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Advanced mesh generation and update methods for parallel 3D computation of complex¯ow problems are presented. The complexities of the class of problems targeted include complex geometries, unsteady behavior, and moving boundaries and interfaces, such as those encountered in¯uid-object interactions. Parallel 3D simulation of 1000 spheres falling in a liquid-®lled tube, and other computations, are presented in this paper to demonstrate the challenges involved in this class of¯ow problems and the methods developed to address these challenges.