On the impact of the scheme for solving the higher–dimensional equation in coupled population balance systems

Abstract

Population balance systems are models for processes in nature and industry which lead to a coupled system of equations (Navier–Stokes equations, transport equations, ...) where the equations are defined in domains with different dimensions. This paper will study the impact of using different schemes for solving the three–dimensional equation of a precipitation process in a two–dimensional flow domain. The numerical schemes for the three–dimensional equation are assessed with respect to the median of the volume fraction of the particle size distribution and the computational costs. It turns out that in the case of a structured flow field with small variations in time all schemes give qualitatively the same results. For a highly time–dependent flow field, the evolution of the median of the volume fraction differs considerably between first order and higher order schemes.