A data-parallel implementation of the DSMC method on the Connection Machine

In some regions, such as low-density hypersonic flow, the Navier-Stokes equations yield poor approximations to the physics of gas dynamics. Aerospace vehicles such as the Space Shuttle, the National Aerospace Plane (NASP), unmanned rockets and satellites must all fly through these regimes. For these flows, the governing equation is the Boltzmann equation of kinetic theory, which is at least an order of magnitude more difficult to solve than the full Navier-Stokes equations and has eluded most attempts to numerically solve it. When one also considers chemical non-equilibrium (dissociation), the problem is almost intractable. The most effective algorithm for solving low-density hypersonic flow is the Direct Simulation Monte Carlo (DSMC) method. This code, however, can require hundreds of hours of supercomputer time per run. This paper describes how the DSMC algorithm can be mapped onto a massively parallel computer (the 65,536 processor Connection Machine). The program is shown to be scalable, with computer time roughly proportional to the number of molecules or number of processors.