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Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media. (English) Zbl 0859.76048

Summary: Two classes of discretization methods are proposed for control-volume formulations on quadrilateral grids in two space dimensions. Curvilinear grids are considered as a special case. The methods are applicable for any system of conservation laws where the flux is defined by a gradient law, like Darcy’s law for porous-medium flow. A strong feature of the methods is the ability to handle medium inhomogeneities in combination with full-tensor anisotropy and/or non-orthogonality of the grid. Further properties of the methods will be discussed and examples of their use will be presented.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76S05 Flows in porous media; filtration; seepage
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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