Free Access
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S251 - S278
Published online 26 February 2021
  1. R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys. 186 (2003) 361–396. [Google Scholar]
  2. R. Akiyoshi, S. Nishio and I. Tanasawa, A study on the effect of non-condensible gas in the vapor film on vapor explosion. Int. J. Heat Mass Trans. 33 (1990) 603–609. [CrossRef] [Google Scholar]
  3. G. Allaire, S. Clerc and S. Kokh, A five-equation model for the numerical simulation of interfaces in two-phase flows. C.R. Acad. Sci. Ser. I – Math. 331 (2000) 1017–1022. [Google Scholar]
  4. M. Bachmann, S. Müller, P. Helluy and H. Mathis, A simple model for cavitation with non-condensable gases. In: Vol. 18 of Hyperbolic Problems: Theory, Numerics and Applications. World Scientific (2012) 289–296. [Google Scholar]
  5. M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. J. Multiphase Flows 12 (1986) 861–889. [CrossRef] [Google Scholar]
  6. T. Barberon and P. Helluy, Finite volume simulation of cavitating flows. Comput. Fluids 34 (2005) 832–858. [Google Scholar]
  7. F. Barre and M. Bernard, The CATHARE code strategy and assessment. Nucl. Eng. Des. 124 (1990) 257–284. [CrossRef] [Google Scholar]
  8. G. Berthoud, Vapor explosions. Ann. Rev. Fluid Mech. 32 (2000) 573–611. [CrossRef] [Google Scholar]
  9. H. Boukili and J.-M. Hérard, Relaxation and simulation of a barotropic three-phase flow model. ESAIM: M2AN 53 (2019) 1031–1059. [CrossRef] [EDP Sciences] [Google Scholar]
  10. H. Boukili and J.-M. Hérard, Simulation and preliminary validation of a three-phase flow model with energy. Working paper or preprint. (2020). [Google Scholar]
  11. M. Chuberre and N. Seguin, Étude asymptotique pour des écoulements compressibles diphasiques. Tech. Rep., Université Rennes 1, IRMAR (2019). [Google Scholar]
  12. F. Coquel, T. Gallouët, J.-M. Hérard and N. Seguin, Closure laws for a two-fluid two-pressure model. C.R. Math. 334 (2002) 927–932. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Coquel, J.-M. Hérard and K. Saleh, A splitting method for the isentropic Baer-Nunziato two-phase flow model. ESAIM: Proc. Surv. 38 (2012) 241–256. [CrossRef] [Google Scholar]
  14. F. Coquel, J.-M. Hérard, K. Saleh and N. Seguin, A class of two-fluid two-phase flow models. In: 42nd AIAA Fluid Dynamics Conference and Exhibit. AIAA, New Orleans, United States (2012). [Google Scholar]
  15. F. Coquel, J.-M. Hérard, K. Saleh and N. Seguin, A robust entropy-satisfying finite volume scheme for the isentropic Baer-Nunziato model. ESAIM: M2AN 48 (2014) 165–206. [CrossRef] [EDP Sciences] [Google Scholar]
  16. F. Coquel, J.-M. Hérard, K. Saleh and N. Seguin, Two properties of two-velocity two-pressure models for two-phase flows. Commun. Math. Sci. 12 (2014). [Google Scholar]
  17. F. Coquel, J.-M. Hérard and K. Saleh, A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model. J. Comput. Phys. 330 (2017) 401–435. [Google Scholar]
  18. P. Downar-Zapolski, Z. Bilicki, L. Bolle and J. Franco, The non-equilibrium relaxation model for one-dimensional flashing liquid flow. Int. J. Multiphase Flow 22 (1996) 473–483. [CrossRef] [Google Scholar]
  19. 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] [EDP Sciences] [Google Scholar]
  20. T. Flåtten and H. Lund, Relaxation two-phase flow models and the subcharacteristic condition. Math. Models Methods Appl. Sci. 21 (2011) 2379–2407. [Google Scholar]
  21. T. Gallouët, J.-M. Hérard and N. Seguin, Numerical modeling of two-phase flows using the two-fluid two-pressure approach. Math. Models Methods Appl. Sci. 14 (2004) 663–700. [Google Scholar]
  22. S. Gavrilyuk, The structure of pressure relaxation terms: the one-velocity case. Tech. Rep., EDF report, H-I83-2014-0276-EN (2014). [Google Scholar]
  23. 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]
  24. S. Gavrilyuk and R. Saurel, Rankine-Hugoniot relations for shocks in heterogeneous mixtures. J. Fluid Mech. 575 (2007) 495–507. [Google Scholar]
  25. S. Gavrilyuk, N. Makarenko and S. Sukhinin, Waves in Continuous Media. Springer (2017). [CrossRef] [Google Scholar]
  26. V. Guillemaud, Modelling and numerical simulation of two-phase flows using the two-fluid two-pressure approach, Ph.D. thesis, (in French), Université de Provence – Aix-Marseille I (2007). [Google Scholar]
  27. 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. [Google Scholar]
  28. M. Hantke and S. Müller, Analysis and simulation of a new multi-component two-phase flow model with phase transitions and chemical reactions. Q. Appl. Math. 76 (2018) 253–287. [Google Scholar]
