A new technique for a parallel dealiased pseudospectral Navier–Stokes code

Abstract

A novel aspect of a parallel procedure for the numerical simulation of the solution of the Navier–Stokes equations through the Fourier–Galerkin pseudospectral method is presented. It consists of a dealiased (“3/2” rule) transposition of the data that organizes the computations in the distributed direction in such a way that whenever a Fast Fourier Transform must be calculated, the algorithm will employ data stored solely on the proper memory of the processor which is computing it. This provide for the employment of standard routines for the computations of the Fourier transform. The aliasing removal procedure has been directly inserted into the transposition algorithm. The code is written for distributed memory computers, but not specifically for a peculiar architecture. The use on a variety of machines is allowed by the adoption of the Message Passing Interface library. The portability of the code is demonstrated by the similar performances, in particular the high efficiency, that all the machines tested show up to a number of parallel processors equal to 1/2 the truncation parameter N/2. Explicit time integration is used. The present code organization is relevant to physical and mathematical problems which require a three dimensional spectral treatment.