Direct numerical simulation of turbulence on a SGI origin 3800

摘要

This contribution concerns the parallel solution of the incompressible Navier-Stokes equations for direct numerical simulation (DNS) of turbulent flow. The parallelization is based on the idea of splitting the flow domain into smaller subdomains which can be treated independent of each other. To compute the convective and diffusive term in parallel, the flow domain is partitioned in the streamwise direction. The computational time of this part of the algorithm scales superlinear with the number of processors, as the cache is more efficiently used as the problemsize per processor decreases. To solve the pressure in parallel, we make explicitly use of the fact that the turbulent flow under consideration is statistically homogeneous in the spanwise direction. The Poisson equation for the pressure can then be solved using a combination of a Fast Fourier Transform method in the spanwise direction and an Incomplete Choleski Conjugate Gradient method in the spectral space. The FFT is computed in parallel by treating the unknowns simultaneously in the streamwise direction, while the ICCG is computed in parallel by treating the unknowns simultaneously in the spanwise direction. The MPI implementation of the FFT/ICCG solver shows a very good scalability that is very close to ideal speed-up.