平衡态气体分子间碰撞过程的分子动力学模拟方法研究

Novel Algorithm in Simulation of Gas Molecule Collision in Equilibrium State

以平衡态气体分子间的相互碰撞过程为研究对象,尝试刻画微观机制过程的统计学规律,开展分子动力学模拟的新方法研究。提出基于最短自由飞行时间确定时间步长的新模拟算法,给出对应的分子碰撞判别式和三维空间非对心碰撞速度更新式,建立具有周期边界的正方体模拟空间模型,按照1∶1真实比例投放模拟分子数目,利用C语言自编程序,模拟了两个不同空间模型内的气体分子运动全过程。结果表明:气体分子间碰撞次数、分子碰壁次数、分子的速度分布、自由程分布以及自由飞行时间分布的模拟统计结果,与理论计算值高度一致或误差处于概率波动范围内,从而证明了本模拟方法的正确性。本模拟方法为进一步研究非平衡态混合气体中各种扩散迁移过程的微观机制提供了可行的新计算方法,并有助于解决一些实际工程应用问题。

A novel algorithm was developed for molecular dynamics simulation of gas molecule collision in equilibrium state. The original work includes： i） the non-constant time step defined as the shortest free flight time; ii）the derivation of molecular collision criteria; iii） a realistic number of gas molecules;（ iv） the scheme for updating3 D non-centroid collision velocity; and v） a self-developed simulation program in C-language. Collision of air molecules in two cubic boxes was simulated in the new algorithm and evaluated in molecular dynamics. The simulated and theoretically calculated statistical results,including but not limited to the numbers of molecule-molecule/molecule-wall collisions,distributions of velocity,free-path and free-flight time,were in good agreement and within probability fluctuation range. We suggest that the novel algorithm be of some basic and technological interest in understanding the microscopic mechanisms responsible for diffusion and/or migration of non-equilibrium gas-mixtures.