基于能量均分原理的微颗粒布朗运动LBM模拟

LBM simulation of microparticle brownian motion based on the energy equipartition principle

基于格子Boltzmann方法(LBM)结合Ghost Fluid边界格式和格线反弹格式建立了模拟微颗粒布朗运动的动力学模型,在不添加能量方程的情况下,利用能量均分原理对郎之万方程中的布朗力直接执行修正,相对于涨落LBM模型大幅降低了计算量,降低了LBM的人工压缩性和等温假设带来的误差,提高了计算精度.本文模拟了二维圆型颗粒和三维球型颗粒的布朗运动,结果表明,采用该方法模拟所得颗粒运动的平动温度与转动温度均可以达到稳定的热平衡,且与周围流体的温度基本一致,颗粒运动的均方位移与观察时间间隔符合实验结果和理论解,验证了该方法的可行性与准确性.

This paper built a dynamic model for the simulation of micro-particles Brownian motion, which combined the lattice Boltzmann method（LBM） and a Ghost Fluid / Link-bounce-back boundary scheme. Without the addition of the energy equation, the Brownian force in the Langevin equation was directly corrected by the energy equipartition principle. With the premise of ensuring the accuracy and reducing the compressibility of error, this means greatly reduced the price of computation relative to fluctuation LB method. The article simulated a Brownian motion of two-dimensional circular particle and three-dimensional spherical particles. The results showed that the translational temperature and rotational temperature of micro-particle motion using the method could satisfy stable thermal equilibrium, and agree with the temperature of surrounding fluid eventually. The mean square displacement of the particle motion and the observation time interval satisfied the Einstein relation. The method was proved to be reasonable and practicable.