Convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage population balance equations

Rajesh Kumar; Jitendra Kumar; Gerald Warnecke

doi:10.3934/krm.2014.7.713

Article Contents

2014, Volume 7, Issue 4: 713-737. Doi: 10.3934/krm.2014.7.713

This issue Previous Article A review of the mean field limits for Vlasov equations Next Article Convergence of the compressible isentropic magnetohydrodynamic equations to the incompressible magnetohydrodynamic equations in critical spaces

Convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage population balance equations

1.
RICAM, Austrian Academy of Sciences, Altenberger Strasse 69, Linz, 4040
2.
Department of Mathematics, IIT Kharagpur, Kharagpur, 721302
3.
Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universitatsplatz 2, Magdeburg, D-39106

Received: February 28, 2014

Revised: July 31, 2014

Published: November 2014

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Abstract

This paper presents stability and convergence analysis of a finite volume scheme for solving aggregation, breakage and the combined processes by showing consistency of the method and Lipschitz continuity of numerical fluxes. It is investigated that the finite volume scheme is second order convergent independently of the meshes for pure breakage problem while for pure aggregation and coupled problems, it indicates second order convergence on uniform and non-uniform smooth meshes. Furthermore, it gives only first order accuracy on non-uniform meshes. The mathematical results of convergence analysis are also demonstrated numerically for several test problems.

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Mathematics Subject Classification: Primary: 45K05, 65R20; Secondary: 45L05.

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