We describe our approach to computing accurate solutions for time dependent fluid flows in complex geometry. This consists of an adaptive mesh refinement algorithm coupled with our strategy for treating geometric complexity using non-body-fitted grids. In all cases we use regular, embedded Cartesian grids whenever possible. Trade-offs of using block-structured vs. unstructured data structures are discussed. Several open problems are discussed that need to be resolved both to automate and improve the accuracy of computations.

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1996-1997 Mathematics in High Performance Computing