| Abstract: | We present an unsplit second-order finite difference algorithm for hyperbolic conservation laws in several variables. Although the method can be directly implemented for general hyperbolic systems, we focus in this article on reducing grid orientation effects in porous media flow. In particular, we consider miscible and immiscible displacement processes. Our main concern is to develop a scheme that can easily be implemented into existing standard finite-difference-based reservoir simulators as an option to be used if grid orientation effects occur. The principle of the scheme is to build a higher order scheme to reduce numerical dispersion and that does not split the spatial operator to reduce the effect of the grid orientation. Numerical results are presented, which show that the method presented here reduces the effect of the numerical dispersion to a level that minimizes the grid orientation effects in a computationally efficient manner. © 1996 John Wiley & Sons, Inc. |
