10-03
Convergence analysis of sectional methods for solving aggregation population balance equations: The cell average technique
by A.K. Giri, J. Kumar, G. Warnecke
Preprint series: 10-03, Preprints
- MSC:
- 45J05 Integro-ordinary differential equations
- 65R20 Integral equations
- 45L10 Numerical approximation of solutions, {For numerical analysis, See 65R20}
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. 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; Consistency; Convergence
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