TY - JOUR

T1 - Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems

AU - Zhao, H.

AU - Maisels, A.

AU - Matsoukas, T.

AU - Zheng, C.

N1 - Funding Information:
H. Zhao wishes to thank “National Key Basic Research and Development Program 2006CB200304 and 2002CB211602” and “the National Natural Science Foundation of China under grant number 90410017 and 20606015” for funds.

PY - 2007/4/10

Y1 - 2007/4/10

N2 - Monte Carlo (MC) constitutes an important class of methods for the numerical solution of the general dynamic equation (GDE) in particulate systems. We compare four such methods in a series of seven test cases that cover typical particulate mechanisms. The four MC methods studied are: time-driven direct simulation Monte Carlo (DSMC), stepwise constant-volume Monte Carlo, constant number Monte Carlo, and multi-Monte Carlo (MMC) method. These MC's are introduced briefly and applied numerically to simulate pure coagulation, breakage, condensation/evaporation (surface growth/dissolution), nucleation, and settling (deposition). We find that when run with comparable number of particles, all methods compute the size distribution within comparable levels of error. Because each method uses different approaches for advancing time, a wider margin of error is observed in the time evolution of the number and mass concentration, with event-driven methods generally providing better accuracy than time-driven methods. The computational cost depends on algorithmic details but generally, event-driven methods perform faster than time-driven methods. Overall, very good accuracy can be achieved using reasonably small numbers of simulation particles, O(103), requiring computational times of the order 102-103 s on a typical desktop computer.

AB - Monte Carlo (MC) constitutes an important class of methods for the numerical solution of the general dynamic equation (GDE) in particulate systems. We compare four such methods in a series of seven test cases that cover typical particulate mechanisms. The four MC methods studied are: time-driven direct simulation Monte Carlo (DSMC), stepwise constant-volume Monte Carlo, constant number Monte Carlo, and multi-Monte Carlo (MMC) method. These MC's are introduced briefly and applied numerically to simulate pure coagulation, breakage, condensation/evaporation (surface growth/dissolution), nucleation, and settling (deposition). We find that when run with comparable number of particles, all methods compute the size distribution within comparable levels of error. Because each method uses different approaches for advancing time, a wider margin of error is observed in the time evolution of the number and mass concentration, with event-driven methods generally providing better accuracy than time-driven methods. The computational cost depends on algorithmic details but generally, event-driven methods perform faster than time-driven methods. Overall, very good accuracy can be achieved using reasonably small numbers of simulation particles, O(103), requiring computational times of the order 102-103 s on a typical desktop computer.

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U2 - 10.1016/j.powtec.2006.12.010

DO - 10.1016/j.powtec.2006.12.010

M3 - Article

AN - SCOPUS:33947417663

SN - 0032-5910

VL - 173

SP - 38

EP - 50

JO - Powder Technology

JF - Powder Technology

IS - 1

ER -