×

A strictly hyperbolic equilibrium phase transition model. (English) Zbl 1109.35066

Summary: This note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a fluid. The proof is valid for a very wide class of fluids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a definite negative Hessian matrix for each phase entropy as a function of the specific volume and internal energy.

MSC:

35L40 First-order hyperbolic systems
76N15 Gas dynamics (general theory)
76T10 Liquid-gas two-phase flows, bubbly flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. Barberon, Modélisation mathématique et numérique de la cavitation dans des écoulements multiphasiques compressibles, Ph.D. Thesis, Université de Toulon et du Var, 2002; T. Barberon, Modélisation mathématique et numérique de la cavitation dans des écoulements multiphasiques compressibles, Ph.D. Thesis, Université de Toulon et du Var, 2002
[2] Barberon, T.; Helluy, Ph., Finite volume simulations of cavitating flows, Computers and Fluids, 34, 7, 832-858 (2005) · Zbl 1134.76392
[3] Benoist, J.; Hiriart-Urruty, J.-B., What is the subdifferential of the closed convex hull of a function?, SIAM J. Math. Anal., 27, 6, 1661-1679 (1996) · Zbl 0876.49018
[4] Callen, H. B., Thermodynamics and an Introduction to Thermostatistics (1985), John Wiley & Sons · Zbl 0989.80500
[5] F. Caro, Modélisation et simulation numérique des transitions de phase liquide-vapeur, Ph.D. Thesis, École Polytechnique, 2004; F. Caro, Modélisation et simulation numérique des transitions de phase liquide-vapeur, Ph.D. Thesis, École Polytechnique, 2004
[6] F. Caro, F. Coquel, D. Jamet, S. Kokh, DINMOD, in: S. Cordier, T. Goudon, M. Gutnic, E. Sonnerdrücker (Eds.), Numerical Method for Hyperbolic and Kinetic Problems, Proceedings of the CEMRACS 2003, IRMA Series in Mathematics and Theoretical Physics, 2005; F. Caro, F. Coquel, D. Jamet, S. Kokh, DINMOD, in: S. Cordier, T. Goudon, M. Gutnic, E. Sonnerdrücker (Eds.), Numerical Method for Hyperbolic and Kinetic Problems, Proceedings of the CEMRACS 2003, IRMA Series in Mathematics and Theoretical Physics, 2005
[7] F. Caro, F. Coquel, D. Jamet, S. Kokh, Phase change simulation for isothermal compressible two-phase flows, in: AIAA Computational Fluid Dynamics, 2005, number AIAA-2005-4697; F. Caro, F. Coquel, D. Jamet, S. Kokh, Phase change simulation for isothermal compressible two-phase flows, in: AIAA Computational Fluid Dynamics, 2005, number AIAA-2005-4697 · Zbl 1210.76147
[8] Caro, F.; Coquel, F.; Jamet, D.; Kokh, S., A simple finite-volume method for compressible isothermal two-phase flows simulation, Int. J. Finite Volumes (2006) · Zbl 1490.76145
[9] G. Faccanoni, Modélisation fine d’Écoulements diphasiques : contribution à l’Étude de la crise d’Ébullution, Ph.D. Thesis, École Polytechnique, in preparation; G. Faccanoni, Modélisation fine d’Écoulements diphasiques : contribution à l’Étude de la crise d’Ébullution, Ph.D. Thesis, École Polytechnique, in preparation
[10] Ph. Helluy. Simulation numérique des écoulements multiphasiques : de la théorie aux applications, Thèse d’HDR, 2005; Ph. Helluy. Simulation numérique des écoulements multiphasiques : de la théorie aux applications, Thèse d’HDR, 2005
[11] Helluy, Ph.; Seguin, N., Relaxation models of phase transition flows, M2AN Math. Model. Numer. Anal., 40, 2, 331-352 (2006) · Zbl 1108.76078
[12] S. Jaouen, Étude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase, Ph.D. Thesis, Université Paris 6, 2001; S. Jaouen, Étude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase, Ph.D. Thesis, Université Paris 6, 2001
[13] LeVeque, R. J., Finite Volume Methods for Hyperbolic Problems, Applied Mathematics (2002), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1010.65040
[14] Le Métayer, O.; Massoni, J.; Saurel, R., Modelling evaporation fronts with reactive Riemann solvers, J. Comput. Phys., 205, 567-610 (2005) · Zbl 1088.76051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.