume::ctype	extrusionFactor
	)

Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t.

Parameters

fvGeometry	The element-centered control volume geometry
scv	The iv-local sub-control volume
scvf	The grid sub-control volume face
t	The tensor living in the scv
extrusionFactor	The extrusion factor of the scv

computeMpfaTransmissibility() [2/4]

template<class EG , class IVSubControlVolume , class Tensor , std::enable_if_t< Dune::IsNumber< Tensor >::value, int > = 1>

Dune::FieldVector< Tensor, IVSubControlVolume::myDimension > Dumux::computeMpfaTransmissibility	(	const EG &	fvGeometry,
		const IVSubControlVolume &	scv,
		const typename EG::SubControlVolumeFace &	scvf,
		const Tensor &	t,
		typename IVSubControlVolume::ctype	extrusionFactor
	)

Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t, where t is a scalar.

Parameters

fvGeometry	The element-centered control volume geometry
scv	The iv-local sub-control volume
scvf	The grid sub-control volume face
t	the scalar quantity living in the scv
extrusionFactor	The extrusion factor of the scv

computeMpfaTransmissibility() [3/4]

template<class EG , class IVSubControlVolume , class Tensor >

Dune::FieldVector< typename Tensor::field_type, IVSubControlVolume::myDimension > Dumux::computeMpfaTransmissibility	(	const IVSubControlVolume &	scv,
		const typename EG::SubControlVolumeFace &	scvf,
		const Tensor &	t,
		typename IVSubControlVolume::ctype	extrusionFactor
	)

Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t.

Parameters

scv	The iv-local sub-control volume
scvf	The grid sub-control volume face
t	The tensor living in the scv
extrusionFactor	The extrusion factor of the scv

computeMpfaTransmissibility() [4/4]

template<class EG , class IVSubControlVolume , class Tensor , std::enable_if_t< Dune::IsNumber< Tensor >::value, int > = 1>

Dune::FieldVector< Tensor, IVSubControlVolume::myDimension > Dumux::computeMpfaTransmissibility	(	const IVSubControlVolume &	scv,
		const typename EG::SubControlVolumeFace &	scvf,
		const Tensor &	t,
		typename IVSubControlVolume::ctype	extrusionFactor
	)

Free function to evaluate the Mpfa transmissibility associated with the flux (in the form of flux = t*gradU) across a sub-control volume face stemming from a given sub-control volume with corresponding tensor t, where t is a scalar.

Parameters

scv	The iv-local sub-control volume
scvf	The grid sub-control volume face
t	the scalar quantity living in the scv
extrusionFactor	The extrusion factor of the scv

maxNumBoundaryVolVars()

template<class FVElementGeometry >

std::size_t Dumux::CCMpfa::maxNumBoundaryVolVars

(

const FVElementGeometry &

fvGeometry

)

Computes how many boundary vol vars come into play for flux calculations on an element (for a given element finite volume geometry). This number here is probably always higher than the actually needed number of volume variables. However, we want to make sure it is high enough so that enough memory is reserved in the element volume variables below.

Todo:

TODO What about non-symmetric schemes? Is there a better way for estimating this?

Parameters

fvGeometry

the element finite volume geometry