Convergence analysis of sectional methods for solving aggregation population balance equations: The fixed pivot technique

2013/03/25 by Ankik Kumar Giri, Giri, Ankik Kumar, Erika Hausenblas +1
Engineering · Environmental Science · #Coagulation and Flocculation Studies #Enhanced Oil Recovery Techniques #FOS: Mathematics #Field-Flow Fractionation Techniques #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1303.6063

openalex publication_date 2013/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the convergence analysis of the fixed pivot technique given by S.Kumar and Ramkrishna \citeKumar:1996-1 for the nonlinear aggregation population balance equations which are of substantial interest in many areas of science: colloid chemistry, aerosol physics, astrophysics, polymer science, oil recovery dynamics, and mathematical biology. In particular, we investigate the convergence for five different types of uniform and non-uniform meshes which turns out that the fixed pivot technique is second order convergent on a uniform and non-uniform smooth meshes. Moreover, it yields first order convergence on a locally uniform mesh. Finally, the analysis exhibits that the method does not converge on an oscillatory and non-uniform random meshes. Mathematical results of the convergence analysis are also demonstrated numerically.

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