描述离散系统动力学演变的Monte Carlo方法分析

ANALYSIS OF FOUR MONTE CARLO METHODS FOR THE DYNAMIC EVOLUTION IN DISPERSED SYSTEMS

通用动力学方程通过描述离散系统中颗粒尺度分布的演变过程来量化颗粒动力学演变过程,而Monte Carlo(MC)算法是求解通用动力学方程的重要方法.目前几种主流的MC算法为Liffman的直接模拟Monte Carlo算法(DSMC)、阶梯式常体积法、常数目法和多重Monte Carlo(MMC)算法.利用这些MC算法描述理想的纯凝并工况和纯破碎工况,发现:由于避免了多个动力学事件之间的解耦过程,基于事件驱动的MC算法比基于时间驱动的MC算法具有更高的计算精度和更低的计算代价;由于尽量减少对整体系统的扰动,阶梯式恢复模拟颗粒数目的MC算法比连续式恢复模拟颗粒数目的MC算法具有更高的精度;由于始终保持计算区域体积,多重Monte Carlo算法具有更友好的扩展性.

General Dynamic Equation(GDE)describes quantitatively the dynamic process in dis- persed systems by means of the time evolution of particle size distribution(PSD).Monte Carlo method is one of the important approaches to take account of GDE.Four commonly used MC methods include Liffman's direct simulation Monte Carlo(DSMC),stepwise constant volume method,constant number method,and multi-Monte Carlo(MMC)method.These MCs are realized numerically to simulate pure coagulation and pure breakage cases.The following conclusions are made:event-driven MC methods, which avoid the uncoupling process of dynamic events,have higher precision and higher efficiency than time-driven MC methods;those stepwise constant number MCs,which avoid the disturbance on the whole system as possible,show better performances than those constant number MCs;multi-Monte Carlo method,which maintains the computational domain,exhibits friendlier expansibility than other MCs.