Finite volume approximation of multidimensional aggregation population balance equation on triangular grid

Abstract

The present work shows the first ever implementation of two-order moments conserving finite volume scheme (FVS) for approximating a multidimensional aggregation population balance equations (PBE’s) on a structured triangular grid. This scheme is based on preservation of the zeroth and conservation of the first order moments. Our main aim is to demonstrate the ability of the FVS to adapt the structured triangular grid well, hence, improves the accuracy of number density function as well as various order moments. The numerical results obtained by the FVS on a triangular grid are compared with the cell average technique. The comparison is also enhanced to illustrate that the FVS with a triangular grid provides the numerical results with higher precision and at lesser computational time as compared to the FVS with a rectangular grid. Additionally, we also study the mixing state of a bicomponent population of clusters (granules) characterized by the normalized variance of excess solute, χ, a parameter that measures the deviation of the composition of each granule from the overall mean. It is shown that the accuracy of the total variance of the excess solute improves when a triangular grid is used in place of a rectangular grid.