06-29
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.
Preprint series: 06-29, 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 resolution schemes, moving mesh method, hyperbolic conservation laws, crystallization, nucleation and growth.
The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.