二维粒子运动模型的模拟和解析研究

Simulation and analysis of two-dimensional particle motion model

文章采用元胞自动机模型建立存在位置交换的对向粒子流模型,粒子运动发生冲突时,根据周围环境判断是否交换位置,通过计算机仿真,出现系统平均速度随着密度上升先减小后增加的现象。有学者采用简单平均场方法解析对向粒子流模型,但是该方法忽略粒子之间的相关性,解析结果存在较大的误差。该文利用考虑粒子之间相关性的簇平均场方法对模型进行解析,发现解析结果与仿真结果较为吻合,验证了平均场方法的准确性,同时也发现通过位置交换可以有效地提高粒子运动效率,降低堵塞的发生。

In this paper,the cellular automaton model is used to establish the model of the opposite particle flow with position exchange.The position exchange is judged according to the surrounding environment when the particles are on a collision course.Through computer simulation,the average speed of the system decreases first and then increases with the increase of density.Some scholars use the simple mean-field method to analyze the opposite particle flow model,but this method ignores the correlation between particles,and the analytical results have large errors.In this paper,the cluster mean-field method considering the correlation between particles is adopted.It is found that the analytical results are in good agreement with the simulation results,thus verifying the accuracy of the mean-field method.And through the position exchange,the efficiency of particle motion can be improved and the occurrence of congestion can be reduced.