### 2007-12

by Kumar, J., Warnecke, G..

**Series:** 2007-12, Preprints

- MSC:
- 65R99 None of the above, but in this section
- 65M99 None of the above, but in this section

**Abstract:**

This paper presents a finite volume scheme for solving breakage population balance equations. It is accomplished by converting the population balance equation into a mass conserving formulation. The proposed scheme is the coupled with the existing numerical scheme developedd by Filbet and Laurecot (2004, SIAM J. Sci. Comp. 25, 2004-2028) for solving aggregation problems. The effectiveness of the methods is demonstrated by several test problems where analytical solutions are available. Furhtermore, numerical results obtained by the finite volume scheme and the cell average technique, recently proposed by the authors (J. Kumar et al. 2006, Chem. Eng. Sci. 61, 3327-3342), are then compared. The advantages and disadvantages are pointed out between the two different approaches of solving th population balance equations. It is concluded that the finite volume scheme predicts more accurate results for particle number density on fine grids, on the other hand quite reasonable results for number density as well as for its moments can be obtained using the cell average scheme even on coarse grids.

**Keywords:**

Population balance, finite volume, aggregation, breakage, particle