A volume conserving discrete formulation of aggregation population balance equations on non-uniform meshes

Aggregation is an important size enlargement process in many industries. The modelling and design of the process can be done using the population balance framework, however, in almost every case a numerical solution of the equations must be obtained. In this paper, we present a new numerical scheme (NFVS) for the one-dimensional aggregation population balance equation or Smoluchowski equation on non-uniform grids. We compare the new scheme with a current scheme by Forestier-Coste and Mancini [2012] (FVS) considering some classical examples. The simplicity and generality to apply on uniform and non-uniform meshes are main features of the new scheme. Furthermore, the proposed new numerical scheme not only conserves the total volume of individuals in the system and is consistent with the total number of individuals, also higher-order moments are predicted well by the new scheme.