In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and boundary value problems without nonphysical restrictive assumptions such as linearization and discretization. It gives the solution in the form of series with easily computable solution components. The outcome of this study reveals that the proposed method can avoid numerical stability problems which often characterize in general numerical techniques related to this area. Several examples including Austin's kernel available in literature are examined to demonstrate the accuracy and applicability of the proposed method.
a b s t r a c tIn this work, a finite volume scheme for the numerical solution of bivariate pure aggregation population balance equations on non-uniform meshes is derived. The new method has a simple mathematical structure and it provides high accuracy with respect to the number density distribution as well as different moments. The method relies on weights to conserve the total mass of the system. The new method is compared to a recently developed finite volume scheme by Forestier-Coste and Mancini (2012) for some selected benchmark problems. It is shown that the proposed method is not only computationally more efficient but also more accurate than the method by Forestier-Coste and Mancini (2012).
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