  We compare the Kurganov-Tadmor (KT) two-dimensional second order
semi-discrete central scheme in dimension by dimension formulation with a new
two-dimensional approach introduced here and applied in numerical simulations
for two-phase, two-dimensional flows in heterogeneous formations. This
semi-discrete central scheme is based on the ideas of Rusanov's method using a
more precise information about the local speeds of wave propagation computed at
each Riemann Problem in two-space dimensions. We find the KT dimension by
dimension has a much simpler mathematical description than the genuinely
two-dimensional one with a little more numerical diffusion, particularly in the
presence of viscous fingers. Unfortunately, as one can see, the KT with the
dimension by dimension approach might produce incorrect boundary behavior in a
typical geometry used in the study of porous media flows: the quarter of a five
spot. This problem has been corrected by the authors with the new semi-discrete
scheme proposed here. We conclude with numerical examples of two-dimensional,
two-phase flow associated with two distinct flooding problems: a
two-dimensional flow in a rectangular heterogeneous reservoir (called slab
geometry) and a two-dimensional flow in a 5-spot geometry homogeneous
reservoir.
