Convergence analysis of sectional methods for solving aggregation population balance equations: The cell average technique Ankik Kumar Giri 1∗ , Jitendra Kumar 2 , Gerald Warnecke 1 1 Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universit¨atsplatz 2, D-39106 Magdeburg, Germany 2 Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India December 30, 2009 Abstract. The paper deals with the convergence analysis of the cell average technique given by J. Kumar et al. [3] to solve the nonlinear aggregation population balance equations. Similarly to our previous paper Giri et al. [1], which considered the fixed pivot technique, the main emphasis here is to check the convergence for five different types of uniform and non-uniform meshes. First, we observed that the cell average technique is second order convergent on a uniform, locally uniform and non-uniform smooth meshes. Secondly, the scheme is examined closely on an oscillatory and non-uniform random meshes. It is found that the scheme is only first accurate there. In spite of this, the cell average technique gives one order higher accuracy than the fixed pivot technique for locally uniform, oscillatory and random meshes. Several numerical simulations verify the mathematical results of the convergence analysis. Finally the numerical results obtained are also compared with those for the case of the fixed pivot technique. Keywords: Particles; Aggregation; Cell average technique; Consistency; Convergence. Mathematics Subject Classification (2000) 45J05, 65R20, 45L10 1 Introduction The population balance equations (PBEs) are analytically solvable only for some restricted class of kernels. Because of restrictions, it has been of great interest to develop new numerical meth- ods and assess them by means of mathematical analysis. As noticed by Kostoglou [2] among all numerical sectional methods for solving PBE, the fixed pivot technique [7] is the most popular and widely used in the literature. A new step in the development of sectional methods is due to the recently introduced cell average technique developed by J. Kumar et al. [3]. In a recent paper by Giri et al. [1], convergence analysis of the fixed pivot technique has been discussed for solving aggregation PBE. It has been observed that the fixed pivot technique is second order * Corresponding author. Tel +49 391 6711629; Fax +49 391 6718073 Email address: ankik.giri@ovgu.de 1