Parallel Benchmarks of Turbulencein Complex Geometries ?

In this paper we present benchmark results from the parallel implementation of the three{dimensional Navier{Stokes solver Prism on diierent parallel platforms of current interest: IBM SP2 (all three types of processors), SGI Power Challenge XL and Cray C90. The numerical method is based on mixed spectral element{ Fourier expansions in (x ? y) and z?directions, respectively. Each (or a group) of Fourier modes can be computed on a separate processor as the linear contributions in Navier{Stokes equations (Helmholtz solves) are completely uncoupled. Coupling is obtained via the nonlinear contributions (advection terms) and requires a global transpose of the data and one{dimensional multiple{point FFTs. We rst analyze the computational complexity of Prism identifying basic computational kernels and communication bottlenecks. These kernels are benchmarked separately on several computer architectures. More speciically, we obtain timings for BLAS routines on all aforementioned processors but also on the SP1, Cray J90, the Intel Paragon, and the DEC AlphaServer 8400 5/300. A two{dimensional version of Prism is also benchmarked on most processors testing both direct and iterative methods of solution. Next, we deene two three{dimensional benchmark ow problems in prototype complex geometries, and measure parallel scalability and performance using diierent message passing libraries. Special emphasis is placed on runtime data processing, e.g. turbulence statistics computed during the simulation. Our results provide a measure of MFlop/s sustained performance of individual processors, and indicate the limitations of the current communications software for typical problems in computational mechanics based on spectral or nite element discretizations.