ABSTRACT
In this work, numerical approximations for solving the one dimensional Smoluchowski coagulation equation on non-uniform meshes has been analyzed. Among the various available numerical methods, finite volume and sectional methods have explicit advantage such as mass conservation and an accurate prediction of different order moments. Here, a recently developed efficient finite volume scheme (Singh et al., 2015Singh, M., Kumar, J., Bück, A. and Tsotsas, E., A volume-consistent discrete formulation of aggregation population balance equations. Mathematical Methods in the Applied Sciences 39(9), 2275-2286 (2015).) and the cell average technique (Kumar et al., 2006Kumar, J., Peglow, M., Warnecke, G., Heinrich, S. and Mörl, L., Improved accuracy and convergence of discretized population balance for aggregation: The Cell Average Technique. Chemical Engineering Science 61(10), 3327-3342 (2006).) are compared. The numerical comparison is established for both analytically tractable as well as physically relevant kernels. It is concluded that the finite volume scheme predicts both number density as well as different order moments with higher accuracy than the cell average technique. Moreover, the finite volume scheme is computationally less expensive than the cell average technique.
Key words:
Aggregation; Particles; Population balance equation; Finite volume scheme; Cell average technique; Non-uniform grids
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