Numerical Solution of the Drop Population Balance Equation Using Weighted Residual and Finite Volume Methods

This article presents a comparison of numerical results obtained by two different approximations of population balances—the spectral orthogonal collocation and finite volume methods. In particular, the population balance equation for a homogeneous dispersed liquid–liquid system in a batch reactor was considered in the present numerical study. The focus was placed on the accuracy of the numerical approximation of the particle property density distribution. An advantage of the finite volume method is the easy of distributing the points in a nonuniform discretization. It is supposed that the spectral-element orthogonal collocation method may benefit by dividing the computational domain into elements of various polynomial orders. For the present problems studied, the orthogonal collocation in the spectral framework does not perform as well as the finite volume method.