Technical Report 154, c4e-Preprint Series, Cambridge

Authors: Kok Foong Lee, Robert I. A. Patterson, Wolfgang Wagner, and Markus Kraft*

Reference: Technical Report 154, c4e-Preprint Series, Cambridge, 2015

Associated Themes:
 

• Problems concerning multi-compartment population balance equations are studied
• A class of fragmentation weight transfer functions is presented
• Three stochastic weighted algorithms are compared against the direct simulation algorithm
• The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate
• The algorithms are applied to a multi-dimensional granulation model

This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.

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