Open Access
Issue
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
Page(s) 1569 - 1598
DOI https://doi.org/10.1051/m2an/2021032
Published online 29 July 2021
  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. [Google Scholar]
  2. 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. [Google Scholar]
  3. 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. [Google Scholar]
  4. A. Ambroso, J.-M. Hérard and O. Hurisse, A method to couple HEM and HRM two-phase flow models. Comput. Fluids 38 (2009) 738–756. [Google Scholar]
  5. T. Barberon and P. Helluy, Finite volume simulations of cavitating flows. In: Finite Volumes for Complex Applications, III (Porquerolles, 2002). Lab. Anal. Topol. Probab (2002) 441–448 (electronic). [Google Scholar]
  6. T. Barberon and P. Helluy, Finite volume simulation of cavitating flows. Comput. Fluids 34 (2005) 832–858. [Google Scholar]
  7. K.H. Bendiksen, D. Maines, R. Moe and S. Nuland, The dynamic two-fluid model OLGA: theory and application. SPE Prod. Eng. 6 (1991) 171–180. [Google Scholar]
  8. M. Bernard, S. Dellacherie, G. Faccanoni, B. Grec and Y. Penel, Study of a low mach nuclear core model for two-phase flows with phase transition I: stiffened gas law. ESAIM: M2AN 48 (2014) 1639–1679. [CrossRef] [EDP Sciences] [Google Scholar]
  9. R.A. Berry, J.W. Peterson, H. Zhang, R.C. Martineau, H. Zhao, L. Zou, D. Andrs and J. Hansel, Relap-7 theory manual. Technical report, Idaho National Lab.(INL), Idaho Falls, ID (United States) (2018). [Google Scholar]
  10. T. Berstad, C. Dørum, J.P. Jakobsen, S. Kragset, H. Li, H. Lund, A. Morin, S.T. Munkejord, M.J. Mølnvik, H.O. Nordhagen and E. Østbya, CO2 pipeline integrity: a new evaluation methodology. Energy Proc. 4 (2011) 3000–3007. [Google Scholar]
  11. D. Bestion, The physical closure laws in the CATHARE code. Nucl. Eng. Des. 124 (1990) 229–245. [Google Scholar]
  12. Z. Bilicki and J. Kestin, Physical aspects of the relaxation model in two-phase flow. Proc. R. Soc. London. A. Math. Phys. Sci. 428 (1990) 379–397. [Google Scholar]
  13. H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edition. John Wiley & Sons (1985). [Google Scholar]
  14. M. de Lorenzo, Modelling and numerical simulation of metastable two-phase flows. Ph.D. thesis, Université Paris-Saclay (2018). [Google Scholar]
  15. M. de Lorenzo, P. Lafon, M. Di Matteo, M. Pelanti, J.-M. Seynhaeve and Y. Bartosiewicz, Homogeneous two-phase flow models and accurate steam-water table look-up method for fast transient simulations. Int. J. Multiphase Flow 95 (2017) 199–219. [Google Scholar]
  16. S. Dellacherie, On a low Mach nuclear core model. ESAIM Proc. 35 (2012) 79–106. [Google Scholar]
  17. S. Dellacherie, E. Jamelot and O. Lafitte, A simple monodimensional model coupling an enthalpy transport equation and a neutron diffusion equation. Appl. Math. Lett. 62 (2016) 35–41. [Google Scholar]
  18. S. Dellacherie, E. Jamelot, O. Lafitte and R. Mouhamad, Numerical results for the coupling of a simple neutronics diffusion model and a simple hydrodynamics low mach number model. In: IEEE, editor, SYNASC (2016). [Google Scholar]
  19. S. Dellacherie, G. Faccanoni, B. Grec and Y. Penel, Accurate steam-water equation of state for two-phase flow LMNC model with phase transition. Appl. Math. Model. 65 (2019) 207–233. [Google Scholar]
  20. 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. [Google Scholar]
  21. P. Embid, Well-posedness of the nonlinear equations for zero Mach number combustion. Comm. Part. Differ. Equ. 12 (1987) 1227–1283. [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 (November 2008). [Google Scholar]
  23. E. Faucher, J.-M. Herard, M. Barret and C. Toulemonde, Computation of flashing flows in variable cross-section ducts. Int. J. Comput. Fluid Dyn. 13 (2000) 365–391. [Google Scholar]
  24. F. Filbet and S. Jin, A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources. J. Comput. Phys. 229 (2010) 7625–7648. [Google Scholar]
