A note on sectional and finite volume methods for solving population balance equations

Abstract

In this work, we survey some numerical methods for solving population balance equations (PBEs). Among several numerical methods available in the literature, sectional and finite volume methods offer distinct advantages like conservation of mass and the accurate prediction of moments. The sectional methods are obtained from the standard form of PBE while the finite volume method is applied by transforming the PBE into a mass conservation law. Here we summarize these discretisation methods, mainly the cell average technique and the finite volume technique for solving aggregation-breakage PBEs. The cell average technique was developed by the authors. Furthermore, we also discuss possible extensions of the methods for solving higher dimensional population balance equations. There are two different approaches to deal with an n-dimensional PBE: computation on a reduced model and on a complete model. In contrast to the complete model we perform computation on a set of n one-dimensional PBEs in the reduced model approach. The computation time reduces drastically in the reduced model approach but it is not possible to capture the complete information of the particle property distribution. © Springer Berlin Heidelberg 2008.