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Population balance models; High resolution finite volume schemes; Method of characteristics; Nucleation; Growth; Aggregation; Breakage; Hyperbolic conservation laws
Abstract:
This work is concerned with the modeling and simulation of population balance equations (PBEs) for combined particulate processes. In this study a PBE with simultaneous nucleation, growth, aggregation and breakage processes is considered. In order to apply the finite volume schemes (FVS) a reformulation of the original PBE is introduced. This reformulation not only help us to treat the aggregation and breakage processes in a manner similar to the growth process in the FVS but also in deriving a stable numerical scheme. Two numerical methods are proposed for the numerical approximation of the resulting reformulated PBE. The first method combines a method of characteristics (MOC) for growth process with an FVS for aggregation and breakage processes. The second method purely uses a semidiscrete FVS for all processes. Both schemes use the same FVS for aggregation and breakage processes. The numerical results of the schemes are compared with each other and with the available analytical solutions. The numerical results were found to be in good agreement with analytical solutions.
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[accessed May 11, 2009]
