基于Boltzmann模型方程的气体运动论HPF并行算法

Gas Kinetic HPF Parallel Algorithm Using Boltzmann Model Equation

从修正的BGK Boltzmann模型方程出发,引入离散速度坐标技术对气体分子速度分量进行离散降维,基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式,发展直接求解气体分子速度分布函数的气体运动论有限差分数值格式,提出一套能有效模拟各流域三维绕流问题的气体运动论统一算法.在分析研究气体运动论数值算法内在并行度的基础上,开展各流域三维绕流问题统一算法的HPF(高性能FOR TRAN)并行化程序设计,建立一套能有效模拟各流域复杂外形体绕流的HPF并行算法软件.并进行了不同Knudsen(克努森)数下三维球体绕流及类"神舟号"返回舱外形体绕流的初步数值实验,将计算结果与过渡区有关实验数据及各流域气体绕流现象进行比较分析,证实了发展的气体运动论HPF并行算法在求解稀薄流到连续流不同流域复杂绕流问题方面的可行性.

Based on the revised BGK\|Boltzmann model equation,the unified simplified velocity distribution function equation describing microscopic molecular transport phenomena of various flow regimes can be cast into hyperbolic conservation law form with a nonlinear source term by introducing the discrete velocity ordinate technique to remove the velocity space dependency of the distribution function.The gas kinetic finite difference second\|order scheme directly solving the molecular velocity distribution function is constructed by the aid of the unsteady time\|splitting method and the non\|oscillatory,containing no free parameters,and dissipative(NND) scheme.As a result,a unified simplified gas kinetic algorithm is established for the three\|dimensional flows from rarefied transition to continuum.Based on analyzing the inner parallel degree of the unified algorithm,the parallel strategy adapted to the gas kinetic numerical algorithm is studied,and then the HPF(High Performance Fortran) parallel processing software for the unified algorithm is developed.To test the reliability of the present HPF parallel algorithm to solve the gas dynamical complex problems from rarefied transition to continuum,the flows around three\|dimensional sphere and spacecraft with various Knudsen numbers are simulated.The computational results are found in high resolution of the flow fields and good agreement with the related experimental results.