处理多分散颗粒凝并和冷凝/蒸发问题的多重Monte Carlo算法

Multi-Monte Carlo method for simultaneous coagulation and condensation/evaporation of polydisperse particles

提出一个新的多重Monte Carlo (MMC) 算法来求解同时考虑凝并和冷凝/蒸发的通用动力学方程(GDE),该算法基于时间驱动, 模拟过程中保持模拟颗粒数目不变和计算区域体积不变. 描述了时间步长确定方法, 同时处理凝并和冷凝/蒸发的方案 针对常凝并核和常冷凝核, 常凝并核和线性冷凝核, 线性凝并核和线性冷凝核三种特殊工况, MMC算法模拟了颗粒尺度分布函数的时间演变, 与理论分析解进行了比较, 表明MMC算法能解决普通Monte Carlo算法的计算精度和计算代价不能协调的矛盾, 具有较小的计算代价和较高的计算精度, 能够适用于工程应用.

The time evolution of particle size distribution (PSD) is of fundamental interest and a key issue. PSD along with time is described by general dynamic equation (GDE). There is an antinomy of computation cost and computation precision in some ordinary Monte Carlo methods for GDE. A new multi-Monte Carlo (MMC) method is presented to consider GDE for simultaneous coagulation and condensation/evaporation of polydisperse particles. The MMC method is based on time-driven, constant number technique and constant volume technique. Firstly the MMC method is described in detail, including the setting of time step, the scheme of handling simultaneous coagulation and condensation/evaporation. Then the MMC method is validated by three kinds of special cases: constant coagulation kernel and constant condensation kernel (case 1), constant coagulation kernel and linear condensation kernel (case 2), and linear coagulation kernel and linear condensation kernel (case 3). The simulation results of the MMC method for GDE agreed with analytical solution well, which proved that MMC method could resolve the contradiction between computation cost and computation precision, i.e., MMC method has both lesser computation cost and better computation precision.