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

Laurent Boudin; Benjamin Boutin; Bruno Fornet; Thierry Goudon; Pauline Lafitte; Frédéric Lagoutière; Benoît Merlet

doi:10.1051/proc/2009047

Laurent Boudin ^1,² ; Benjamin Boutin ^1,³ ; Bruno Fornet ⁴ ; Thierry Goudon ^5,⁶ ; Pauline Lafitte ^5,⁶ ; Frédéric Lagoutière ^5,⁷ ; Benoît Merlet ⁸

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

ESAIM. Proceedings, Tome 28 (2009), pp. 195-210

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Résumé

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.

DOI : 10.1051/proc/2009047

Affiliations des auteurs :

Laurent Boudin ^{1
,

2} ; Benjamin Boutin ^{1
,

3} ; Bruno Fornet ⁴ ; Thierry Goudon ^{5
,

6} ; Pauline Lafitte ^{5
,

6} ; Frédéric Lagoutière ^{5
,

7} ; Benoît Merlet ⁸

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;

@article{EP_2009_28_a12,
     author = {Laurent Boudin and Benjamin Boutin and Bruno Fornet and Thierry Goudon and Pauline Lafitte and Fr\'ed\'eric Lagouti\`ere and Beno{\^\i}t Merlet},
     title = {Fluid-Particles {Flows:} {A} {Thin} {Spray} {Model} with {Energy} {Exchanges}},
     journal = {ESAIM. Proceedings},
     pages = {195--210},
     year = {2009},
     volume = {28},
     doi = {10.1051/proc/2009047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009047/}
}

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AU  - Benjamin Boutin
AU  - Bruno Fornet
AU  - Thierry Goudon
AU  - Pauline Lafitte
AU  - Frédéric Lagoutière
AU  - Benoît Merlet
TI  - Fluid-Particles Flows: A Thin Spray Model with Energy Exchanges
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VL  - 28
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%A Benjamin Boutin
%A Bruno Fornet
%A Thierry Goudon
%A Pauline Lafitte
%A Frédéric Lagoutière
%A Benoît Merlet
%T Fluid-Particles Flows: A Thin Spray Model with Energy Exchanges
%J ESAIM. Proceedings
%D 2009
%P 195-210
%V 28
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/2009047/
%R 10.1051/proc/2009047
%G en
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Laurent Boudin; Benjamin Boutin; Bruno Fornet; Thierry Goudon; Pauline Lafitte; Frédéric Lagoutière; Benoît Merlet. Fluid-Particles Flows: A Thin Spray Model with Energy Exchanges. ESAIM. Proceedings, Tome 28 (2009), pp. 195-210. doi: 10.1051/proc/2009047

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