07-32
Analytical and Numerical Investigations of a Batch Crystallization Model
by Qamar, Shamsul; Warnecke, Gerald
Preprint series: 07-32, Preprints
The paper is published: submitted to a Journal
- MSC:
- 35L65 Conservation laws
- 35L45 Initial value problems for hyperbolic systems of first-order PDE
- 35L67 Shocks and singularities, See also {58C27, 76L05}
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 resolution finite volume schemes, crystallization processes, hyperbolic conservation laws, existence, uniqueness, convergence
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