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We compare the Kurganov-Tadmor (KT) two-dimensional second ordersemi-discrete central scheme in dimension by dimension formulation with a newtwo-dimensional approach introduced here and applied in numerical simulationsfor two-phase, two-dimensional flows in heterogeneous formations. Thissemi-discrete central scheme is based on the ideas of Rusanov's method using amore precise information about the local speeds of wave propagation computed ateach Riemann Problem in two-space dimensions. We find the KT dimension bydimension has a much simpler mathematical description than the genuinelytwo-dimensional one with a little more numerical diffusion, particularly in thepresence of viscous fingers. Unfortunately, as one can see, the KT with thedimension by dimension approach might produce incorrect boundary behavior in atypical geometry used in the study of porous media flows: the quarter of a fivespot. This problem has been corrected by the authors with the new semi-discretescheme proposed here. We conclude with numerical examples of two-dimensional,two-phase flow associated with two distinct flooding problems: atwo-dimensional flow in a rectangular heterogeneous reservoir (called slabgeometry) and a two-dimensional flow in a 5-spot geometry homogeneousreservoir.

A New two-dimensional Second Order Non-oscillatory Central Scheme Applied to multiphase flows in heterogeneous porous media