Massively Parallel Algorithms for Nonequilibrium Gas Dynamics

非平衡气体动力学的大规模并行算法

• 批准号: 9009998
• 负责人: Lyle Long
• 金额: $ 5.94万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-08-15 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9009998&HistoricalAwards=false
• 关键词: Massively; Parallel; Algorithms; Nonequilibrium; Gas

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.

在某些流动状态下，Navier-Stokes方程产生差的 气体动力学物理的近似。 比如说， 等离子体动力流，低密度流，大流量 克努森数，或在几个平均自由路径的表面。 基本上，当流动涉及热力学或化学 非平衡，人们必须经常诉诸动力学理论， 气. 单原子分子和二元分子的控制方程 碰撞是玻尔兹曼方程。 玻尔兹曼方程是 至少要比我们所知道的 完整的Navier-Stokes方程，并避开了大多数尝试， 数值求解。当一个人也考虑化学（在 除了平移）非平衡，问题变得 几乎完全难以处理 求解非平衡气体的最有效算法 动态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 必须进一步发展和仔细比较， 实验 本研究项目将调查DMSC如何 算法可以改进并映射到大规模并行 连接机（Connection Machine） 由于算法非常 很难矢量化，它在大多数 传统超级计算机 因此，它通常是运行在 小型计算机的时间延长（长达数周， 单一问题）。 然而，该方法的部分内容高度复杂 适合于大规模并行计算机，因为它 最近邻特征 特别是SIMD机器 例如连接nachine非常适合这些 问题