A new sorting algorithm-based merging weighted fraction Monte Carlo method for solving the population balance equation for particle coagulation dynamics
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 29 September 2022
Issue publication date: 5 January 2023
Abstract
Purpose
The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency.
Design/methodology/approach
In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme.
Findings
The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost.
Originality/value
The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.
Keywords
Acknowledgements
This work was supported by the research studentship grant and Department of Mechanical Engineering of The Hong Kong Polytechnic University.
Citation
Wang, F. and Chan, T.L. (2023), "A new sorting algorithm-based merging weighted fraction Monte Carlo method for solving the population balance equation for particle coagulation dynamics", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 2, pp. 881-911. https://doi.org/10.1108/HFF-06-2022-0378
Publisher
:Emerald Publishing Limited
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