Aavatsmark, I.; Barkve, T.; Bøe, O.; Mannseth, T. Discretization on unstructured grids for inhomogeneous, anisotropic media. I: Derivation of the methods. (English) Zbl 0951.65080 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) Cited in 2 ReviewsCited in 106 Documents 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 PDF BibTeX XML Cite \textit{I. Aavatsmark} et al., SIAM J. Sci. Comput. 19, No. 5, 1700--1716 (1998; Zbl 0951.65080) Full Text: DOI OpenURL