## Finite difference solutions to grid orientation problems using IMPES (implicit pressure explicit saturation)

It is well known that numeric solutions by the standard 5-point difference schemes for 2-phase flow equations exhibit grid orientation effects in 2 and more dimensions. To minimize such effects, 9-point difference of the differential operator often is proposed. However, it has been observed that this approach does not give satisfactory results in the case of nonuniform grids. An alternate 9-point formula is proposed based on a more accurate integration of fluid fluxes across cell faces. Numeric results are presented which demonstrate that this formula greatly reduces the sensitivity to grid orientation in both uniform and nonuniform grids.