Numerical solutions of population balance models in preferential crystallization

This article focuses on the implementation of numerical schemes to solve model equations describing preferential crystallization for enantiomers. Two types of numerical methods are proposed for this purpose. The first method uses high resolution finite volume schemes, while the second method is the so-called method of characteristics (MOC). On the one hand, the finite volume schemes which were derived for general system in divergence form are computationally efficient, give desired accuracy on coarse grids, and are robust. On the other hand, the MOC offers a technique which is in general a powerful tool for solving growth processes, has capability to overcome numerical diffusion and dispersion, gives highly resolved solutions, as well as being computationally efficient. Several numerical test examples for a preferential crystallization model with and without fines dissolution under isothermal and non-isothermal conditions are considered. The comparison of the numerical schemes demonstrates clear advantages of the finite volume schemes and the MOC for the current model.