A weighted finite volume scheme for multivariate aggregation population balance equation

For solving multivariate aggregation population balance equation, two new discretizations based on number and mass distributions are presented. These proposed schemes are relatively simple to implement and computationally very efficient. Moreover, the mathematical structure of the schemes remains unchanged with the change in dimension. Hence, these methods are ideally suited for solving multidimensional aggregation problems on non-uniform grids. The accuracy of the new schemes is shown by comparing number density as well as different order moments with exact results as well as with the numerical results of Forestier and Mancini (2012). Besides preservation of the zeroth and first order moments, the new schemes also predict higher order moments and number density very accurately. In conclusion, the proposed schemes are more accurate and efficient than the scheme of Forestier and Mancini (2012).