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2006-29

Adaptive High Resolution Schemes for Multidimensional Population Balances in Crystallization Processes

by Qamar, S., Ashfaq, A., Warnecke, G., Angelov, I., Elsner, M. P., Seidel-Morgenstern, A..


Series: 2006-29, Preprints

MSC:
65M99 None of the above, but in this section
35L99 None of the above, but in this section
35Q99 None of the above, but in this section

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 H. Tang and T. Tang (2003) 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, nevertheless 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.

Keywords:
Population balance models, distributed parameter systems, high resolutio