05-26
A Comparative Study of High Resolution Schemes for Solving Population Balances in Crystallization
by Qamar, S.; Elsner, M. P.; Angelov, I.; Warnecke, G.; Seidel-Morgenstern, A.
Preprint series: 05-26, Preprints
- MSC:
- 65M99 None of the above but in this section
- 65Y20 Complexity and performance of numerical algorithms, See also {68Q25}
- 35L65 Conservation laws
Abstract: This article demonstrates the applicability and usefulness of high resolution finite volume schemes for the solution of population balance equations (PBEs) in crystallization processes. The population balance equation is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the other(s) are \'property coordinate(s)\', e.g., the particle size in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes. These include crystallization, polymerization, emulsion and cell dynamics. The high resolution schemes were originally developed for compressible fluid dynamics. The schemes resolve sharp peaks and shock discontinuities on coarse girds, as well as avoid numerical diffusion and numerical dispersion. The schemes are derived for general purposes and can be applied to any hyperbolic model. Here we test the schemes on the one-dimensional population balance models with nucleation and growth. The article mainly concentrates on the re-derivation of a high resolution scheme of Koren (B. Koren, 1993) which is then compared with other high resolution finite volume schemes. The numerical test cases reported in this paper show clear advantages of high resolutions schemes for the solution of population balances.
Keywords: Population balance models, distributed paramter systems, high resolution schemes, hyperbolic conservation laws, crystallization, nucleation and growth.
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