Implementation Issues for High Performance CFD

Many important phenomena in nature are modeled by partial di erential equations (PDEs). Such equations describe ow of air, water, oil and other substances and propagation of electromagnetic and sound waves in di erent media. Also, PDEs arise in many other application areas ranging from chemistry to economy. In the present paper, the focus is on computational uid dynamics, CFD. Issues regarding e cient implementation of CFD programs on modern parallel computers are considered. We study a computational kernel for a solver for compressible ow problems, e.g. arising when computing the air ow around an aircraft, using a state-of-the-art algorithm of Jameson-type. The solver uses a nite volume discretization combined with a GaussSeidel-Newton technique to solve the Euler equations. This PDE is non-linear, the solution is vector valued and the computations are carried out on a three dimensional curvilinear grid. Furthermore, modern numerical techniques such as multigrid and ux-splitting schemes are used in the solution process. We have experimented with di erent optimization techniques in order to make the implementation e cient. The program uses the red-black ordering for the Gauss-Seidel smoother, and preliminary results for a parallel version show that it scales well on a sharedmemory machine.