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

Aavatsmark, Ivar; Barkve, T.; Bøe, Ø.; Mannseth, T.

J. Comput. Phys. 127, No. 1, 2-14 (1996).

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

Keywords:

control-volume formulations; system of conservation laws; gradient law; Darcy’s law; full-tensor anisotropy