基于Boltzmann模型方程的气体运动论统一算法研究

模型方程出发,研究确立含流态控制参数可描述不同流域气体流动特征的气体分子速度分布函数方程; 研究发展气体运动论离散速度坐标法, 借助非定常时间分裂数值计算方法和NND差分格式, 结合DSMC方法关于分子运动与碰撞去耦技术, 发展直接求解速度分布函数的气体运动论耦合迭代数值格式; 研制可用于物理空间各点宏观流动取矩的离散速度数值积分方法, 由此提出一套能有效模拟稀薄流到连续流不同流域气体流动问题统一算法. 通过对不同Knudsen数下一维激波内流动、二维圆柱、三维球体绕流数值计算表明, 计算结果与有关实验数据及其它途径研究结果(如DSMC模拟值、N-S数值解)吻合较好, 证实气体运动论统一算法求解各流域气体流动问题的可行性. 尝试将统一算法进行HPF并行化程序设计, 基于对球体绕流及类``神舟'返回舱外形绕流问题进行HPF初步并行试算, 显示出统一算法具有很好的并行可扩展性, 可望建立起新型的能有效模拟各流域飞行器绕流HPF并行算法研究方向. 通过将气体运动论统一算法推广应用于微槽道流动计算研究, 已初步发展起可靠模拟二维短微槽道流动数值算法; 通过对Couette流、Poiseuille流、压力驱动的二维短槽道流数值模拟, 证实该算法对微槽道气体流动问题具有较强的模拟能力, 可望发展起基于Boltzmann模型方程能可靠模拟MEMS微流动问题气体运动论数值计算方法研究途径. 

STUDY ON GAS KINETIC NUMERICAL ALGORITHM USING BOLTZMANN MODEL EQUATION

Based on the kinetic Shakhov model equation, a unified simplified velocity distribution function equation describing gas transport phenomena for various flow regimes is proposed. The discrete velocity ordinate technique is studied and applied to the velocity distribution function equation. With the decoupling technique of the DSMC method and the unsteady time-splitting method, the gas-kinetic finite difference method for directly solving the velocity distribution functions is established by coupling and iteration. The discrete velocity numerical integration methods are developed and applied to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas-kinetic numerical algorithm is obtained for flows from rarefied transition to continuum. To test the present method, one-dimensional shock structure problems, two-dimensional flows past cylinder, and three-dimensional flows around sphere with various Knudsen numbers are simulated. The computational results with high resolution of the flow fields are found in good agreement with the theoretical, DSMC, N-S and experimental data. The computing results confirm a good precision and reliability of the algorithm in solving the gas dynamical problems from rarefied flow to continuum. The HPF parallel strategy is studied for the gas-kinetic numerical method. The gas flows around three-dimensional sphere and spacecraft-like shape with various Knudsen numbers are computed with massive scale parallel schemes. A good parallel efficiency and speed-up ratio have been found so that it is practical and possible that an HPF parallel algorithm can be developed for solving three-dimensional complex problems in various flow regimes. The gas kinetic algorithm is extended and applied to study the micro-channel gas flows. The numerical algorithm is developed for the gas flows in two-dimensional short micro-channels with various Knudsen numbers. The classical Couette flows, the pressure-driven plane Poiseuille flow, and the pressure-driven gas flows in twodimensional short micro-channels are simulated and compared with the approximate solutions of the linear Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary, and the experimental data. The numerical experience shows that the gas kinetic algorithm may be a powerful tool in the numerical simulation of micro-scale gas flows in the Micro-Electro-Mechanical System (MEMS).