The major issues for parallel solver in a modern reservoir simulator are robustness, scalability, efficiency, and flexibility. There is significant interest in running fast field-scale simulation for complex giant Middle-East reservoirs which will require tens to hundreds of millions of grid cells to give reasonable resolution. At the same time, significant geologic complexity will require the treatment of dual permeability regions, faulting and fractures, and high variations of reservoir and fluid properties. Of course, the methods should also work well for extracted sector simulation with local grid refinements in both the structured and unstructured discretization. The preconditioning methods considered in this work include both the single-stage and multistage frameworks. In the single-stage framework, a novel method in addition to the well-known variants of incomplete LU factorizations [ILU0, ILU(k), and ILUT] is considered. The new method is a highly parallel method which in this paper will be referred to as the unstructured line solve power series (LSPS) method. The method will be discussed and contrasted in light of key issues for parallel linear solvers. The unstructured LSPS has certain interesting properties in the parallel construct which makes it a highly effective component.

The multistage method researched in this work is of the constraint pressure residual (CPR) framework. The method uses approximate pressure solve as the first stage preconditioning to the full system preconditioning. A number of original adaptations based on this concept were researched. Here, the use of the parallel algebraic multigrid (AMG) method and other single-level methods mentioned above in combinations within the multistage CPR framework were explored. Certain methods constructed in this way are found to be highly efficient, scalable, and robust. The methods developed will be discussed and several test problems included in this paper.

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