Abstract
In the solution of adverse mobility ratio displacement problems by five-point difference schemes fluids appear to flow along grid lines. This results in solutions that depend on the orientation and size of the grid. Hence different results are obtained when, for example, the same one-quarter five-spot problem is solved by grids that are parallel and diagonal to the line joining the injector and the producer. This Grid Orientation Effect (GOE) is a result of coupling between the anisotropic numerical diffusion and the physical instability of the displacement front. In this paper, a linear stability analysis is applied to the finite difference equations to examine the interaction between numerical diffusion and the growth of numerical errors due to physical instability. The results show that in general the GOE cannot be overcome with grid refinement. For a certain range of parameters, however, first the GOE decreases under grid refinement, reaching a minimum, and then increases again on finer grids. A technique is provided for estimating reasonable block size for a given displacement problem.
