Free Access
Volume 48, Number 6, November-December 2014
Page(s) 1639 - 1679
Published online 24 September 2014
  1. TRACE V5.0 Theory Manual, Field Equations, Solution Methods and Physical Models. Technical report, U.S. Nuclear Regulatory Commission (2008). [Google Scholar]
  2. A. Acrivos, Method of characteristics technique. Application to heat and mass transfer problems. Ind. Eng. Chem. 48 (1956) 703–710. [CrossRef] [Google Scholar]
  3. G. Allaire, G. Faccanoni and S. Kokh, A strictly hyperbolic equilibrium phase transition model. C. R. Acad. Sci. Paris Ser. I 344 (2007) 135–140. [Google Scholar]
  4. A.S. Almgren, J.B. Bell, C.A. Rendleman and M. Zingale, Low Mach number modeling of type Ia supernovae. I. hydrodynamics. Astrophys. J. 637 (2006) 922. [NASA ADS] [CrossRef] [Google Scholar]
  5. A.S. Almgren, J.B. Bell, C.A. Rendleman and M. Zingale, Low Mach number modeling of type Ia supernovae. II. energy evolution. Astrophys. J. 649 (2006) 927. [NASA ADS] [CrossRef] [Google Scholar]
  6. M. Bernard, S. Dellacherie, G. Faccanoni, B. Grec, O. Lafitte, T.-T. Nguyen and Y. Penel. Study of low Mach nuclear core model for single-phase flow. ESAIM Proc. 38 (2012) 118–134. [CrossRef] [EDP Sciences] [Google Scholar]
  7. D. Bestion. The physical closure laws in the CATHARE code. Nucl. Eng. Des. 124 (1990) 229–245. [CrossRef] [Google Scholar]
  8. H. B. Callen, Thermodynamics and an Introduction to Thermostatistics. 2nd edition. John Wiley and sons (1985). [Google Scholar]
  9. V. Casulli and D. Greenspan, Pressure method for the numerical solution of transient, compressible fluid flows. Int. J. Numer. Methods Fluids 4 (1984) 1001–1012. [CrossRef] [Google Scholar]
  10. S. Clerc, Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows. J. Comput. Phys. 181 (2002) 577–616. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Colella and K. Pao, A projection method for low speed flows. J. Comput. Phys. 149 (1999) 245–269. [CrossRef] [Google Scholar]
  12. J.M. Delhaye, Thermohydraulique des réacteurs. EDP sciences (2008). [Google Scholar]
  13. S. Dellacherie, On a diphasic low Mach number system. ESAIM: M2AN 39 (2005) 487–514. [CrossRef] [EDP Sciences] [Google Scholar]
  14. S. Dellacherie, Numerical resolution of a potential diphasic low Mach number system. J. Comput. Phys. 223 (2007) 151–187. [CrossRef] [Google Scholar]
  15. S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number. J. Comput. Phys. 229 (2010) 978–1016. [Google Scholar]
  16. S. Dellacherie, On a low Mach nuclear core model. ESAIM Proc. 35 (2012) 79–106. [CrossRef] [EDP Sciences] [Google Scholar]
  17. S. Dellacherie, G. Faccanoni, B. Grec, F. Lagoutière, E. Nayir and Y. Penel, 2D numerical simulation of a low Mach nuclear core model with stiffened gas using Freefem++. ESAIM. Proc. (accepted). [Google Scholar]
  18. S. Dellacherie, G. Faccanoni, B. Grec and Y. Penel, Study of low Mach nuclear core model for two-phase flows with phase transition II: tabulated EOS. In preparation. [Google Scholar]
  19. M. Drouin, O. Grégoire and O. Simonin, A consistent methodology for the derivation and calibration of a macroscopic turbulence model for flows in porous media. Int. J. Heat Mass Transfer 63 (2013) 401–413. [CrossRef] [Google Scholar]
  20. D.R. Durran, Numerical methods for fluid dynamics, With applications to Geophysics, vol. 32 of Texts in Applied Mathematics. Springer, 2nd edition. New York (2010). [Google Scholar]
  21. P. Embid, Well-posedness of the nonlinear equations for zero Mach number combustion. Comm. Partial Differ. Equ. 12 (1987) 1227–1283. [CrossRef] [Google Scholar]
  22. 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]
  23. 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 1029–1054 2012. [CrossRef] [EDP Sciences] [Google Scholar]
  24. P. Fillion, A. Chanoine, S. Dellacherie and A. Kumbaro, FLICA-OVAP: A new platform for core thermal-hydraulic studies. Nucl. Eng. Des. 241 (2011) 4348–4358. [CrossRef] [Google Scholar]
  25. E. Goncalvès and R.F. Patella, Numerical study of cavitating flows with thermodynamic effect. Comput. Fluids 39 (2010) 99–113. [CrossRef] [Google Scholar]
  26. J.M. Gonzalez-Santalo and R.T. Jr Lahey, An exact solution for flow transients in two-phase systems by the method of characteristics. J. Heat Transfer 95 (1973) 470–476. [CrossRef] [Google Scholar]
  27. W. Greiner, L. Neise and H. Stöcker, Thermodynamics and statistical mechanics. Springer (1997). [Google Scholar]
  28. H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low Mach number limit. Comput. Fluids 28 (1999) 63–86. [CrossRef] [MathSciNet] [Google Scholar]
  29. S. Jaouen, Étude mathématique et numérique de stabilité pour des modeles hydrodynamiques avec transition de phase. Ph.D. thesis, Université Paris 6, France (2001). [Google Scholar]
  30. M.F. Lai, J.B. Bell and P. Colella. A projection method for combustion in the zero Mach number limit, in Proc. of 11th AIAA Comput. Fluid Dyn. Conf. (1993) 776–783. [Google Scholar]
  31. 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. Therm. Sci. 43 (2004) 265–276,. [CrossRef] [Google Scholar]
  32. 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]
  33. E.W. Lemmon, M.O. McLinden and D.G. Friend, Thermophysical Properties of Fluid Systems. National Institute of Standards and Technology, Gaithersburg MD, 20899. [Google Scholar]
  34. A. Majda and K.G. Lamb, Simplified equations for low Mach number combustion with strong heat release, Dynamical issues in combustion theory, vol. 35 of IMA Vol. Math. Appl. Springer-Verlag (1991). [Google Scholar]
  35. A. Majda and J. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Technol. 42 (1985) 185–205. [Google Scholar]
  36. 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]
  37. 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]
  38. Y. Penel, An explicit stable numerical scheme for the 1D transport equation. Discrete Contin. Dyn. Syst. Ser. S 5 (2012) 641–656. [CrossRef] [MathSciNet] [Google Scholar]
  39. Y. Penel, Existence of global solutions to the 1D abstract bubble vibration model. Differ. Integral Equ. 26 (2013) 59–80. [Google Scholar]
  40. 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]
  41. G.I. Sivashinsky, Hydrodynamic theory of flame propagation in an enclosed volume. Acta Astronaut. 6 (1979) 631–645. [CrossRef] [Google Scholar]
  42. G. Volpe, Performance of compressible flow codes at low Mach numbers. AIAA J. 31 (1993) 49–56. [Google Scholar]
  43. A. Voss, Exact Riemann solution for the Euler equations with nonconvex and nonsmooth equation of state. Ph.D. thesis, RWTH Aachen (2005). [Google Scholar]
  44. N. Zuber, Flow excursions and oscillations in boiling, two-phase flow systems with heat addition, in Symposium on Two-phase Flow Dynamics, Eindhoven EUR4288e (1967) 1071–1089. [Google Scholar]

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