Finite volume approximation of nonlinear agglomeration population balance equation on triangular grid

Abstract

In this present work, a finite volume scheme for approximating a multidimensional nonlinear agglomeration population balance equation on a regular triangular grid is developed. The finite volume schemes developed in literature are restricted to a rectangular grid [43]. However, the accuracy and efficiency of finite volume scheme can be enhanced by considering triangular grids. The triangular grid is generated using the concept of ‘Voronoi Partitioning’ and ‘Delaunay Triangulation’. To test the accuracy and efficiency of the scheme on a triangular grid, the numerical results are compared with the sectional method, namely Cell Average Technique [38] for various analytically tractable kernels. The results reveal that the finite volume scheme on a triangular grid is computationally less expensive and predicts the number density function along with the different order moments more accurately than the cell average technique. Furthermore, the numerical comparison is extended by comparing the finite volume scheme on a rectangular grid. It also demonstrates that the finite volume scheme with a regular triangular grid computes the numerical results more accurately and efficiently than the finite volume scheme with a rectangular grid.