  25. 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. [Google Scholar]
  26. 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]
  27. J. Gale, I. Tiselj and A. Horvat, Two-fluid model of the waha code for simulations of water hammer transients. Multiphase Sci. Technol. 20 (2008). [Google Scholar]
  28. J.M. Greenberg and A.-Y. LeRoux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1–16. [Google Scholar]
  29. W. Greiner, L. Neise and H. Stöcker, Thermodynamics and Statistical Mechanics. Springer (1997). [Google Scholar]
  30. L. Gurault and J.-M. Hérard, A two-fluid hyperbolic model in a porous medium. ESAIM: M2AN 44 (2010) 1319–1348. [EDP Sciences] [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. O. Hurisse, Application of an homogeneous model to simulate the heating of two-phase flows. Int. J. Finite 11 (2014) 1–37. [Google Scholar]
  33. 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. [Google Scholar]
  34. S. Jin, Runge-kutta methods for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys. 122 (1995) 51–67. [Google Scholar]
  35. S. Jin, Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review. Riv. Math. Univ. Parma (N.S.) 3 (2012) 177–216. [Google Scholar]
  36. 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. [Google Scholar]
  37. G. Le Coq, S. Aubry, J. Cahouet, P. Lequesne, G. Nicolas and S. Pastorini, The “THYC” computer code. A finite volume approach for 3 dimensional two-phase flows in tube bundles. Bulletin de la Direction des Etudes et Recherches, Serie A (1989) 61–76. [Google Scholar]
  38. 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. [Google Scholar]
  39. O. Le Métayer, J. Massoni and R. Saurel, Modelling evaporation fronts with reactive Riemann solvers. J. Comput. Phys. 205 (2005) 567–610. [Google Scholar]
  40. O. Le Métayer and R. Saurel, The Noble-Abel Stiffened-Gas equation of state. Phys. Fluids 28 (2016). [Google Scholar]
  41. E.W. Lemmon, M.O. McLinden and D.G. Friend, Thermophysical Properties of Fluid Systems. National Institute of Standards and Technology, Gaithersburg, MD (1998). [Google Scholar]
  42. G. Linga and T. Flåtten, A hierarchy of non-equilibrium two-phase flow models. ESAIM: Proc. Surv 66 (2019) 109–143. [Google Scholar]
  43. H. Lund, A hierarchy of relaxation models for two-phase flow. SIAM J. Appl. Math. 72 (2012) 1713–1741. [Google Scholar]
  44. A. Majda and K.G. Lamb, Simplified equations for low Mach number combustion with strong heat release. In: Vol. 35 of IMA Vol. Math. Appl. Dynamical Issues in Combustion Theory. Springer-Verlag (1991). [Google Scholar]
  45. J.P. Mañes, V.H. Sánchez Espinoza, S. Chiva Vicent, M. Böttcher and R. Stieglitz, Validation of NEPTUNE-CFD two-phase flow models using experimental data. Sci. Technol. Nucl. Installations 2014 (2014). [Google Scholar]
  46. H. Mathis, Étude théorique et numérique des écoulements avec transition de phase. Ph.D. thesis, Université de Strasbourg (2010). [Google Scholar]
  47. H. Paillere, C. Viozat, A. Kumbaro and I. Toumi, Comparison of low mach number models for natural convection problems. Heat Mass Transfer 36 (2000) 567–573. [Google Scholar]
  48. L. Quibel, Simulation d’ écoulements diphasiques eau-vapeur en présence d’incondensables. Ph.D. thesis, Université de Strasbourg (2020). [Google Scholar]
  49. L. Quibel, Simulation of water-vapor two-phase flows with non-condensable gas. Theses, Université de Strasbourg (September 2020). [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. [Google Scholar]
  51. J.W. Spore, et al., TRAC-M/FORTRAN 90 Theory Manual. Los Alamos National Laboratory, Los Alamos, NM. Technical report, NUREG/CR-6724 (2001). [Google Scholar]
  52. M.D. Thanh and A. Izani Md Ismail, A well-balanced scheme for a one-pressure model of two-phase flows. Phys. Scr. 79 (2009). [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