HYBRID SPECTRAL FINITE-DIFFERENCE SIMULATIONS OF STRATIFIED TURBULENTFLOWS ON DISTRIBUTED-MEMORY ARCHITECTURES

A method for efficient implementation of a combined spectral finite di fference algorithm for computation of incompressible stratified turbul ent flows on distributed memory computers is presented. The solution t echnique is the fractional step method with a semi-implicit time advan cement scheme. A single-programme multiple-data abstraction is used in conjunction with a static data-partitioning scheme. The distributed F FTs required in the explicit step are based on the transpose method an d the large sets of independent tridiagonal systems of equations arisi ng in the implicit steps are solved using the pipelined Thomas algorit hm. A speed-up analysis of a model problem is presented for three part itioning schemes, namely unipartition, multipartition and transpose pa rtition. It is shown that the unipartitioning scheme is best suited fo r this algorithm. Performance measurements of the overall as well as i ndividual stages of the algorithm are presented for several different grids and are discussed in the context of associated dependency and co mmunication overheads. An unsealed speed-up efficiency of up to 91% on doubling the number of processors and up to 60% on an eightfold incre ase in the number of processors was obtained on the Intel Paragon and iPSC/860 Hypercube. Absolute performance of the code was evaluated by comparisons with performance on the Cray-YMP. On 128 Paragon processor s, performance up to five times that of a single-processor Cray-YMP wa s obtained. The validation of the method and results of grid refinemen t studies in stably stratified turbulent channel flows are presented. (C) 1997 by John Wiley & Sons, Ltd.