Abstract
In this paper, we present a mathematical modeling of some magnetohydrodynamic effects arising in an aluminum production cell as well as its numerical approximation by a finite element method. We put the emphasis on the magnetic effects which live in the whole three dimensional space and which are solved numerically with a domain decomposition method.
Similar content being viewed by others
References
Moreau, R., Ziegler, D.: Stability of aluminum cells, a new approach, Light Metals, 359–364 (1986)
Descloux, J., Flueck, M., Romerio, M.V.: Spectral aspects of an industrial problem. In: Spectral Analysis of Complex Structures, pp. 17–33. Hermann éditeurs des sciences et des arts, Paris (1995)
Descloux, J., Flueck, M., Romerio, M.V.: A modelling of the stability of aluminum electrolysis cells. In: Cioranescu, D., Lions, J.L. (eds.) Nonlinear partial differential equations and their applications. Collège de France Seminars, Vol. XIII Pitman Research Notes in Mathematics Series, vol. 391, pp. 117–133. Addison Wesley, Longman (1998)
Gerbeau, J.-F., Le Bris, C., Lelièvre, T.: Mathematical Methods for the Magnetohydrodynamics of Liquid Metals. Numerical Mathematics and Scientific Cumputation Series. Oxford Science Publications, Oxford (2006)
Gerbeau, J.-F., Le Bris, C., Lelièvre, T.: Metal pad roll instabilities, proceeding of the 2002 TMS Annual Meeting and Exhibition. Light Metals 483–487 (2002)
Lions, P.L.: Mathematical Topics in Fluid Mechanics, vol. 1. Oxford University Press, Oxford (1996)
Glowinski, R.: Finite element methods for incompressible viscous flow. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. IX, pp. 498–541. North-Holland, Elsevier (2003)
Dean, E.J., Glowinski, R., Kuo, Y.M., Nasser, G.: On the Discretization of Some Second Order. In: Balakrisknan, A.V. (ed.) Time Differential Equations Applications to Nonlinear Wave Problems. Computational Techniques in Identification and Control of Flexible Flight Structures, pp. 199–246. Optimization Software, Inc., Los Angeles (1990)
Picasso, M., Rappaz, J.: Stability of time-splitting schemes for the Stokes problem with stabilized finite elements. Numer. Methods Partial Differ. Equ. 17(6), 632–656 (2001)
Flueck, M., Rappaz, J., Steiner, G.: On a domain decomposition method for numerically solving a magnetic induction problem. Scientific report in Analysis and Numerical Analysis, EPFL
Davidson, P.A., Lindsay, R.I.: Stability of interfacial waves in aluminium reduction cells. J. Fluid Mech. 362, 273–295 (1998)
Flueck, M., Hofer, T., Janka, A., Rappaz, J.: Numerical methods for ferromagnetic plates. Scientific report in Analysis and Numerical Analysis, EPFL
Munger, D.: Simulation numérique des instabilités magnétohydro-dynamiques dans les cuves de production de l’aluminium. Master’s thesis, Université de Montréal (2004)
Sele, T.: Instabilities of the metal surface in electrolytic cells. 1, pp. 7–24 (1977)
Brezina, M., Mandel, J., Vanek, P.: Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88(3), 559–579 (2001)
George, P.-L., Hecht, F., Saltel, E., Borouchaki, H.: GHS3D web site: http://ralyx.inria.fr/2006/Raweb/gamma/uid31.html. Projet Gamma, INRIA
George, P.-L., Hecht, F., Saltel, E.: Fully automatic mesh generator for 3d domains of any shape. Impact Comp. Sci. Eng. 2, 187–218 (1990)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by Alcan Company, Laboratoire de Recherche et Fabrication, Saint Jean de Maurienne, France.
Rights and permissions
About this article
Cite this article
Flueck, M., Janka, A., Laurent, C. et al. Some Mathematical and Numerical Aspects in Aluminum Production. J Sci Comput 43, 313–325 (2010). https://doi.org/10.1007/s10915-008-9227-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10915-008-9227-3