Abstract: A targeted heterogeneous medium in the form of an underground layered formation is gridded into a layered structured grid or a layered semi-unstructured grid. The structured grid can be of the irregular corner-point-geometry grid type or the simple Cartesian grid type. The semi-unstructured grid is really unstructured, formed by arbitrarily connected control-volumes derived from the dual grid of a suitable triangulation; but the connectivity pattern does not change from layer to layer. Problems with determining fluid movement and other state changes in the formation are solved by exploiting the layered structure of the medium. The techniques are particularly suited for large-scale simulation by parallel processing on a supercomputer with multiple central processing units (CPU's).