GRK-Mikro-Makro-Wechselwirkungen in strukturierten Medien und Partikelsystemen "Numerical methods for population balance equations with high property space dimension"

The topic of this project is the numerical analysis and computation of population balance equations (PBEs).
Aggregation and breakage PBEs can be rewritten in mass conservative form whereas growth is number conserving. Therefore, one of our aims is to achieve the coupling of all the particulate processes in such a way that both number and mass are preserved. We investigated mathematically and verified numerically schemes which are both number and mass preserving for the coupled processes. The second aim is to study the existence of approximated solution using the finite volume scheme for binary aggregation and general breakage problem. Further, we explored the stability and the convergence analysis of the method for non-linear aggregation and linear breakage problem. This is an extension of the results given by J.P. Bourgade and F. Filbet. Moreover, we also study the two-dimensional problems by using sectional methods such as the cell average and the fixed pivot techniques. The doctoral thesis was submitted in November 2010.