Comparison of High Resolution Schemes for Solving Population Balances

The physical properties of particulate products such as crystals and polymers are strongly dependent on their size distribution which is usually modeled by a population balance equation (PBE). The PBE is an integro-partial differential equation and due to its hyperbolic nature, steep fronts are encountered in the solution profile. When solved numerically, the discretization of the PBE has to be performed with care to avoid numerical diffusion, and dispersion and appropriate numerical methods have to be chosen for that purpose. In this work, an extensive investigation of the performance of several high resolution discretization methods when applied to the PBE is performed with the objective to determine the most promising among them in terms of accuracy and computation time. The comparison is performed on standard benchmark problems and on a practical PBE that arises from modeling the growth of a seed of particles in emulsion polymerization.