### 2007-39

by Kumar, J., Warnecke, G..

**Series:** 2007-39, Preprints

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

**Abstract:**

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.

**Keywords:**

Population Balance, Convergence, Fixed Pivot, Breakage, Particles