PARALLEL FINITE ELEMENT COMPUTATION OF 3D INCOMPRESSIBLE FLOWS ON MPPs

In this chapter we present numerical simulations of the Navier-Stokes equations with the stabilized finite element methods on the massively parallel CM-5 supercomputer. These computations are based on implicit methods and their implementations are based on the assumption that the mesh is unstructured. The use of matrix-free iterations eliminates the need to store element-level matrices, thus providing us with the potential to solve problems with complex 3D geometries and with more than 4,000,000 coupled nonlinear equations. The unsteady flow past a stationary cylinder is investigated at Reynolds numbers 300 and 800. Our results indicate strong threedimensionality arising from the instability of the columnar vortices forming the Karman street. We also present results from the unsteady flow past a sphere, where intricate vortex shedding patterns are observed. Comparisons are made between computations on a semi-stuctured hexahedral mesh and an unstructured tetrahedral mesh. Finallv we present a preliminary simulation of flow around high-speed trains in a tunnel. For fixed domains, we use a semi-discrete formulation. and for the trains problem we use the Deformable-Spatial-Domain/Stabilized-Space-Time(DSD/SST)