CONVERGENCE ANALYSIS OF A FINITE VOLUME SCHEME FOR SOLVING NON-LINEAR AGGREGATION-BREAKAGE POPULATION BALANCE EQUATIONS

This paper presents stability and convergence analysis of a finite volume scheme for solving aggregation, breakage and the combined processes by showing consistency of the method and Lipschitz continuity of numerical fluxes. It is investigated that the finite volume scheme is second order convergent independently of the meshes for pure breakage problem while for pure aggregation and coupled problems, it indicates second order convergence on uniform and non-uniform smooth meshes. Furthermore, it gives only first order accuracy on non-uniform meshes. The mathematical results of convergence analysis are also demonstrated numerically for several test problems.