Massively Parallel Algorithms for Nonequilibrium Gas Dynamics

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In some flow regimes, the Navier-Stokes equations yield poor approximations to the physics of gas dynamics. For example, plasma dynamic flows, low-density flows, flows with large Knudsen numbers, or within a few mean free paths of a surface. Basically when the flows involve thermodynamic or chemical nonequilibrium, one must often resort to the kinetic theory of gases. The governing equation for monatomic molecules and binary collisions is the Boltzmann equation. The Boltzmann equation 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 (in addition to translational) nonequilibrium, the problem becomes almost completely intractable. The most effective algorithm for solving nonequilibrium gas dynamics is the Direct Simulation Monte Carlo (DMSC) method (1). However, this algorithm uses a number of phenomenological models that must be developed further and carefully compared to experiment. This research project will investigate how the DMSC algorithm can be improved and mapped onto a massively parallel computer (the Connection Machine). Since the algorithm is very difficult to vectorize, it operates very inefficiently on most traditional supercomputers. Consequently it is usually run on minicomputers for extended periods of time (up to weeks for a single problem). However, portions of the method are highly suited to massively parallel computers due to its nearest-neighbor characteristics. In particular, SIMD machines such as the Connection nachine are highly suited to these problems.