High⁃efficiency DSMC implement method based on combination of dual spatial grids
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摘要:
基于双重空间网格结合策略，发展了一种高效率的贴体DSMC（direct simulation Monte Carlo）方法。通过将仿真分子在物理空间结构网格的位置坐标映射于计算空间的直角网格中，并在计算空间中完成分子所属网格单元的定位以及分子与边界是否发生作用的判断，从而结合结构网格的贴体性和直角网格的高效率计算的优点，提高DSMC方法的贴体性和计算效率。基于双重空间网格结合策略，通过直接映射和间接映射法分别建立DSMC程序，对微尺度收缩扩张喷管气体流动和超声速圆柱绕流进行模拟。数值结果表明：两种方法均很好地模拟出微喷管因尺度缩小导致的黏性效应和速度滑移现象以及超声速圆柱绕流发生的激波现象，具备有效性。与传统结构网格方法对比，两种方法的计算效率平均分别提高了3.85倍和2.85倍，具备高效性。
Abstract:Based on the combination strategy of dual spatial grids，a high⁃efficiency body⁃fitting DSMC （direct simulation Monte Carlo） method was developed.By mapping the coordinate of the simulated molecule in structural grid in the physical space to the Cartesian grid in the calculation space，and by completing the location of the grid unit to which the molecule belongs and the judgment of whether the molecule and the boundary are interacting in the calculation space，the body⁃fitness and computational efficiency of the DSMC method were both improved，in combination with the advantages of the body⁃fitness of the structured grid and the high⁃efficiency calculation of the Cartesian grid.Based on the combination strategy of dual spatial grids，DSMC programs were established through direct and indirect mapping methods to simulate the gas flow through the microscale contraction expansion nozzle and the supersonic flow past circular cylinder.Numerical results showed that the two methods were effective in simulating the viscous effect and the velocity slip phenomenon due to the shrinkage of the micro nozzle and the shock wave phenomenon caused by the supersonic flow past circular cylinder，demonstrating the effectiveness of the methods.Compared with the traditional structural grid method，the calculation efficiency of the two methods was respectively increased by 3.85 times and 2.85 times on average，showing the high efficiency of the methods.
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图 1 分子位置信息和分子所属网格信息通讯示意图
Figure 1. Schematic diagram of communication of molecular location information and grid information to which the molecule belongs
图 2 分子与边界作用信息通讯示意图
Figure 2. Schematic diagram of communication of interaction information between molecular and boundary
图 8 出口截面亚声速边界层厚度和推力分别与雷诺数的关系
Figure 8. Relationships of the subsonic boundary layer thickness at the exit section and the thrust with the Reynolds number
图 11 气流沿驻点线的马赫数分布图
Figure 11. Distribution of Mach number of the gas flow along the stagnation point line
图 12 圆柱绕流上壁面的压力系数分布图
Figure 12. Distribution of pressure coefficient on the upper wall of the flow past circular cylinder
表 1 微喷管流动模拟三种方法的耗时比较
Table 1. Time consumption comparison of three methods for the simulation of the micro-nozzle flow
方法 单步长平均耗时/s 总耗时/h 直接映射法 0.20 27.3 间接映射法 0.30 41.7 传统结构网格方法 0.78 108.3 
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表 2 超声速圆柱绕流模拟三种方法的耗时比较
Table 2. Time consumption comparison of three methods for the simulation of the supersonic flow past circular cylinder
方法 单步长平均耗时/s 总耗时/h 直接映射法 0.25 13.9 间接映射法 0.30 16.7 传统结构网格方法 0.95 52.8
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