Development and Convergence Analysis of a Finite Volume Scheme for Solving Breakage Equation

Abstract

In this paper, we develop a new discretization method based on a finite volume approach for solving the breakage population balance equation. The scheme is designed to conserve the total mass of the system, and predict the total number of particles as well as the complete particle size distribution very accurately. The new method is computationally very efficient, easy to code, and robust to apply on uniform and nonuniform meshes. Development of the method is completed by providing a detailed mathematical analysis that includes consistency and convergence of the numerical solution. It is proved that the scheme is second order convergent independently of the type of mesh. Moreover, numerical results are compared against several test cases, including analytically tractable and practically oriented problems. It is found that the new method predicts the complete particle size distribution and its moments with high accuracy. The mathematical results of convergence analysis are also validated numerically.