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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..

Series: 2005-26, Preprints

65M99 None of the above, but in this section
65Y20 Complexity and performance of numerical algorithms
35L65 Conservation laws

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.

Population balance models, distributed paramter sys