Staggered Grid Finite Volume Method

Discretization for the momentum balance of the Navier-Stokes equations. Can be used to build a marker-and-cell scheme (MAC) together with Tpfa for the discretization of the mass balance equation. More...

Description

The finite volume method on a staggered grid is a classical discretization scheme for the momentum balance of the Navier-Stokes equations [36]. It is constructed on Cartesian (tensor product) grids. Here, we use the same abstraction as for other finite volume and CVFE schemes and split the staggered (shifted) control volumes into element-wise parts: sub control volumes. Fluxes are assembled over sub control volumes faces, where two control volume faces are fully contained in an element (these are called frontal faces), and two faces are shared between neighboring elements and therefore split into two sub control volume faces (these are called lateral faces).

Control volume partitioning for the staggered method.

The image shows the control volume partition in 2D. It also shows the neighboring degrees of freedom involved in the interpolation of gradients at the flux integration points.

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Classes
class	Dumux::FaceCenteredLocalAssemblerBase< TypeTag, Assembler, Implementation, implicit >
	A base class for all local cell-centered assemblers. More...
class	Dumux::FaceCenteredLocalAssembler< TypeTag, Assembler, diffMethod, implicit, Implementation >
	An assembler for Jacobian and residual contribution per element (Face-centered methods). More...
class	Dumux::FaceCenteredLocalAssembler< TypeTag, Assembler, DiffMethod::numeric, true, Implementation >
	Face-centered scheme local assembler using numeric differentiation and implicit time discretization. More...
class	Dumux::FaceCenteredLocalAssembler< TypeTag, Assembler, DiffMethod::numeric, false, Implementation >
	TODO docme. More...
class	Dumux::FaceCenteredLocalAssembler< TypeTag, Assembler, DiffMethod::analytic, true, Implementation >
	TODO docme. More...
class	Dumux::FaceCenteredLocalAssembler< TypeTag, Assembler, DiffMethod::analytic, false, Implementation >
	TODO docme. More...
class	Dumux::FaceCenteredLocalResidual< TypeTag >
	The element-wise residual for the box scheme. More...
class	Dumux::FaceCenteredStaggeredConnectivityMap< GridGeometry >
	Stores the dof indices corresponding to the neighboring scvs that contribute to the derivative calculation. More...
class	Dumux::FaceCenteredStaggeredElementBoundaryTypes< BTypes >
	This class stores an array of BoundaryTypes objects. More...
class	Dumux::FaceCenteredStaggeredElementFluxVariablesCache< GFVC, cachingEnabled >
	The flux variables caches for an element. More...
class	Dumux::FaceCenteredStaggeredElementFluxVariablesCache< GFVC, true >
	The flux variables caches for an element with caching enabled. More...
class	Dumux::FaceCenteredStaggeredElementFluxVariablesCache< GFVC, false >
	The flux variables caches for an element with caching disabled. More...
class	Dumux::FaceCenteredStaggeredElementSolution< FVElementGeometry, PV >
	The global face variables class for staggered models. More...
class	Dumux::FaceCenteredStaggeredElementVolumeVariables< GridVolumeVariables, cachingEnabled >
	Base class for the face variables vector. More...
class	Dumux::FaceCenteredStaggeredElementVolumeVariables< GVV, true >
	Class for the face variables vector. Specialization for the case of storing the face variables globally. More...
class	Dumux::FaceCenteredStaggeredElementVolumeVariables< GVV, false >
	Class for the face variables vector. Specialization for the case of not storing the face variables globally. More...
class	Dumux::FaceCenteredStaggeredFVElementGeometry< GG, true >
	Stencil-local finite volume geometry (scvs and scvfs) for face-centered staggered models Specialization for grid caching enabled. More...
class	Dumux::FaceCenteredStaggeredFVElementGeometry< GG, false >
	Stencil-local finite volume geometry (scvs and scvfs) for face-centered staggered models Specialization for grid caching disabled. More...
struct	Dumux::FaceCenteredStaggeredDefaultGridGeometryTraits< GridView >
	The default traits for the face-center staggered finite volume grid geometry Defines the scv and scvf types and the mapper types. More...
class	Dumux::FaceCenteredStaggeredFVGridGeometry< GridView, cachingEnabled, Traits >
	Base class for the finite volume geometry vector for face-centered staggered models This builds up the sub control volumes and sub control volume faces for each element. More...
class	Dumux::FaceCenteredStaggeredFVGridGeometry< GV, true, Traits >
	Base class for the finite volume geometry vector for staggered models This builds up the sub control volumes and sub control volume faces for each element. Specialization in case the FVElementGeometries are stored. More...
class	Dumux::FaceCenteredStaggeredFVGridGeometry< GV, false, Traits >
	Base class for the finite volume geometry vector for face-centered staggered models This builds up the sub control volumes and sub control volume faces for each element. Specialization in case the FVElementGeometries are stored. More...
class	Dumux::FaceCenteredStaggeredGeometryHelper< GridView >
	Face centered staggered geometry helper. More...
struct	Dumux::FaceCenteredStaggeredDefaultGridFVCTraits< P, FVC, FVCF >
	Flux variable caches traits. More...
class	Dumux::FaceCenteredStaggeredGridFluxVariablesCache< Problem, FluxVariablesCache, FluxVariablesCacheFiller, cachingEnabled, Traits >
	Flux variable caches on a gridview. More...
class	Dumux::FaceCenteredStaggeredGridFluxVariablesCache< P, FVC, FVCF, true, Traits >
	Flux variable caches on a gridview with grid caching enabled. More...
class	Dumux::FaceCenteredStaggeredGridFluxVariablesCache< P, FVC, FVCF, false, Traits >
	Flux variable caches on a gridview with grid caching disabled. More...
class	Dumux::FaceCenteredStaggeredGridVolumeVariables< Traits, cachingEnabled >
	Base class for the grid volume variables. More...
class	Dumux::Detail::FaceCenteredStaggeredLocalIntersectionIndexMapper< GridView, false >
	Provides a mapping of local intersection indices (indexInInside) such that the local indices always follow the order of a reference element, regardless of how the element is oriented. More...
class	Dumux::Detail::FaceCenteredStaggeredLocalIntersectionIndexMapper< GridView, true >
	Provides a mapping of local intersection indices (indexInInside) such that the local indices always follow the order of a reference element, regardless of how the element in oriented. More...
struct	Dumux::FaceCenteredDefaultScvGeometryTraits< GridView >
	Default traits class to be used for the sub-control volumes for the face-centered staggered scheme. More...
class	Dumux::FaceCenteredStaggeredSubControlVolume< GridView, T >
	Face centered staggered sub control volume. More...
struct	Dumux::FaceCenteredDefaultScvfGeometryTraits< GridView >
	Default traits class to be used for the sub-control volume face for the face-centered staggered finite volume scheme. More...
class	Dumux::FaceCenteredStaggeredSubControlVolumeFace< GridView, T >
	Face centered staggered sub control volume face. More...
class	Dumux::SubDomainFaceCenteredLocalAssemblerBase< id, TypeTag, Assembler, Implementation, dm, implicit >
	A base class for all face-centered staggered local assemblers. More...
class	Dumux::SubDomainFaceCenteredLocalAssembler< id, TypeTag, Assembler, DM, implicit >
	The face-centered staggered scheme multidomain local assembler. More...
class	Dumux::SubDomainFaceCenteredLocalAssembler< id, TypeTag, Assembler, DiffMethod::numeric, true >
	Face-centered staggered scheme multi domain local assembler using numeric differentiation and implicit time discretization. More...
class	Dumux::SubDomainFaceCenteredLocalAssembler< id, TypeTag, Assembler, DiffMethod::numeric, false >
	Face-centered staggered scheme multi domain local assembler using numeric differentiation and explicit time discretization. More...

