Fluid-Particles Flows: A Thin Spray Model with Energy Exchanges

Free access article

Issue		ESAIM: Proc. Volume 28, 2009 CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids


Page(s)		195 - 210
DOI		http://dx.doi.org/10.1051/proc/2009047
Published online		23 November 2009

ESAIM: Proc., 2009, Vol. 28, pp. 195-210
DOI: 10.1051/proc/2009047

Fluid-Particles Flows: A Thin Spray Model with Energy Exchanges

Laurent Boudin^{1, 2}, Benjamin Boutin^{1, 3}, Bruno Fornet⁴, Thierry Goudon^{5, 6}, Pauline Lafitte^{5, 6}, Frédéric Lagoutière^{5, 7} and Benoît Merlet⁸

¹ UPMC Paris 06, Lab. J.-L. Lions, 175 rue du Chevaleret, BC 187, F-75013 Paris, France;
² INRIA Paris-Rocquencourt, REO Project team, BP 105, F-78153 Le Chesnay Cedex, France. &
³ CEA, DEN/DANS/DM2S/SFME/LETR, F-91191 Gif-sur-Yvette, France.
⁴ DTIM/ONERA Centre de Toulouse, 2 avenue Edouard Belin, 31055 Toulouse, France.
⁵ Project-Team SIMPAF, INRIA Lille Nord Europe Research Centre Park Plazza, 40 avenue Halley 59650 Villeneuve d'Ascq CEDEX, France;
⁶ Laboratoire Paul Painlevé, USTL-CNRS UMR 8524, Cité Scientifique, 59655 Villeneuve d'Ascq CEDEX, France. & &
⁷ Université Paris Diderot-Paris 7, Lab. J.-L. Lions, 175 rue du Chevaleret, BC 187, F-75013 Paris, France.
⁸ Université Paris Nord - Institut Galilée LAGA (Laboratoire d'Analyse, Géométrie et Applications) Avenue J.B. Clément 93430 Villetaneuse, France;

laurent.boudin@upmc.fr
boutin@ann.jussieu.fr
bruno.fornet@onera.fr
thierry.goudon@inria.fr
pauline.lafitte-godillon@math.univ-lille1.fr
lagoutie@math.jussieu.fr
merlet@math.univ-paris13.fr

Published online: 23 November 2009

Abstract
This paper is devoted to an asymptotic analysis of a fluid-particles coupled model, in the bubbling regime. On the theoretical point of view, we extend the analysis done in [4] for the case of an isentropic gas to the case of an ideal gas, thus adding the internal energy, or temperature, which is unknown. We formally derive the bubbling limit system in the same way as in [4] and propose a numerical scheme to solve this limit system.  The numerical resolution of the non-limit system, and the numerical analysis of the asymptotic properties of the scheme (e.g. the asymptotic preserving property), as performed in [4], is at study.

Résumé
Nous proposons ici une analyse asymptotique formelle d'un modèle de couplage entre une densité de particules et un fluide, dans la limite dite bubbling. Cette analyse est effectuée en suivant les pas de [4] où le fluide considéré est isentropique tandis qu'il est ici un gaz parfait (où donc l'énergie interne, ou la température, est une inconnue supplémentaire). Nous identifions le système limite et proposons un algorithme pour le résoudre de manière approchée.  La suite de ce travail, en cours, concerne l'écriture d'un algorithme de résolution du système non limite, et l'étude des propriétés asymptotiques dudit schéma.

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