A two-phase sequential IMPLICIT three dimensional reservoir simulator has been developed for massively parallel computer systems. The parallel algorithm is based on recently developed domain decomposition methods. The simulator has been tested using a 16384 processor MasPar MP-2.

The simulator building blocks are robust Krylov space iterations using Additive Schwarz as the preconditioner. This approach naturally supports a distributed data structure with overlapping subdomains. In the simulator each subdomain is treated as a small reservoir in its own right, and each subdomain communicates with the neighbouring subdomains through boundary conditions. Previous work has shown that the use of minimal overlap is sufficient and computationally nearly optimal for these problems.

To solve the pressure equation we use a two level Additive Schwarz preconditioner. The coarse grid problem is solved by a multigrid solver and each subdomain problem can be solved with a range of simple iterative or direct methods depending on time, space or robustness considerations. The saturation equation is solved by splitting the equation into one hyperbolic saturation equation and one elliptic saturation equation, The hyperbolic saturation equation is solved by the Modified Method of Characteristics. The solution of the (nonsymmet-ric) elliptic saturation equation is again obtained using an Additive Schwarz preconditioner.

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