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2007-32

Analytical and Numerical Investigations of a Batch Crystallization Model

by Qamar, Shamsul, Warnecke, Gerald.


Series: 2007-32, Preprints

MSC:
35L65 Conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35L67 Shocks and singularities

Abstract:
This article is concerned with the analytical and numerical

investigations of a one-dimensional population balance

model for batch crystallization processes. We start with a

one-dimensional batch crystallization model and prove the

local existence and uniqueness of the solution of this model.

For this purpose Laplace transformation is used as a basic tool. A semi-discrete

high resolution finite volume scheme

is proposed for the numerical solution of the current model. The issues of positivity (monotonicity),

consistency, stability and convergence of the proposed scheme for the current model are analyzed and proved.

Finally, we give a numerical test problem. The numerical results of the proposed

high resolution scheme are compared with the solution of the reduced four-moments model

and the first order upwind scheme.

Keywords:
Population balance models, high r

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