  29. M. Hantke and S. Müller, Closure conditions for a one temperature non-equilibrium multi-component model of baer-nunziato type. ESAIM: Proc. Surv. 66 (2019) 42–60. [CrossRef] [Google Scholar]
  30. P. Helluy and H. Mathis, Pressure laws and fast Legendre transform. Math. Models Methods Appl. Sci. 21 (2010) 745–775. [Google Scholar]
  31. P. Helluy and N. Seguin, Relaxation models of phase transition flows. ESAIM: M2AN 40 (2006) 331–352. [CrossRef] [EDP Sciences] [Google Scholar]
  32. P. Helluy, O. Hurisse and L. Quibel, Assessment of numerical schemes for complex two-phase flows with real equations of state. Comput. Fluids 196 (2020) 104347. [Google Scholar]
  33. J.-M. Hérard, A three-phase flow model. Math. Comput. Model. 45 (2007) 732–755. [Google Scholar]
  34. J.-M. Hérard, An hyperbolic two-fluid model in a porous medium. C.R. Mec. 336 (2008) 650–655. [CrossRef] [Google Scholar]
  35. J.-M. Hérard, A class of compressible multiphase flow models. C.R. Math. 354 (2016) 954–959. [CrossRef] [Google Scholar]
  36. J.-M. Hérard and O. Hurisse, A fractional step method to compute a class of compressible gas–liquid flows. Comput. Fluids 55 (2012) 57–69. [Google Scholar]
  37. J.-M. Hérard and H. Lochon, A simple turbulent two-fluid model. C.R. Mec. 344 (2016) 776–783. [CrossRef] [Google Scholar]
  38. J.-M. Hérard and H. Mathis, A three-phase flow model with two miscible phases. ESAIM: M2AN 53 (2019) 1373–1389. [CrossRef] [EDP Sciences] [Google Scholar]
  39. M. Hillairet, On Baer-Nunziato multiphase flow models. ESAIM: Proc. Surv. 66 (2019) 61–83. [CrossRef] [Google Scholar]
  40. J. Huang, J. Zhang and L. Wang, Review of vapor condensation heat and mass transfer in the presence of non-condensable gas. Appl. Thermal Eng. 89 (2015) 469–484. [CrossRef] [Google Scholar]
  41. O. Hurisse, Numerical simulations of steady and unsteady two-phase flows using a homogeneous model. Comput. Fluids 152 (2017) 88–103. [Google Scholar]
  42. O. Hurisse and L. Quibel, A homogeneous model for compressible three-phase flows involving heat and mass transfer. ESAIM: Proc. Surv. 66 (2019) 84–108. [CrossRef] [Google Scholar]
  43. D. Iampietro, Contribution to the simulation of low-velocity compressible two-phase flows with high pressure jumps using homogeneous and two-fluid approaches. Theses. Aix-Marseille Université (2018). [Google Scholar]
  44. IRSN, Accidents graves pouvant affecter un réacteur à eau pressurisée. (2011). [Google Scholar]
  45. M. Ishii, Thermo-Fluid Dynamics Theory of Two-Phase Flow. Eyrolles (1975). [Google Scholar]
  46. J. Jung, Numerical simulations of two-fluid flow on multicores accelerator. Ph.D. thesis, Université de Strasbourg (2013). [Google Scholar]
  47. A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son and D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations. Phys. Fluids 13 (2001) 3002–3024. [CrossRef] [Google Scholar]
  48. T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Ration. Mech. Anal. 58 (1975) 181–205. [Google Scholar]
  49. R. Lewandowski and B. Mohammadi, Existence and positivity results for the φθ and a modified kε two-equation turbulence models. Math. Models Methods Appl. Sci. 3 (1993) 195–215. [Google Scholar]
  50. H. Lochon, Modélisation et simulation d’écoulements transitoires eau-vapeur en approche bifluide. Ph.D. thesis. Aix Marseille Université, 2016. [Google Scholar]
  51. H. Mathis, A thermodynamically consistent model of a liquid-vapor fluid with a gas. ESAIM: M2AN 53 (2019) 63–84. [CrossRef] [EDP Sciences] [Google Scholar]
  52. R. Meignen, B. Raverdy, S. Picchi and J. Lamome, The challenge of modeling fuel–coolant interaction: Part II–steam explosion. Nucl. Eng. Des. 280 (2014) 528–541. [CrossRef] [Google Scholar]
  53. S. Müller, M. Hantke and P. Richter, Closure conditions for non-equilibrium multi-component models. Continuum Mech. Thermodyn. 28 (2016) 1157–1189. [CrossRef] [MathSciNet] [Google Scholar]
  54. K. Saleh, A relaxation scheme for a hyperbolic multiphase flow model. Part I: Barotropic EOS. ESAIM: M2AN 53 (2019) 1763–1795. [CrossRef] [EDP Sciences] [Google Scholar]
  55. K. Saleh and N. Seguin, Some mathematical properties of a barotropic multiphase flow model. Working paper or preprint (2018). [Google Scholar]
  56. R. Saurel, S. Gavrilyuk and F. Renaud, A multiphase model with internal degrees of freedom: application to shock–bubble interaction. J. Fluid Mech. 495 (2003) 283–321. [Google Scholar]
  57. D.W. Schwendeman, C.W. Wahle and A.K. Kapila, The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow. J. Comput. Phys. 212 (2006) 490–526. [Google Scholar]
  58. S. Tokareva and E.F. Toro, HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow. J. Comput. Phys. 229 (2010) 3573–3604. [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