Numerical analysis of finite volume schemes for Population balance equations (PBEs)

First part of this talk deals with the stability and convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage PBEs. The proof is based on the basic existing theorems and definitions from the book
of Hundsdorfer and Verwer[1] and the paper of Linz[2]. It is shown that the scheme is second order convergent independent of the meshes for linear problem while for non-linear it depends on the meshes taken for computations.
The results are verified numerically by taking two test problems.

Next we introduce the definition of moment preservation. Based upon it we discuss one-moment and two-moments preserving numerical methods to
solve the couple mass and number preserving PBEs. We use finite volume schemes for solving aggregation, breakage and growth terms whereas upwind scheme is used for source terms. Numerical verifications are made for various
coupled processes.

References:
[1] W. Hundsdorfer and J.G. Verwer. Numerical solution of time-dependent
advection-diffusion-reaction equations. Springer-Verlag, New York, USA, 1st
edition 2003.
[2] P. Linz. Convergence of a discretization method for integro-differential
equations. Numer. Math., 25:103-107, 1975.