ADVANCES OF NUMERICAL METHODS FOR GENERAL DYNAMIC EQUATION DESCRIBING DISPERSED SYSTEM
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摘要: 离散系统中的颗粒物在凝并、破碎、冷凝/蒸发、成核、沉积等事件作用下颗粒尺度分布的时间演变由通用动力学方程所描述.该方程为一典型的部分积分微分方程,普通数值方法难以求解.本文详细介绍了求解通用动力学方程的矩方法、分区法、离散法、离散-分区法、MonteCarlo方法等几种算法的原理、优缺点和最新的研究进展,并着重介绍了MonteCarlo算法,包括基于时间驱动Monte Carlo方法、基于事件驱动MonteCarlo方法、常数目法、常体积法以及多重Monte Carlo算法.Abstract: The time evolution of particle size distribution (PSD)in dispersed systems is described by the General Dynamic Equation (GDE),taking accout of coagulation, breakage, condensation/evaporation, nucleation,deposition, etc. GDE is a typical partially integro-differentialequation.Consequently, normal numerical methods can hardly be used to solve it.The paper discusses the theoretical foundations, advantages anddisadvantages, and the recent development of some numerical methods for GDE,including the moments of method, sectional method, discrete method,discrete-sectional method, and Monte Carlo method. The paper paysspecial attention to the MonteCarlo method, including the ``time-driven'' Monte Carlo method, ``event-driven''Monte Carlo method, constant number method, constant volume method.
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