by Qamar, Shamsul, Warnecke, Gerald.
Series: 2007-32, Preprints
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.
Population balance models, high r
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