A volume-consistent discrete formulation of aggregation population balance equations

In this paper, a new finite volume scheme for the numerical solution of the pure aggregation population balance equation, or Smoluchowski equation, on non-uniform meshes is derived. The main feature of the new method is its simple mathematical structure and high accuracy with respect to the number density distribution as well as its moments. The new method is compared with the existing schemes given by Filbet and Laurençot (SIAM J. Sci. Comput., 25 (2004), pp. 2004-2028) and Forestier and Mancini (SIAM J. Sci. Comput., 34 (2012), pp. B840-B860) for selected benchmark problems. It is shown that the new scheme preserves all the advantages of a conventional finite volume scheme and predicts higher-order moments as well as number density distribution with high accuracy.