Open Access
Issue
ESAIM: M2AN
Volume 53, Number 1, January–February 2019
Page(s) 63 - 84
DOI https://doi.org/10.1051/m2an/2018044
Published online 02 April 2019
  1. G. Allaire, G. Faccanoni and S. Kokh, A strictly hyperbolic equilibrium phase transition model. C. R. Math. Acad. Sci. Paris 344 (2007) 135–140. [CrossRef] [Google Scholar]
  2. M. Bachmann, S. Müller, P. Helluy and H. Mathis, A simple model for cavitation with non-condensable gases. Hyperbolic problems: theory, numerics and applications. I. In Vol. 17 of Computational Methods in Applied Mathematics (CMAM). World Sci. Publishing, Singapore (2012) 289–296. [Google Scholar]
  3. M.R. Baer and J.W. Nunziato, A two phase mixture theory for the deflagration to detonation (ddt) transition in reactive granular materials. Int. J. Multiphase Flow 12 (1986) 861–889. [CrossRef] [Google Scholar]
  4. T. Barberon and P. Helluy, Finite volume simulation of cavitating flows. Comput. Fluids 34 (2005) 832–858. [CrossRef] [Google Scholar]
  5. J. Bartak, A study of the rapid depressurization of hot water and the dynamics of vapour bubble generation in superheated water. Int. J. Multiph. Flow 16 (1990) 789–98. [CrossRef] [Google Scholar]
  6. H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edition. Wiley and Sons (1985). [Google Scholar]
  7. F. Caro, Modélisation et simulation numérique des transitions de phase liquide-vapeur. Ph.D. thesis, École polytechnique (2004). [Google Scholar]
  8. F. Coquel and B. Perthame, Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics. SIAM J. Numer. Anal. 35 (1998) 2223–2249. [CrossRef] [MathSciNet] [Google Scholar]
  9. J.-P. Croisille, Contribution à l’étude théorique et à l’approximation par éléments finis du système hyperbolique de la dynamique des gaz multidimensionnelle et multiespèces. Ph.D. thesis, Université Paris VI (1991). [Google Scholar]
  10. S. Dellacherie, Relaxation schemes for the multicomponent Euler system. ESAIM: M2AN 37 (2003) 909–936. [CrossRef] [Google Scholar]
  11. S. Dellacherie and N. Rency, Relations de fermeture pour le système des équations d’euler multi-espèces. construction et étude de schémas de relaxation en multi-espèces et en multi-constituants. Technical report, Rapport CEA externe CEA-R-5999 (2001). [Google Scholar]
  12. W. Dreyer, F. Duderstadt, M. Hantke and G. Warnecke, Bubbles in liquids with phase transition. Part 1: On phase change of a single vapor bubble in liquid water. Contin. Mech. Thermodyn. 24 (2012) 461–483. [CrossRef] [Google Scholar]
  13. W. Dreyer, M. Hantke and G. Warnecke, Bubbles in liquids with phase transition. Part 2: on balance laws for mixture theories of disperse vapor bubbles in liquid with phase change. Contin. Mech. Thermodyn. 26 (2014) 521–549. [CrossRef] [Google Scholar]
  14. L.C. Evans, A survey of entropy methods for partial differential equations. Bull. Amer. Math. Soc. (N.S.) 41 (2004) 409–438. [CrossRef] [Google Scholar]
  15. G. Faccanoni, S. Kokh and G. Allaire, Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. ESAIM: M2AN 46 (2012) 1029–1054. [CrossRef] [Google Scholar]
  16. T. Flåtten and H. Lund, Relaxation two-phase flow models and the subcharacteristic condition. Math. Models Methods Appl. Sci. 21 (2011) 2379–2407. [CrossRef] [MathSciNet] [Google Scholar]
  17. S. Gavrilyuk and R. Saurel, Mathematical and numerical modeling of two-phase compressible flows with micro-inertia. J. Comput. Phys. 175 (2002) 326–360. [Google Scholar]
  18. J.W. Gibbs, The Collected Works of J. Willar Gibbs, vol. I: Thermodynamics. Yale University Press (1948). [Google Scholar]
  19. E. Godlewski and P.-A. Raviart, Hyperbolic systems of conservation laws, Mathématiques & Applications (Paris) [Mathematics and Applications]. Ellipses, Paris (1991). [Google Scholar]
  20. E. Han, M. Hantke and S. Müller, Efficient and robust relaxation procedures for multi-component mixtures including phase transition. J. Comput. Phys. 338 (2017) 217–239. [CrossRef] [Google Scholar]
  21. P. Helluy, O. Hurisse and E. Le Coupanec, Verification of a two-phase flow code based on an homogeneous model. Int. J. Finite. In: EDF Special Workshop (2015). Preprint https://hal.archives-ouvertes.fr/hal-01396200 [Google Scholar]
  22. P. Helluy and J. Jung, Interpolated pressure laws in two-fluid simulations and hyperbolicity. In Finite Volumes for Complex Applications. VII. Methods and Theoretical Aspects. Vol. 77 of Springer Proceedings in Mathematics & Statistics. Springer, Cham (2014) 37–53. [CrossRef] [Google Scholar]
