In the multidimensional numerical simulation of certain multiphase fluid flow processes, many phenomena are sufficiently localized and transient that self-adaptive local grid refinement techniques are necessary to resolve the local physical behavior. For large-scale simulation problems, efficiency is the key to the choice of specific adaptive strategies. Several different types of grid refinement methods will be discussed and briefly compared. The differences in accuracy of the local finite difference stars, complexity of the data structure, and efficiency of the solution techniques will be explained. Concepts for incorporating these methods in existing large-scale simulators will be presented.

Many man-years have been invested in developing large-scale numerical simulators which do an excellent job of resolving most of the larger length-scale phenomena in our production processes. Although adaptive local refinement methods are crucial for many applications, most techniques which have been developed to date either cannot be incorporated in our codes or are so computationally complex that they destroy the efficiency of existing simulators. Recently new preconditioning techniques have been developed which allow grid refinement methods to be used efficiently in existing codes without disrupting the basic solution process. These techniques are also highly amenable to vectorization and parallelization of the algorithms. They are also a first step in allowing complex well models to be incorporated into large field-scale codes and applications.

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