Convergence analysis of sectional methods for solving breakage population balance equations-II: the cell average technique

Abstract

This work presents the convergence of the cell average technique (Kumar et al. in Powder Technol 179:205–228, 2007) for solving breakage population balance equation. Similarly to our paper Kumar and Warnecke (Numerische Math, 2008) of this series, we study convergence on four different types of meshes. A second order convergence is proved for uniform, locally uniform and non-uniform smooth meshes. Finally the scheme is analyzed on random mesh and it is found that the scheme is only first order accurate. Nevertheless we obtain for locally uniform as well as for random mesh one order higher accuracy than the fixed pivot technique discussed by the authors in the first paper. All mathematical observations of convergence analysis are also validated numerically and numerical results are compared with the results of the first part.