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Efficient numerical simulation of batch crystallization processes governed by partial differential equations

This paper deals with the simulation problem of crystallization processes. The dynamics of crystallization processes are governed by hyperbolic partial differential equations. We propose to simulate the processes in the one-dimensional size case using the method of characteristics. We observe that the method of characteristics has no numerical diffusion compared with the finite difference method. Moreover the method of characteristics can be extended to simulate the processes in the two-dimensional size case. In the paper we develop an algorithm based on the method of characteristics and carry out different simulations to test the practical reliability of the method. It turns out that the algorithm is notably efficient: fast and accurate. Therefore it takes less time and make less numerical error in order to be used for control of the processes.