用多重蒙特卡罗算法研究超细微颗粒物同时发生的凝并和破碎

MULTI-MONTE CARLO METHOD FOR SIMULTANEOUS COAGULATION ANDBREAKAGE OF NANOPARTICLES

超细微颗粒物的尺度分布由通用动力学方程(GDE)描述,该文发展了求解同时考虑凝并和破碎的GDE的一种多重MonteCarlo(MMC)算法,该算法可以抛弃当前MonteCarlo算法中广泛采用的“子系统”的概念,引入了加权的“虚拟颗粒”的概念,且基于时间驱动,模拟过程中保持虚拟颗粒数目和计算区域体积不变。首先详细描述了MMC算法,包括时间步长的确定方法、同时处理凝并和破碎的方案、凝并和破碎事件发生的判断准则、凝并伙伴的确定、处理凝并和破碎事件的后果时保持虚拟颗粒数目恒定的方法等;然后利用MMC算法对几种特殊工况进行了数值模拟,模拟结果与理论值符合很好,验证了MMC算法的计算精度,且该算法具有较小的计算代价。

Nanoparticle size distribution is described by general dynamic equation （GDE）. A new multi-Monte Carlo （MMC） method is promoted to solve for simultaneous coagulation and breakage of nanoparticles. MMC method can discard the concept of “subsystem” which is widely adopted by popular Monte Carlo methods. Instead MMC method introduces the concept of “weighted fictitious particle”. MMC method is based on “time-driven” MC technique and conserves constant number of fictitious particles and constant volume with the evolution of time. Firstly MMC method is described in details, including the setting of time step, the scheme of simultaneous coagulation and breakage, the judgment of the occurrence of coagulation and breakage event, the choice of fictitious coagulation partner, and the consequential treatment of particle coagulation and breakage event. Then MMC method is used to simulate three special cases in which complete or partial analytical solutions exist： The simulation results of MMC method for GDE agree with analytical solutions well, which proves that MMC method can assort with computation cost and computation precision and has a lesser computation cost and higher computation precision.