Event-driven sorting algorithm-based Monte Carlo method with neighbour merging method for solving aerosol dynamics

Fei Wang, Liang An, Tat Leung Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


A new event-driven sorting algorithm-based merging Monte Carlo (SAMMC) method is proposed and developed for solving the general dynamic equation in aerosol dynamics. A neighbour merging method is proposed to maintain a constant-volume and constant-number scheme with minimal interference to the numerical particle population, where absolute volume difference (AVD) and relative volume difference (RVD) are used as the crucial merging criteria. The SAMMC method can be used for simulating all aerosol dynamic processes with very high computational accuracy, especially effective in those aerosol dynamic processes generating additional numerical particles. In the present study, comprehensive computational conditions are used to study their impacts on computational accuracy and efficiency by comparing the SAMMC method to previous MC methods and analytical solutions. Numerical results show that the SAMMC method has excellent agreement with analytical solutions for all specified cases of different aerosol dynamic processes and shows higher computational accuracy than equal-weight-based MC methods. In addition, the computational accuracy of the SAMMC method in the total particle number concentration is much higher than those of the weighted fraction Monte Carlo (WFMC) method and sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method in non-homogeneous coagulation. The SAMMC method can also achieve the same computational precision as the multi-Monte Carlo (MMC) method at only slightly higher computational cost in homogeneous coagulation. More importantly, the SAMMC method can deal with breakage-related processes and simultaneous coagulation and nucleation with very high computational accuracy and efficiency, while the numerical results of the MMC method may significantly deviate from analytical solutions due to the introduction of systematic errors. Furthermore, the RVD can achieve higher computational accuracy in multi-breakage modelling than AVD, but AVD and RVD have almost the same computational efficiency and accuracy in other aerosol dynamic processes.

Original languageEnglish
Pages (from-to)833-862
Number of pages30
JournalApplied Mathematical Modelling
Publication statusPublished - Aug 2023


  • Aerosol dynamics
  • Event driven
  • General dynamic equation
  • Monte Carlo
  • Neighbour merging
  • Sorting algorithm

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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