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2005-10

Improved Accuracy and Convergence of Discretized Population Balance: The Cell Average Technique

by Kumar, J., Peglow, M., Warnecke, G., Heinrich, S., Mörl, L..


Series: 2005-10, Preprints

MSC:
65M99 None of the above, but in this section
82C80 Numerical methods (Monte Carlo, series resummation, etc.)
45K05 Integro-partial differential equations

Abstract:
A new discretization method for aggregation equations is developed. It is compared to the fixed pivot technique proposed by Kumar and Ramkrishna (1996, Chem. Eng. Sci. 51, 1311-1332). The numerical results for aggregation problems by discretized population balances are consistently overpredicting and diverge before the gelling point in the case of a gelling kernel. The present work establishes a new technique which assigns the particles within the intervals more precisely. This is achieved by taking first the average the newborn particles within the interval and then assigning them to the neighboring nodes such that pre-chosen properties are exactly preserved. The new technique preserves all the advantages of the conventional discretized methods and provides a significant improvement in predicting the particle size distribution (PDS). In addition, it is found that the technique is a powerful tool for the computation of gelling problems. The effectiveness of the technique is illustrated by application to serveral aggergation problems for suitably selected aggregation kernels.

Keywords:
Population balance, discretization, aggregation, particle, batch, gelation