摘要
传统随机粒子方法的时空离散步长受分子碰撞尺度(分子平均自由程和平均碰撞时间)的限制,当空间和时间离散尺度远大于碰撞特征尺度时,其输运系数的数值误差显著增加,因此如直接利用这类方法对跨流域流动精确求解,其计算效率往往是极低的(如DSMC方法,Fokker-Planck和BGK模型随机粒子方法)。通过对随机粒子方法输运系数离散误差的分析可知,这主要是因为传统算法将模拟分子的运动和碰撞解耦计算引起的。针对这一问题,本文介绍了适合于跨流域流动模拟的多尺度Fokker-Planck和BGK模型随机粒子方法。通过分子运动求解中耦合碰撞作用,在连续流区域,改进的随机粒子方法在较大的时间步长下仍能够满足宏观流体力学方程的输运性质。理论和计算结果显示,多尺度Fokker-Planck和BGK模型随机粒子方法可以高效准确地模拟从稀薄流到连续流的跨流域气体流动。
The spatial and temporal discretization of traditional stochastic particle methods are limited by the inherent collision scales (such as the molecular mean free path and mean collision time). When they are larger than the collision scales,the numerical error of the transport coefficients is significant. Therefore,the computational efficiency is extremely low in the multi-scale flow simulation using traditional stochastic particle methods,such as the DSMC method and stochastic particle methods based on the Fokker-Planck/BGK models. It is noted that their transport coefficients depend on the ratio of time step and mean collision time. This dependence is caused by the decoupling of molecule motion and collision. To overcome these problems,the multi-scale stochastic particle methods based on the Fokker-Planck and BGK model are developed. They can eliminate the restriction of the inherent collision scales by coupling collision in molecule motion. These improved particle schemes can ensure the accuracy of the transport properties in the whole flow regimes independent of the spatial-temporal discretization,and compute the gas flows from rarefied to continuum regimes efficiently and accurately.
作者
费飞
张俊
柳朝晖
FEI Fei;ZHANG Jun;LIU Zhaohui(School of Aerospace Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;School of Aeronautic Science and Engineering,Beihang University,Beijing 100191,China;State Key Laboratory of Coal Combustion,School of Energy and Power Engineering, Huazhong University of Science and Technology,Wuhan 430074,China)
出处
《空气动力学学报》
CSCD
北大核心
2019年第5期731-739,共9页
Acta Aerodynamica Sinica
基金
国家自然科学基金青年项目（51506063）
国家数值风洞项目（NNW2018-ZT3B07）
