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.


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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