[An hyperbolic two-fluid model in a porous medium]
We introduce an hyperbolic two-fluid two-pressure model to compute unsteady two-phase flows in porous media. The closure laws comply with the entropy inequality, and a unique set of jump conditions holds within each field.
On introduit dans cette Note un modèle d'écoulement bifluide hyperbolique pour simuler les écoulements diphasiques en milieu poreux, en configuration instationnaire. Les lois de fermeture proposées sont consistantes avec l'inégalité d'entropie, et les relations de saut sont uniques champ par champ.
Accepted:
Published online:
Keywords: Computational fluid mechanics, Two-fluid models, Porous media
Jean-Marc Hérard 1
@article{CRMECA_2008__336_8_650_0, author = {Jean-Marc H\'erard}, title = {Un mod\`ele hyperbolique diphasique bi-fluide en milieu poreux}, journal = {Comptes Rendus. M\'ecanique}, pages = {650--655}, publisher = {Elsevier}, volume = {336}, number = {8}, year = {2008}, doi = {10.1016/j.crme.2008.06.005}, language = {fr}, }
Jean-Marc Hérard. Un modèle hyperbolique diphasique bi-fluide en milieu poreux. Comptes Rendus. Mécanique, Volume 336 (2008) no. 8, pp. 650-655. doi : 10.1016/j.crme.2008.06.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.06.005/
[1] Closure laws for a two-fluid two-pressure model, C. R. Acad. Sci. Paris, Ser. I, Volume 332 (2002), pp. 927-932
[2] Numerical modelling of two phase flows using the two-fluid two-pressure approach, Math. Models Methods Appl. Sci., Volume 14 (2004) no. 5, pp. 663-700
[3] A multiphase model with internal degrees of freedom: application to shock-bubble interaction, J. Fluid Mech., Volume 495 (2005), pp. 283-322
[4] A two-phase mixture theory for the deflagration to detonation transition (DDT) in reactive granular materials, Int. J. Multiphase Flow, Volume 12 (1986) no. 6, pp. 861-889
[5] Two-phase modeling of a DDT: structure of the velocity relaxation zone, Phys. Fluids, Volume 9 (1997) no. 12, pp. 3885-3897
[6] Two-phase flow modelling of a fluid mixing layer, J. Fluid Mech., Volume 378 (1999), pp. 119-143
[7] Mathematical and numerical modelling of two-phase compressible flows with micro-inertia, J. Comp. Phys., Volume 175 (2002), pp. 326-360
[8] A mean field description of two-phase flows with phase changes, Int. J. Multiphase Flow, Volume 29 (2003), pp. 511-525
[9] Fermetures entropiques pour les systèmes bifluides à sept équations, C. R. Mecanique, Volume 333 (2005), pp. 838-842
[10] Computing hyperbolic two-fluid models with a porous interface, Aussois, France, June 8–13, ISTE-Wiley (2008), pp. 193-200
[11] A three-phase flow model, Math. Comput. Modelling, Volume 45 (2007), pp. 732-755
[12] A simple method to compute two-fluid models, Int. J. Comp. Fluid Dynam., Volume 19 (2005) no. 7, pp. 475-482
[13] J.M. Hérard, A relaxation scheme to compute three-phase flow models, AIAA paper 2007-4455, http://www.aiaa.org/, 2007
[14] V. Guillemaud, Modélisation et simulation numérique des écoulements diphasiques par une approche bifluide à deux pressions, Thèse de Doctorat, Université Aix-Marseille I, Marseille, France, 27/03/2007
[15] Comparison of Roe-type methods for solving the two-fluid model with and without pressure relaxation, Computers and Fluids, Volume 36 (2007), pp. 1061-1080
[16] Evolution of the volumetric interfacial area in two-phase mixtures, C. R. Mecanique, Volume 332 (2004), pp. 103-108
Cited by Sources:
Comments - Policy