Massively Parallel Algorithms for Nonequilibrium Gas Dynamics

在某些流动状态下，Navier-Stokes方程不能很好地近似于气体动力学物理。例如，等离子体动态流动，低密度流动，大克努森数流动，或在表面的几个平均自由路径内的流动。基本上，当流动涉及热力学或化学不平衡时，人们通常必须求助于气体动力学理论。单原子分子和二元碰撞的控制方程是玻尔兹曼方程。波尔兹曼方程比完整的纳维-斯托克斯方程至少要难解一个数量级，而且大多数数值解的尝试都失败了。当一个人考虑化学（除了平移）不平衡时，这个问题几乎变得完全难以解决。求解非平衡气体动力学最有效的算法是直接模拟蒙特卡罗（DMSC）方法(1)。然而，该算法使用了许多现象学模型，这些模型必须进一步发展并与实验进行仔细比较。该研究项目将研究如何改进DMSC算法并将其映射到大规模并行计算机（连接机）上。由于该算法很难矢量化，因此在大多数传统的超级计算机上运行效率很低。因此，它通常在小型计算机上运行较长时间（单个问题长达数周）。然而，由于其最近邻特性，该方法的某些部分非常适合大规模并行计算机。特别地，SIMD机器（如Connection机器）非常适合处理这些问题。

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.