Effect of different discretizations on the numerical solution of 2D aggregation population balance equation

This work is concerned with the assessment of the various discretizations used to obtain the numerical solutions of the bivariate aggregation population balance equation. It was illustrated in the literature that the accuracy and the efficiency of the numerical approximations is majorly controlled by the directionality and orientation of the grid selected for the domain discretization [4,6,35]. Therefore, to analyze the effect of directionality on the soution of a 2D aggregation population balance equation, four different types of discretizations have been considered and treated with a mass conserving finite volume scheme [40]. All discretizations are generated using the notion of the ‘Voronoi Partitioning’ and ‘Delaunay Triangulation’. To examine the accuracy and efficiency of the finite volume scheme with various grids, the numerical results are compared with the exact results for several analytically tractable kernels. The comparison demonstrates that the finite volume scheme using X-type grid with logarithmic scale in the radial direction estimate different order moments as well as number density function with higher precision and efficiency as compared to the other discretizations.