Comparison of the Method of Characteristics with a Finite Difference Scheme for Crystallization Process Simulation

Abstract

The method of characteristics is a numerical algorithm which is well suited to the simulation of first-order, partial differential equations. In this study, the method of characteristics is extended to enablethe simulation of crystallization processes even when the crystal growth rate varies with crystal size. A finite difference scheme and the method of characteristics are compared in terms of simulation results of a crystallization process. When the method of characteristics is employed, the numerical result is not affected by the mesh size, whereas the numerical solution obtained by applying a finite difference scheme shows strong mesh dependency. Since the numerical results obtained using the finite difference scheme are significantly different from those obtained using the method of characteristics, it is shown that the finite difference solution is strongly influenced by the numerical dispersion.