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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Numerical analysis of a Hele-Shaw free boundary problem
by
Abdelhamid Laquar
Department of Mathematics , University of Annaba, Algeria

In this work, we studie the numerical analysis of a Hele-Shaw free boundary problem. It consists in determining, at each time t > 0, the interface separating zone occupied by viscous fluid and the non occupied zone betwen the beginning of the injection and the moment when the fluid reaches one of the lateral walls.
We use the method of lines coupled with S.O.R iterative method in order to transform the multidimensional boundary into a system of unidimensional free boundary problem.The method of invariant imbbeding combined with Reccati transformation has been used to solve this problem. We therefore obtain multi-point equation which we can solved numerically by the trapezium quadrature rule for which solution is a point of the interface.

Date received: February 15, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-64.