Two moments consistent discrete formulation for binary breakage population balance equation and its convergence

Abstract A numerical scheme based on the finite volume approach is developed to solve a binary breakage population balance equation (PBE) on nonuniform meshes. The key feature of the new scheme is that it is free of the common requirement of redistributing the particle mass to neighboring pivots, its formulation is simpler compared to other methods such as cell average and fixed pivot techniques. The new scheme produces accurate results for the distribution and its first two moments while consuming less computational time. The accuracy and efficiency of the proposed scheme is validated against the recently developed volume conserving finite volume scheme for various benchmark problems. We prove that convergence exhibits second-order consistency and confirm the conclusion by numerical calculation of the experimental order of convergence in different meshes. The new approximation is the first ever two-order moment conserving finite volume scheme for a binary breakage PBE that is free from constraint that the particles are concentrated on the representative of the cell.