Adaptive high-resolution schemes for multidimensional population balances in crystallization processes

Abstract

This article focuses on the application of adaptive high-resolution finite volume schemes for solving multidimensional population balance models (PBM) in crystallization processes. For the mesh redistribution, we use the moving mesh technique of Tang and Tang [Tang, H.-Z. & Tang, T. (2003). Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. SIAM Journal of Numerical Analysis, 41, 487–515] which they have developed for hyperbolic conservation laws in conjuction with finite volume schemes. In this technique, an iterative procedure is used to redistribute the mesh by moving the spatial grid points. The corresponding numerical solution at the new grid points is obtained by solving a linear advection equation. The method avoids the usual unsatisfactory, interpolation procedure for updating the solution. The finite volume schemes were originally derived for compressible fluid dynamics. The schemes have already shown their accuracy and efficiency in resolving sharp peaks and shock discontinuities. The accuracy of these schemes has been improved further by using the adaptive meshing techniques. The application of these high-resolution schemes for multidimensional crystallization processes demonstrates their generality, efficiency, and accuracy. The numerical test cases presented in this article show the clear advantage of finite volume schemes and show further improvements when combined with a moving mesh technique.