  23. P. Helluy and H. Mathis, Pressure laws and fast Legendre transform, Math. Models Methods Appl. Sci. 21 (2011) 745–775. [CrossRef] [MathSciNet] [Google Scholar]
  24. P. Helluy and N. Seguin, Relaxation models of phase transition flows. ESAIM: M2AN 40 (2006) 331–352. [CrossRef] [Google Scholar]
  25. J.-M. Hérard, A three-phase flow model. Math. Comput. Modelling 45 (2007) 732–755. [CrossRef] [Google Scholar]
  26. J.-M. Hérard, A class of compressible multiphase flow models. C. R. Math. Acad. Sci. Paris 354 (2016) 954–959. [CrossRef] [Google Scholar]
  27. J.-B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of Convex Analysis. Abridged version of it Convex analysis and minimization algorithms. I [Springer, Berlin, 1993; MR1261420 (95m:90001)] and it II [ibid.; MR1295240 (95m:90002)]. Grundlehren Text Editions. Springer-Verlag, Berlin (2001). [Google Scholar]
  28. O. Hurisse, Application of an homogeneous model to simulate the heating of two-phase flows. Int. J. Finite 11 (2014) 37. [Google Scholar]
  29. O. Hurisse, Numerical simulations of steady and unsteady two-phase flows using a homogeneous model. Comput. Fluids 152 (2017) 88–103. [CrossRef] [Google Scholar]
  30. O. Hurisse and L. Quibel, A homogeneous model for compressible three-phase flows involving heat and mass transfer (2018). [Google Scholar]
  31. S. Jaouen, Étude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase. Ph.D. thesis, Pierre et Marie Curie, University, Paris VI, France (2001). [Google Scholar]
  32. J. Jung, Schémas numériques adaptés aux accélérateurs mutlicoeurs pour les écoulements bifluides. Ph.D. thesis, Université de Strasbourg (2013). [Google Scholar]
  33. A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son and D.S. Stewart, Two-phase modelling of ddt in granular materials: reduced equations. Phys. Fluids 13 (2001) 3002–3024. [CrossRef] [Google Scholar]
  34. F. Lagoutière, Modélisation mathématique et résolution numérique de problèmes de fluides compressibles à plusieurs constituants. Ph.D. thesis, Pierre et Marie Curie University, Paris VI, France (2000). [Google Scholar]
  35. H. Lochon, Modelling and simulation of steam-water transients using the two-fluid approach, Theses, Aix Marseille Université (October, 2016). [Google Scholar]
  36. H. Mathis, Étude théorique et numérique des écoulements avec transition de phase. Institut de Recherche Mathématique Avancée. Université de Strasbourg, Strasbourg, 2010, Thèse, Université Louis Pasteur, Strasbourg (2010). [Google Scholar]
  37. R. Menikoff and B.J. Plohr, The Riemann problem for fluid flow of real materials. Rev. Modern Phys. 61 (1989) 75–130. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  38. I. Müller and W.H. Müller, Fundamentals of Thermodynamics and Applications. Springer-Verlag, Berlin (2009). [Google Scholar]
  39. S. Müller, M. Hantke and P. Richter, Closure conditions for non-equilibrium multi-component models. Contin. Mech. Thermodyn. 28 (2016) 1157–1189. [CrossRef] [MathSciNet] [Google Scholar]
  40. S. Müller and A. Voß, The Riemann problem for the Euler equations with nonconvex and nonsmooth equation of state: construction of wave curves. SIAM J. Sci. Comput. 28 (2006) 651–681. [CrossRef] [Google Scholar]
  41. T. Flåtten, M. Pelanti and K.-M. Shyue, A numerical model for three-phase liquid-vapor-gas flows with relaxation processes, in Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016, edited by C. Klingenberg, and M. Westdickenberg. In: Vol. 237 of Springer Proceedings in Mathematics & Statistics. Springer, Cham (2018). [Google Scholar]
  42. R.T. Rockafellar, Convex analysis. In: Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ (1997). Reprint of the 1970 original, Princeton Paperbacks. [Google Scholar]
  43. H. Söhnholz, Thermal effects in laser-generated cavitation. Ph.D. thesis, University of Göttingen, Gernamy (2016).. [Google Scholar]
  44. A. Voß, Exact Riemann solution for the Euler equations with non-convex and non-smooth equation of state. Ph.D. thesis, RWTH Aachen (2005). [Google Scholar]
  45. M. Xie, Thermodynamic and gasdynamic aspects of a boiling liquid expanding vapour explosion. Ph.D. thesis, TU Delft, Delft University of Technology (2013). [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