模拟颗粒布朗运动的格子Boltzmann模型

Lattice Boltzmann model for particle Brownian motion

通过在格子Boltzmann方法的迭代格式中附加描述分子热运动涨落的分布函数,建立了描述颗粒布朗运动的涨落格子Boltzmann模型,给出了分布函数满足的条件以及在D2Q9格子模型下的具体表达形式.通过Chapman-Enskog展开推导,得到了考虑分子热运动涨落的宏观流体动力学方程.在此基础上,对单颗粒在流场中的布朗运动进行了数值模拟,得到了颗粒运动的均方速度及速度、角速度时间自相关函数.结果表明,均方速度满足能量均分定理,说明颗粒最终达到热平衡;颗粒速度、角速度时间自相关函数符合理论预测的t-1、t-2衰减规律.数值结果证明了所建立模型的正确性,为采用格子Boltzmann方法模拟颗粒的布朗运动提供了有效的方法.

A fluctuating lattice Boltzmann model for particle Brownian motion was established by incorporating a stochastic term into the lattice Boltzmann equation, which represents the thermally-induced fluctuations in the stress tensor. The conditions for the stochastic term were derived and the expressions of the stochastic term for the D2Q9 lattice model were also presented. The fluctuating hydrodynamic equations were derived from the lattice Boltzmann equation through Chapman-Enskog expansion. The Brownian motion of a single circular particle was numerically investigated by the newly developed lattice Boltzmann model. Numerical results including particle mean-square velocity, velocity autocorrelation function and angular velocity autocorrelation function were presented. The energy equipartition theorem was reproduced by the results of mean-square velocity, which indicated that the particle was in thermal equilibrium. The results showed that the velocity autocorrelation function and the angular velocity autocorrelation function decayed as a power law of t^-1 and t^-2 respectively, as theoretically stated. Numerical results showed the accuracy and robustness of the present model, which was proved to be an effective numerical method for the particle Brownian motion.