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Convergence analysis of sectional methods for solving breakage population balance equations-I. The fixed pivot technique.

by Kumar, J., Warnecke, G..

Series: 2007-39, Preprints

65R20 Integral equations
65M99 None of the above, but in this section

In this work we study the convergence of the fixed pivot techniques (Kumar and Ramkrishna, 1996, Chem. Eng. Sci., 51, 1311-1332) for breakage problems. In particular, the convergence is investigated on four different types of uniform and non-uniform meshes. It is shown that the fixed pivot techniqe is second order convergent on a uniform and non-uniform smooth meshes. Furthermore, it gives first order convergence on a locally uniform mesh. Finally the analysis shows that the method does not converge on a non-uniform random mesh. The mathematical results of convergence analysis are also validated numerically.

Population Balance, Convergence, Fixed Pivot, Breakage, Particles