Application of the method of characteristics to crystallizer simulation and comparison with finite difference for controller performance evaluation

Finite di€erence methods are widely used to simulate crystallization processes, although they su€er from numerical dispersion. The method of characteristics can tackle this problem, but the traditional algorithm cannot simulate crystallization processes, if the growth rate depends on crystal size, or if discrete control actions are taken. This paper shows how the method of characteristics can be applied to simulate such processes. Furthermore, the impact of numerical dispersion is discussed by comparing simulation results obtained from these two algorithms. It is revealed that the optimal gains and the responses obtained with a ®nite di€erence method are clearly di€erent from those with the method of characteristics.