Stochastic weighted particle methods for population balance equations

  • Authors:

  • Robert I. A. Patterson;Wolfgang Wagner;Markus Kraft

  • Affiliations:

  • Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany;Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany;Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

A class of coagulation weight transfer functions is constructed, each member of which leads to a stochastic particle algorithm for the numerical treatment of population balance equations. These algorithms are based on systems of weighted computational particles and the weight transfer functions are constructed such that the number of computational particles does not change during coagulation events. The algorithms also facilitate the simulation of physical processes that change single particles, such as growth, or other surface reactions. Four members of the algorithm family have been numerically validated by comparison to analytic solutions to simple problems. Numerical experiments have been performed for complex laminar premixed flame systems in which members of the class of stochastic weighted particle methods were compared to each other and to a direct simulation algorithm. Two of the weighted algorithms have been shown to offer performance advantages over the direct simulation algorithm in situations where interest is focused on the larger particles in a system. The extent of this advantage depends on the particular system and on the quantities of interest.