The grid orientation phenomenon present in numerical models of fluid flow in a porous medium can give rise to unrealistic predictions when simulating adverse mobility displacements. McCracken and Yanosik proposed a nine point finite difference scheme for approximating the solution of the continuity equations that has the potential of eliminating many of the unrealistic predictions that are observed when using five point finite difference operators. Coats and Ramesh have implemented this scheme in a steamflooding model, and have noted that serious grid effects are present in the simulation of an inverted seven spot pattern. Potempa has described a procedure which exhibits minimal grid effects for the problem described by Coats and Ramesh. This paper describes modifications to the McCracken and Yanosik procedure which allow for realistic simulation of this inverted seven spot pattern under a steam drive. These modifications are based upon an approximation scheme that has been previously reported, and affect the incorporation of upstream weighting in a simulator.