基于动理学模型的多尺度随机粒子方法

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.