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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 935-939 (août 2010)
Doi : 10.1016/j.crma.2010.07.004
Received : 18 May 2010 ;  accepted : 6 July 2010
A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density
Discrétisation en temps d'une méthode de caractéristiques pour un système d'interaction fluide–rigide avec densité discontinue

Jorge San Martín a , Jean-François Scheid b , Loredana Smaranda c
a Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile and Centro de Modelamiento Matemático, UMR 2071 CNRS-UChile, Casilla 170/3-Correo 3, Santiago, Chile 
b Institut Elie-Cartan UMR 7502, Nancy-Université - CNRS - INRIA, B.P. 239, F-54506 Vandoeuvre-lès-Nancy cedex, France 
c Department of Mathematics, Faculty of Mathematics and Computer Science, University of Piteşti, Str. Târgu din Vale nr. 1, 110040 Piteşti, Romania 


We propose a new characteristics method for the time discretization of a fluid–rigid system in the case when the densities of the fluid and the solid are different. This method is based on a global weak formulation involving only terms defined on the whole fluid–rigid domain. The main idea is to construct a characteristic function which preserves the rigidity of the solid at the discrete time levels. A convergence result for this semi-discrete scheme is then given.

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Nous présentons un schéma de semi-discrétisation en temps d'une méthode de caractéristiques pour un problème fluide–rigide dans le cas où les densités du fluide et du solide sont différentes. Cette méthode est basée sur une formulation faible globale faisant intervenir uniquement des termes définis sur tout le domaine fluide–rigide. L'idée principale est de construire une fonction caractéristique qui préserve la rigidité du solide d'une itération en temps à l'autre. Le résultat principal porte sur la convergence du schéma semi-discrétisé en temps.

The full text of this article is available in PDF format.

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