Free Access
Volume 46, Number 5, September-October 2012
Page(s) 1029 - 1054
Published online 13 February 2012
  1. G. Allaire, S. Clerc and S. Kokh, A five-equation model for the simulation of interfaces between compressible fluids. J. Comput. Phys. 181 (2002) 577–616. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Allaire, G. Faccanoni and S. Kokh, A strictly hyperbolic equilibrium phase transition model. C. R. Acad. Sci. Paris, Sér. I 344 (2007) 135–140. [CrossRef] [Google Scholar]
  3. K. Annamalai and I.K. Puri, Advanced thermodynamics engineering. CRC Press (2002). [Google Scholar]
  4. Th. Barberon and Ph. Helluy, Finite volume simulations of cavitating flows. Comput. Fluids 34 (2005) 832–858. [CrossRef] [Google Scholar]
  5. J. Benoist and J.-B. Hiriart-Urruty, What is the subdifferential of the closed convex hull of a function? SIAM J. Math. Anal. 27 (1996) 1661–1679. [CrossRef] [MathSciNet] [Google Scholar]
  6. S. Benzoni Gavage, Stability of multi-dimensional phase transitions in a Van der Waals fluid. Nonlinear Anal. 31 (1998) 243–263. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in Mathematics. Birkhäuser Verlag, Basel (2004). [Google Scholar]
  8. J.U. Brackbill, D.B. Kothe and C. Zemach, A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 335–354. [CrossRef] [MathSciNet] [Google Scholar]
  9. H.B. Callen, Thermodynamics and an introduction to thermostatistics. John Wiley & sons, 2nd edition (1985). [Google Scholar]
  10. F. Caro, Modélisation et simulation numérique des transitions de phase liquide-vapeur. Ph.D. thesis, École Polytechnique (2004). [Google Scholar]
  11. F. Caro, F. Coquel, D. Jamet and S. Kokh, A simple finite-volume method for compressible isothermal two-phase flows simulation. International Journal on Finite Volumes (2006). [Google Scholar]
  12. G. Chen, C.D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 47 (1992) 787–830. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Coquel and B. Perthame, Relaxation of energy and approximate Riemann solvers for general pressure laws in fluids dynamics. SIAM J. Numer. Anal. 35 (1998) 2223–2249. [CrossRef] [MathSciNet] [Google Scholar]
  14. J.-M. Delhaye, M. Giot and M.L. Riethmuller, Thermohydraulics of two-phase systems for industrial design and nuclear engineering. Hemisphere Publishing Corporation (1981). [Google Scholar]
  15. J.-M. Delhaye, M. Giot, L. Mahias, P. Raymond and C. Rénault, Thermohydraulique des réacteurs. EDP Sciences (1998). [Google Scholar]
  16. V.K. Dhir, Boiling heat transfer. Ann. Rev. Fluid Mech. 30 (1998) 365–401. [CrossRef] [Google Scholar]
  17. J.E. Dunn and J. Serrin, On the thermomechanics of interstitial working. Arch. Rational Mech. Anal. 88 (1985) 95–133. [MathSciNet] [Google Scholar]
  18. G. Faccanoni, Étude d’un modèle fin de changement de phase liquide-vapeur. Contribution à l’étude de la crise d’ébullition. Ph.D. thesis, École Polytechnique, France (2008). [Google Scholar]
  19. G. Faccanoni, S. Kokh and G. Allaire, Numerical simulation with finite volume of dynamic liquid-vapor phase transition, Finite Volumes for Complex Applications V. ISTE and Wiley (2008) 391–398. [Google Scholar]
  20. G. Faccanoni, G. Allaire and S. Kokh, Modelling and numerical simulation of liquid-vapor phase transition, in Conf. Proc. of EUROTHERM-84, Seminar on Thermodynamics of Phase Changes, Namur (2009). [Google Scholar]
  21. G. Faccanoni, S. Kokh and G. Allaire, Approximation of liquid-vapor phase transition for compressible fluids with tabulated EOS. C. R. Acad. Sci. Paris Sér. I 348 (2010) 473–478. [CrossRef] [Google Scholar]
  22. H. Fan, One phase Riemann problem and wave interactions in systems of conservation laws of mixed type. SIAM J. Math. Anal. 24 (1993) 840–865. [CrossRef] [Google Scholar]
  23. H. Fan, Traveling waves, Riemann problems and computations of a model of the dynamics of liquid/vapor phase transitions. J. Differ. Equ. 150 (1998) 385–437. [CrossRef] [Google Scholar]
  24. H. Fan and M. Slemrod, The Riemann problem for systems of conservation laws of mixed type, in Conf. Proc. on Shock Induced Transitions and Phase Structure in General Media Institute of Mathematics and its Applications. Minneapolis (1990) 61–91. [Google Scholar]
  25. C. Fouillet, Généralisation à des mélanges binaires de la méthode du second gradient et application à la simulation numérique directe de l’ébullition nuclée. Ph.D. thesis, Université Paris 6 (2003). [Google Scholar]
  26. E. Godlewski and N. Seguin, The Riemann problem for a simple model of phase transition. Commun. Math. Sci. 4 (2006) 227–247. [CrossRef] [Google Scholar]
  27. H. Gouin, Utilization of the second gradient theory in continuum mechanics to study the motion and thermodynamics of liquid-vapor interfaces. Physicochemical Hydrodynamics – Interfacial Phenomena B 174 (1987) 667–682. [Google Scholar]
