References and publications


This section summarizes the main references used in the development of the OpenQBMM package, and aims at providing a compact set of references for OpenQBMM users. It includes both references from other research groups and from the OpenQBMM developers. Complete references for specific code components are provided in the header of the corresponding implementation, and can be also seen in the code documentation.

  1. H. Dette, W.J. Studden, Matrix measures, moment spaces and Favard’s theorem for the interval [0,1] and [0,∞), Linear Algebra and Its Applications. 345 (2002) 169–193. doi:10.1016/S0024-3795(01)00493-1.
  2. R.O. Fox, Computational Models for Turbulent Reacting Flows, Cambridge University Press, 2003.
  3. F. Laurent, T.T. Nguyen, Realizable second-order finite-volume schemes for the advection of moment sets of the particle size distribution, Journal of Computational Physics. 337 (2017) 309–338. doi:10.1016/
  4. E. Madadi-Kandjani, A. Passalacqua, An extended quadrature-based moment method with log-normal kernel density functions, Chemical Engineering Science. 131 (2015) 323–339. doi:10.1016/j.ces.2015.04.005.
  5. D.L. Marchisio, R.O. Fox, Computational models for polydisperse particulate and multiphase systems, Cambridge University Press, Cambridge, 2013.
  6. T.T. Nguyen, F. Laurent, R.O. Fox, M. Massot, Solution of population balance equations in applications with fine particles: Mathematical modeling and numerical schemes, Journal of Computational Physics. 325 (2016) 129–156. doi:10.1016/
  7. C. Yuan, R.O. Fox, Conditional quadrature method of moments for kinetic equations, Journal of Computational Physics. 230 (2011) 8216–8246. doi:10.1016/
  8. C. Yuan, B. Kong, A. Passalacqua, R.O. Fox, An extended quadrature-based mass-velocity moment model for polydisperse bubbly flows, The Canadian Journal of Chemical Engineering. 92 (2014) 2053–2066. doi:10.1002/cjce.22006.
  9. C. Yuan, F. Laurent, R.O. Fox, An extended quadrature method of moments for population balance equations, Journal of Aerosol Science. 51 (2012) 1–23. doi:10.1016/j.jaerosci.2012.04.003.
  10. V. Vikas, Z.J. Wang, A. Passalacqua, R.O. Fox, Realizable high-order finite-volume schemes for quadrature-based moment methods, Journal of Computational Physics. 230 (2011) 5328–5352. doi:10.1016/
  11. V. Vikas, C. Yuan, Z.J. Wang, R.O. Fox, Modeling of bubble-column flows with quadrature-based moment methods, Chemical Engineering Science. 66 (2011) 3058–3070. doi:10.1016/j.ces.2011.03.009.


This section lists the articles written by the OpenQBMM developers during the project performance which have currently been published or have been submitted and have been made available as pre-print.

Published articles

  1. E. Madadi-Kandjani, R.O. Fox, A. Passalacqua, Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods, Physics of Fluids. 29 (2017) 065109. doi:10.1063/1.4989421.

Pre-prints (submitted articles)

  1. A. Passalacqua, F. Laurent, E. Madadi-Kandjani, J.C. Heylmun, R.O. Fox, An open-source quadrature-based population balance solver for OpenFOAM, (2017).