8 - Spectral Element and Lattice Gas Methods for Incompressible Fluid Dynamics

Summary

Introduction

The rapid development and introduction of new supercomputer systems over the last decade has opened new opportunities for numerical studies of incompressible fluid flows. A new awareness has also developed that the emerging hardware technologies influence both the nature and implementation of effective algorithms to solve these problems. Specific software implementation issues concern such varied questions as code dependencies, locality, round-off errors, storage access and capacity, input-output, workstation interfaces, cache utilization, . . . and are affected significantly by such computer hardware characteristics as the graininess of parallel systems, vector length, instruction conflicts, instruction set design, network access, distribution and paging of memory, to mention but a few. One significant result of this complex environment has been the stimulation of new ideas to make optimal use of the new supercomputer architectures and to achieve both high accuracy and high computational efficiency in the fluid simulations.

In this paper, we shall review some novel methods that are especially well suited for various aspects of incompressible fluid flow simulation studies. The key dynamical feature of these flows is the absence of shock waves, so many of the results to be stated for incompressible flows should also carry over to shock-free flows at moderate Mach numbers. Even within the context of incompressible flows, there is a wealth of dynamical phenomena to be studied, including laminar flows, transition to turbulence, turbulence, free surface flows, heat transfer, particle transport, fluid-structural interactions, and multiphase flows, among other phenomena.