Abstract Reservoir simulators have become one of the valuable tools which allow petroleum engineers to answer many important questions arising in the studies of petroleum recovery. They are the products of evolution over several decades and the technology is quite matured. There still exist some shortcomings, however. The most significant among them include: 1 In an unfavorable mobility ratio piston-type displacement, the oil recovery is dependent upon the grid system employed, 2 The error caused by the numerical dispersion inherent to low order numerical schemes can be significant in some cases. Much work has been done in the past to alleviate these problems. Since the literature is quite extensive, we will not attempt to review all of it here. The grid orientation effect was first reported by Todd et al.1 and confirmed later by Coats et al.2 Yanosik and McCracken3 proposed a nine-point scheme which has been proved to be effective in alleviating the grid orientation effect for some problems.