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摘要
Multidimensional growth processes play an important role in many fields of applications, such as crystallization processes and cell culture engin- eering. The numerical solution of the corresponding multivariate population balance equations is quite challenging as standard discretization-based methods are not efficient for high dimensional problems. For this reason, the distribution dynamics is often characterized by its moments. However, the moment dynamics generally cannot be calculated in closed form. Existing approximation techniques cannot be implemented efficiently in the multivariate framework, in particular for high dimensional problems. This contribution presents an alternative methodology for the efficient approximate computation of moments for multidimensional growth processes using Monomial Cubatures and the Method of Characteristics (MOC). The procedure will be shown to reproduce the moments accurately for one- and two-dimensional examples which feature nonlinear growth rates and coupling to a continuous phase, respectively. Furthermore numerical effort and accuracy will be analyzed for a five-dimensional benchmark problem.
- 出版日期2014-12
