Large-scale simulation of the three-dimensional Navier-Stokes equations

Abstract Computational fluid dynamics is playing an important role in the development of new technologies, ranging from the design of hypersonic aircraft to the analysis of groundwater flows for environmental studies. The numerical simulation of fluid motion has traditionally demanded the utmost in high performance computing technology coupled with research initiatives to develop more efficient and robust algorithms. Recent research has demonstrated that computer architectures based on a massively parallel ensemble of processors offer an alternative approach to achieving supercomputer performance on realistic scientific and engineering applications. In the present research, we describe a Navier-Stokes solver, capable of simulating three-dimensional, time-dependent fluid flow on a massively parallel multiple instruction multiple data computer. Solutions are presented for a three-dimensional extension of the classical Rayleigh problem for natural convection. In addition, we present the solution of three-dimensional Kelvin-Helmholtz instabilities on 8,400,000 grid cells using 1024 processors of Sandia's nCUBE/2.