求解Boltzmann模型方程的气体运动论大规模并行算法

Massive Parallelization of Gas-kinetic Algorithm for Boltzmann Model Equation

研究各流域三维流动问题的Boltzmann模型方程计算方法,建立直接求解分子速度分布函数的气体运动论耦合迭代数值格式;基于变量依赖关系、数据通信与并行可扩展性分析,使用区域分解并行化方法,建立气体运动论数值算法并行方案,发展求解各流域三维绕流问题的气体运动论并行算法.拟定高低不同马赫数下来自不同流域的三维球体及返回舱绕流算例,进行高性能Fortran(HPF)大规模并行计算,将计算结果与有关实验数据、相关理论预测等进行比较分析,研究揭示不同流区复杂绕流现象及流动机理.研究表明,所发展的气体运动论并行算法具有很好的并行独立性,基本达到线性加速的并行效果,显示出良好的并行可扩展性.

In a numerical study of Bohzmann model equation, a gas-kinetic finite difference scheme with coupling and iteration is constructed to solve molecular velocity distribution function directly. The parallel strategy is established by using parallel technique of domain decomposition based on variable dependency relation, data communication and parallel expansibility. Gas-kinetic HPF （High Performance Fortran） parallel algorithm is developed to solve three-dimensional problems in various flow regimes. Hypersonic gas flows around a sphere and a spacecraft at various Knudsen numbers, Mach numbers and flying angles are computed at a high performance computer with massive scale HPF parallel. The computational results are in good agreement with experimental and theoretical ones. It is shown that the parallel speed-up increases approximately linearly with the numbers of processors. It indicates high parallel efficiency and expansibility with good load balance and data communication. It suggests that a gas-kinetic parallel algorithm on large scale can be used for three-dimensional complex hypersonic flow problems in various flow regimes.