Diamond discretization scheme

Face-centered finite-volume scheme based on non-conforming finite-element spaces. More...

Description

The diamond method is a control-volume finite element scheme with piecewise linear discontinuous basis functions (Crouzeix-Raviart on simplices and Rannacher-Turek on quadrilaterals). The basis functions are continuous only at the element face centers but are generally discontinuous along the facet and thus also at vertices. Control volumes are constructed around the face centers of the element faces of the primary grid. This results in diamond-shaped control volumes that form a dual grid.

Control volume partitioning for the diamond CVFE method.

The diamond CVFE scheme can, for example, be used for the velocity combined with cell-centered FV schemes for the pressure to discretize the incompressible Stokes equation (in formulation with full velocity gradient in the flux term; for the formulation with symmetric velocity gradient additional face stabilization terms are required) on unstructured grids.

Files
file	discretization/facecentered/diamond/fvelementgeometry.hh
file	discretization/facecentered/diamond/fvgridgeometry.hh
file	discretization/facecentered/diamond/geometryhelper.hh
file	discretization/facecentered/diamond/subcontrolvolume.hh
file	discretization/facecentered/diamond/subcontrolvolumeface.hh

Classes
class	Dumux::FaceCenteredDiamondFVElementGeometry< GG, cachingEnabled >
	Element-wise grid geometry (local view) More...
class	Dumux::FaceCenteredDiamondFVElementGeometry< GG, true >
	Element-wise grid geometry (local view) More...
struct	Dumux::FaceCenteredDiamondDefaultGridGeometryTraits< GridView >
	The default traits for the face-centered diamond finite volume grid geometry Defines the scv and scvf types and the mapper types. More...
class	Dumux::FaceCenteredDiamondFVGridGeometry< GV, enableCaching, Traits >
	Grid geometry for the diamond discretization. More...
class	Dumux::DiamondGeometryHelper< GridView, ScvType, ScvfType >
	Helper class to construct SCVs and SCVFs for the diamond scheme. More...
struct	Dumux::FaceCenteredDiamondScvGeometryTraits< GridView >
	Default traits class to be used for the sub-control volumes. More...
class	Dumux::FaceCenteredDiamondSubControlVolume< GridView, T >
	Face centered diamond subcontrolvolume face. More...
struct	Dumux::FaceCenteredDiamondScvfGeometryTraits< GridView >
	Default traits class to be used for the sub-control volumes for the cell-centered finite volume scheme using TPFA. More...
class	Dumux::FaceCenteredDiamondSubControlVolumeFace< GridView, T >
	The SCVF implementation for diamond. More...