Improved higher-order finite volume scheme and its convergence analysis for collisional breakage equation

Abstract

A new volume and number consistent finite volume scheme for the numerical solution of a collisional nonlinear breakage problem is introduced. The number consistency is achieved by introducing a single weight function in the flux formulation of finite volume scheme, whereas existing schemes for a linear fragmentation equation [Kumar et al. SIAM J. Numer. Anal. 53 (4), 1672-1689] and standard collisional nonlinear breakage equation [Das et al. SIAM J. Sci. Comp. 42 (6), B1570-B1598] require two weights for preserving both volume and number of particles. The higher efficiency and robustness of the proposed scheme allow it to be easily coupled with computational fluid dynamics (CFD) softwares such as COMSOL, Ansys and gPROMS, which is currently one of the predominant topics of discussion in particle technology. Consistency and stability via Lipschitz criterion are studied in detail to demonstrate second order convergence rate for the proposed scheme irrespective of both breakage kernel and nature of grids. Several benchmark problems are solved and validated against its analytical solution to analyze the accuracy of the new scheme.