  28. W. Greiner, L. Neise and H. Stöcker, Thermodynamics and statistical mechanics. Springer (1997). [Google Scholar]
  29. Ph. Helluy, Quelques exemples de méthodes numériques récentes pour le calcul des écoulements multiphasiques. Mémoire d’habilitation à diriger des recherches (2005). [Google Scholar]
  30. Ph. Helluy and H. Mathis, Pressure laws and fast Legendre transform. Math. Models Methods Appl. Sci. to appear. [Google Scholar]
  31. Ph. Helluy and N. Seguin, Relaxation models of phase transition flows. ESAIM : M2AN 40 (2006) 331–352. [CrossRef] [EDP Sciences] [Google Scholar]
  32. J.-B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of convex analysis. Grundlehren Text Editions, Springer-Verlag, Berlin (2001). [Google Scholar]
  33. D. Jamet, O. Lebaigue, N. Coutris and J.-M. Delhaye, The second gradient method for the direct numerical simulation of liquid-vapor flows with phase change. J. Comput. Phys. 169 (2001) 624–651. [CrossRef] [MathSciNet] [Google Scholar]
  34. S. Jaouen, Étude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase. Ph.D. thesis, Université Paris 6, France (2001). [Google Scholar]
  35. S. Jin and C.D. Levermore, Numerical schemes for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys. 126 (1996) 449–467. [CrossRef] [Google Scholar]
  36. S. Kokh, Aspects numériques et théoriques de la modélisation des écoulements diphasiques compressibles par des méthodes de capture d’interfaces. Ph.D. thesis, Université Paris 6 (2001). [Google Scholar]
  37. D.J. Korteweg, Sur la forme que prennent les équations des mouvements des fluides si l’on tient compte des forces capillaires par des variations de densité. Arch. Néer. Sci. Exactes Sér. II 6 (1901) 1–24. [Google Scholar]
  38. P.G. LeFloch, Hyperbolic systems of conservation laws. Birkhäuser Verlag, Basel (2002). [Google Scholar]
  39. O. Le Métayer, J. Massoni and R. Saurel, Elaborating equations of state of a liquid and its vapor for two-phase flow models. Int. J. Thermal Sci. 43 (2004) 265–276. [CrossRef] [Google Scholar]
  40. O. Le Métayer, J. Massoni and R. Saurel, Modelling evaporation fronts with reactive Riemann solvers. J. Comput. Phys. 205 (2005) 567–610. [CrossRef] [MathSciNet] [Google Scholar]
  41. E.W. Lemmon, M.O. McLinden and D.G. Friend, Thermophysical properties of fluid systems, in WebBook de Chimie NIST, Base de Données Standard de Référence NIST Numéro 69, National Institute of Standards and Technology, edited by P.J. Linstrom and W.G. Mallard. Gaithersburg MD, 20899, [Google Scholar]
  42. R.J. LeVeque, Finite Volume methods for hyperbolic problems. Cambridge University Press, Cambridge. Appl. Math. (2002). [Google Scholar]
  43. T.P. Liu, Hyperbolic conservation laws with relaxation. Commun. Math. Phys. 108 (1987) 153–175. [CrossRef] [MathSciNet] [Google Scholar]
  44. T. Matolcsi, On the classification of phase transitions. Z. Angew. Math. Phys. 47 (1996) 837–857. [CrossRef] [MathSciNet] [Google Scholar]
  45. R. Menikoff and B. Plohr, The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61 (1989) 75–130. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  46. S. Nukiyama, The maximum and minimum values of the heat Q transmitted from metal to boiling water under atmospheric pressure. Int. J. Heat Mass Transfer 9 (1966) 1419–1433. (English translation of the original paper published in J. Jpn Soc. Mech. Eng. 37 (1934) 367–374). [CrossRef] [Google Scholar]
  47. F. Petitpas, E. Franquet, R. Saurel and O. Le Métayer, A relaxation-projection method for compressible flows. II. Artificial heat exchanges for multiphase shocks. J. Comput. Phys. 225 (2007) 2214–2248. [CrossRef] [Google Scholar]
  48. P. Ruyer, Modèle de champ de phase pour l’étude de l’ébullition. Ph.D. thesis, École Polytechnique (2006). [Google Scholar]
  49. R. Saurel, J.-P. Cocchi and P.-B. Butlers, Numerical study of cavitation in the wake of a hypervelocity underwater projectile. J. Propuls. Power 15 (1999) 513–522. [CrossRef] [Google Scholar]
  50. R. Saurel, F. Petitpas and R. Abgrall, Modelling phase transition in metastable liquids : application to cavitating and flashing flows. J. Fluid Mech. 607 (2008) 313–350. [CrossRef] [MathSciNet] [Google Scholar]
  51. M. Shearer, Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type. Proc. R. Soc. Edinb. 93 (1983) 133–244. [Google Scholar]
  52. M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Rational Mech. Anal. 81 (1983) 301–315. [MathSciNet] [Google Scholar]
  53. L. Truskinovsky, Kinks versus shocks, in Shock induced transitions and phase structures in general media, edited by R. Fosdick et al. Springer Verlag, Berlin (1991). [Google Scholar]
  54. P. Van Carey, Liquid-vapor phase-change phenomena. Taylor and Francis (1992). [Google Scholar]
  55. A. Voß, Exact Riemann solution for the Euler equations with nonconvex and nonsmooth equation of State. Ph.D. thesis, RWTH-Aachen (2004). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you