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

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
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