Typedefs
template<class GridView>
using	Dumux::FaceCenteredStaggeredLocalIntersectionIndexMapper
	Provides a mapping of local intersection indices (indexInInside) such that the local indices always follow the order of a reference element, regardless of how the element is oriented. Does not do anything for grids not supporting rotated elements (such as Dune::YaspGrid).

Functions
template<class Vector>
static std::size_t	Dumux::normalAxis (const Vector &v)
	Returns the normal axis index of a unit vector (0 = x, 1 = y, 2 = z).

Files
file	fclocalassembler.hh
	An assembler for Jacobian and residual contribution per element (face-centered staggered methods).
file	fclocalresidual.hh
	Calculates the element-wise residual for the box scheme.
file	connectivitymap.hh
	Stores the dof indices corresponding to the neighboring scvs that contribute to the derivative calculation.
file	consistentlyorientedgrid.hh
	Helper type to determine whether a grid is guaranteed to be oriented consistently. This means that the intersection indices always correspond to the ones of a reference element or, in other words, the elements are never rotated.
file	elementboundarytypes.hh
	Boundary types gathered on an element.
file	elementfluxvariablescache.hh
	Global flux variable cache.
file	elementsolution.hh
	The global face variables class for staggered models.
file	elementvolumevariables.hh
	Base class for the face variables vector.
file	fvelementgeometry.hh
file	fvgridgeometry.hh
	Base class for the finite volume geometry vector for face-centered staggered models This builds up the sub control volumes and sub control volume faces for each element.
file	geometryhelper.hh
	Geometry helper for face-centered staggered scheme.
file	gridfluxvariablescache.hh
	Global flux variable cache.
file	gridsupportsconcavecorners.hh
	Type trait to determine if a grid supports concave corners (e.g. by cutting out a hole from the domain interior).
file	gridvolumevariables.hh
	The grid volume variables class for face-centered staggered models.
file	localintersectionindexmapper.hh
	Provides a mapping of local intersection indices (indexInInside) such that the local indices always follow the order of a reference element, regardless of how the element is oriented. Does not do anything for grids not supporting rotated elements (such as Dune::YaspGrid).
file	normalaxis.hh
	Base class for the finite volume geometry vector for face-centered staggered models This builds up the sub control volumes and sub control volume faces for each element.
file	subcontrolvolume.hh
	Face centered staggered sub control volume.
file	subcontrolvolumeface.hh
	Face centered staggered sub control volume face.
file	subdomainfclocalassembler.hh
	An assembler for Jacobian and residual contribution per element (face-centered staggered methods) for multidomain problems.

Typedef Documentation

FaceCenteredStaggeredLocalIntersectionIndexMapper

template<class GridView>

using Dumux::FaceCenteredStaggeredLocalIntersectionIndexMapper

Initial value:

 
Detail::FaceCenteredStaggeredLocalIntersectionIndexMapper<GridView, ConsistentlyOrientedGrid<typename GridView::Grid>{}>

Function Documentation

normalAxis()

template<class Vector>

std::size_t Dumux::normalAxis ( const Vector & v )

inlinestatic