Mass-based finite volume scheme for aggregation, growth and nucleation population balance equation

Mehakpreet Singh, Hamza Y. Ismail, Themis Matsoukas, Ahmad B. Albadarin, Gavin Walker

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


In this paper, a new mass-based numerical method is developed using the notion of Forestier-Coste & Mancini (Forestier-Coste & Mancini 2012, SIAM J. Sci. Comput. 34, B840–B860. (doi:10.1137/110847998)) for solving a one-dimensional aggregation population balance equation. The existing scheme requires a large number of grids to predict both moments and number density function accurately, making it computationally very expensive. Therefore, a mass-based finite volume is developed which leads to the accurate prediction of different integral properties of number distribution functions using fewer grids. The new mass-based and existing finite volume schemes are extended to solve simultaneous aggregation-growth and aggregation-nucleation problems. To check the accuracy and efficiency, the mass-based formulation is compared with the existing method for two kinds of benchmark kernels, namely analytically solvable and practical oriented kernels. The comparison reveals that the mass-based method computes both number distribution functions and moments more accurately and efficiently than the existing method.

Original languageEnglish (US)
Article number20190552
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2231
StatePublished - Nov 1 2019

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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