no. 9
Mathematical problems in mechanics
A class of compressible multiphase flow models
[Une classe de modèles multiphasiques compressibles]

Présenté par : Philippe G. Ciarlet

Hérard, Jean-Marc1, 2
1 EDF R&D, 6, quai Watier, 78400 Chatou, France
2 I2M, Aix Marseille Université, 39, rue Joliot-Curie, 13453 Marseille, France
Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 954-959.

On présente dans cette note une classe de modèles multiphasiques barotropes, à structure hyperbolique, et dotés d'une caractérisation entropique. Des lois de fermeture consistantes sont proposées et discutées.

This article presents a class of barotropic multiphase models, with a hyperbolic structure, and endowed with an entropic characterization. Consistent closure laws are proposed and discussed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.07.004
Hérard, Jean-Marc 1, 2

1 EDF R&D, 6, quai Watier, 78400 Chatou, France
2 I2M, Aix Marseille Université, 39, rue Joliot-Curie, 13453 Marseille, France 
@article{CRMATH_2016__354_9_954_0,
     author = {H\'erard, Jean-Marc},
     title = {A class of compressible multiphase flow models},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {954--959},
     publisher = {Elsevier},
     volume = {354},
     number = {9},
     year = {2016},
     doi = {10.1016/j.crma.2016.07.004},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2016.07.004/}
}
TY  - JOUR
AU  - Hérard, Jean-Marc
TI  - A class of compressible multiphase flow models
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 954
EP  - 959
VL  - 354
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2016.07.004/
DO  - 10.1016/j.crma.2016.07.004
LA  - en
ID  - CRMATH_2016__354_9_954_0
ER  - 
%0 Journal Article
%A Hérard, Jean-Marc
%T A class of compressible multiphase flow models
%J Comptes Rendus. Mathématique
%D 2016
%P 954-959
%V 354
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2016.07.004/
%R 10.1016/j.crma.2016.07.004
%G en
%F CRMATH_2016__354_9_954_0
Hérard, Jean-Marc. A class of compressible multiphase flow models. Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 954-959. doi : 10.1016/j.crma.2016.07.004. http://www.numdam.org/articles/10.1016/j.crma.2016.07.004/

[1] Baer, M.R.; Nunziato, J.W. A two phase mixture theory for the deflagration to detonation transition (DDT) in reactive granular materials, Int. J. Multiph. Flow, Volume 12 (1986) no. 6, pp. 861-889

[2] Bo, W.; Jin, H.; Kim, D.; Liu, X.; Lee, H.; Pestiau, N.; Yu, Y.; Glimm, J.; Grove, J.W. Comparison and validation of multiphase closure models, Comput. Math. Appl., Volume 56 (2008), pp. 1291-1302

[3] Chen, Z.; Ewing, R. Comparison of various formulations of three-phase flow in porous media, J. Comput. Phys., Volume 132 (1997), pp. 362-373

[4] Coquel, F.; Cordier, S. CEMRACS en calcul scientifique 1999, Matapli, Volume 62 (2000), pp. 27-58

[5] Coquel, F.; Gallouët, T.; Hérard, J.M.; Seguin, N. Closure laws for a two fluid two-pressure model, C. R. Acad. Sci. Paris, Ser. I, Volume 332 (2002), pp. 927-932

[6] Coquel, F.; Hérard, J.M.; Saleh, K.; Seguin, N. A class of two-fluid two-phase flow models, 2012 http://www.aiaa.org (AIAA paper 2012-3356, 42nd AIAA CFD conference, New Orleans, LA, USA. Available on)

[7] Frid, H.; Shelukhin, V. A quasi-linear parabolic system for three-phase capillary flow in porous media, SIAM J. Math. Anal., Volume 35 (2003) no. 4, pp. 1029-1041

[8] Gavrilyuk, S. The structure of pressure relaxation terms: the one-velocity case, 2014 (EDF report H-I83-2014-0276-EN)

[9] Gavrilyuk, S.; Gouin, H.; Perepechko, Y.V. A variational principle for two fluid models, C. R. Acad. Sci. Paris, Ser. IIb, Volume 324 (1997), pp. 483-490

[10] Gavrilyuk, S.; Saurel, R. Mathematical and numerical modelling of two-phase compressible flows with micro-inertia, J. Comput. Phys., Volume 175 (2002), pp. 326-360

[11] Giambo, S.; La Rosa, V. A hyperbolic three-phase relativistic flow model, ROMAI J., Volume 11 (2015), pp. 89-104

[12] Hérard, J.M. A three-phase flow model, Math. Comput. Model., Volume 45 (2007), pp. 732-755

[13] Hérard, J.M. Modelling multiphase multi-component flows: following the QUEST, 2016 (EDF report H-I8D-2016-0123-EN, in press)

[14] Kapila, A.K.; Son, S.F.; Bdzil, J.B.; Menikoff, R.; Stewart, D.S. Two phase modeling of a DDT: structure of the velocity relaxation zone, Phys. Fluids, Volume 9–12 (1997), pp. 3885-3897

[15] Müller, S.; Hantke, M.; Richter, P. Closure conditions for non-equilibrium multi-component models, Contin. Mech. Thermodyn. (2015), pp. 1-33 (Available online)

[16] Romenski, E.; Belozerov, A.A.; Peshkov, I.M. Conservative formulation for compressible multiphase flows, 2014 (pp. 1–21) | arXiv

Cité par Sources :