WIAS Preprint No. 1597, (2011)

Stochastic weighted particle methods for population balance equations


  • Patterson, Robert I. A.
    ORCID: 0000-0002-3583-2857
  • Kraft, Markus
    ORCID: 0000-0002-4293-8924
  • Wagner, Wolfgang

2010 Mathematics Subject Classification

  • 60J28 65C05 65C35


  • Monte Carlo, weighted particle, coagulation, surface growth, Smoluchowski, simulation




A class of stochastic algorithms for the numerical treatment of population balance equations is introduced. The algorithms are based on systems of weighted particles, in which coagulation events are modelled by a weight transfer that keeps the number of computational particles constant. The weighting mechanisms are designed in such a way that physical processes changing individual particles (such as growth, or other surface reactions) can be conveniently treated by the algorithms. Numerical experiments are performed for complex laminar premixed flame systems. Two members of the class of stochastic weighted particle methods are compared to each other and to a direct simulation algorithm. One weighted algorithm is shown to be consistently better than the other with respect to the statistical noise generated. Finally, run times to achieve fixed error tolerances for a real flame system are measured and the better weighted algorithm is found to be up to three times faster than the direct simulation algorithm.

Appeared in

  • J. Comput. Phys., 230 (2011) pp. 7456--7472 .

Download Documents