Discretization on unstructured grids for inhomogeneous, anisotropic media. I: Derivation of the methods. (English) Zbl 0951.65080

Aavatsmark, I.; Barkve, T.; Bøe, O.; Mannseth, T.

SIAM J. Sci. Comput. 19, No. 5, 1700-1716 (1998).

Space discretization methods are considered for conservation laws with a flux term defined by the gradient law. A control volume formulation is recalled. Flux-conservative discretization methods are developed for unstructured triangular and polygonal grids in two space dimensions. Following special cases are considered in details: \(K\)-orthogonal grids when the 2-point approximation of the flux is available; for homogeneous media explicit formulas for transmissibilities (i.e.coefficients in the scheme corrsponding to nodes except of the cell center) are given; for the inhomogeneous case with no flow boundary conditions formulas for transmissibilities close by the boundaries are obtained.

Reviewer: Ramaz Bochorishvili (Tbilisi)

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R05	PDEs with low regular coefficients and/or low regular data
65M50	Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws
76M20	Finite difference methods applied to problems in fluid mechanics
76S05	Flows in porous media; filtration; seepage

Keywords:

control-volume discretizations; unstructured grids; anisotropy; inhomogeneity; conservation laws; flux-conservative discretization methods

Citations:

Zbl 0951.65081