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2006-35

Numerical Solution of Population Balance Equations for Nucleation, Growth and Aggregation Processes

by Qamar, S., Warnecke, G..


Series: 2006-35, 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
65L99 None of the above, but in this section

Abstract:
This article focuses on the derivation of numerical schemes for solving population balance models (PBMs) with simultaneous nucleation,
growth and aggregation processes. Two numerical methods are proposed for this purpose.
The first method combines a method of characteristics (MOC) for growth process with a finite volume scheme (FVS)
for aggregation processes. For handling nucleation terms, a cell of nuclei size
is added at a given time level.The second method purely uses a semidiscrete finite volume scheme
for nucleation, growth and aggregation of particles. Note that both schemes use the same finite volume scheme
for aggregation processes. On one hand, the method of characteristics offers a technique which is in general
a powerful tool for solving linear growth processes, has the capability to overcome numerical diffusion and dispersion, is computationally
efficient, as well as give highly resolved solutions. On the other hand, the finite volume schemes which
were derived for a general system in divergence form, are applicable to any grid to control resolution, and are also computationally not expensive. In the first method a combination of finite volume
scheme and the method of characteristics gives a highly accurate and efficient scheme for simultaneous
nucleation, growth and aggregation processes. The second method demonstrates
the applicability, generality, robustness and efficiency of high resolution schemes.
The proposed techniques are tested for pure growth,
simultaneous growth and aggregation, nucleation and growth, as well as simultaneous nucleation, growth and aggregation processes.
The numerical results of both schemes
are compared with each other and are also validated against available analytical solutions.
The numerical results of the schemes are in good agreement with the analytical solutions.

Keywords:
Population balance models, high resolution finite volume sche

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