Explicit and implicit solution of the Navier-Stokes equations on a massively parallel computer

Abstract

We describe the design, implementation and performance of a two-dimensional time-accurate Navier-Stokes solver for the Connection Machine (tin) model CM2. The program uses a single processor for each grid point. Two different time-stepping methods have so far been implemented: an explicit third-order Runge-Kutta method and an implicit approximation-factorization method. The entire flow solver is written in starlisp, a set of parallel extensions to common-lisp, developed by Thinking Machines Corporation. Our code is based on ARC2D, and we are attempting to emulate its functionality. Thus, we can check our Connection Machine results against those of a mature, well-vectorized Cray 2 program, both for correctness and performance. We find the code to be correct and the performance in some cases to be up to several times that of the Cray 2.