The Second Gradient Method for the Direct Numerical Simulation of Liquid-Vapor Flows with Phase Change

Journal of Computational Physics

Volumn 169, Issue 2, 2001, Pages 624-651

  Jamet, D ^a   Lebaigue, O ^a   Coutris, N ^a,b   Delhaye, J M ^a  

^a CEA GRENOBLE   (France)

^b GRENOBLE INSTITUTE OF TECHNOLOGY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; TWO PHASE FLOW;

CONTINUOUS MEDIA; DENSITY GRADIENTS; DIRECT-NUMERICAL-SIMULATION; GRADIENT THEORY; GRADIENT'S METHODS; INTERNAL ENERGIES; LIQUID-VAPOR FLOWS; LIQUID-VAPOR INTERFACE; PHASE CHANGE; PHASE FIELDS;

GRADIENT METHODS;

EID: 0000519708     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6692     Document Type: Article

References (40)

1. Anderson D. M., McFadden G. B., Wheeler A. A. Diffuse-interface models in fluid mechanics. Annu. Rev. Fluid Mech. 30:1998;139.
2. Bi Z., Sekerka R. F. Phase-field model of solidification of a binary alloy. Physica A. 261:1998;95.
3. Brackbill J. U., Kothe D. B., Zemach C. A continuum method for modeling surface tension. J. Comput. Phys. 100:1992;335.
4. Cahn J. W., Hilliard J. E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28:1958;258.
5. Carey V. P. Liquid-Vapor Phase-Change Phenomena: An Introduction to the Thermophysics of Vaporisation and Condensation Processes in Heat Transfer Equipment. 1992.
6. Casal P., Gouin H. Relation entre l'équation de l'énergie et l'équation du mouvement en théorie de Korteweg de la capillarité C. R. Acad. Sci. Paris. 300:1985;231.
7. Casal P., Gouin H. Sur les interfaces liquide-vapeur non isothermes. J. Méc. Théorique Appliquée. 7:1988;689.
8. Chesters A. K. The modeling of coalescence processes in fluid-liquid dispersions: A review of the current understanding. Trans. IChemE. 69:1991;259.
9. Delhaye J. M. Jump conditions and entropy sources in two-phase systems. Local instant formulation. Int. J. Multiphase Flow. 1:1974;395.
10. Dell'Isola F., Gouin H., Rotoli G. Nucleation of spherical shell-like interfaces by second gradient theory: Numerical simulations. Eur. J. Mech. B/Fluids. 15:1996;545.
11. H. Gouin, and, J. M. Delhaye, Material waves of a fluid in the vicinity of the critical point, in edited by, S. Morika and L. van Wijngaarden, IUTAM Symposium on Waves in Liquid/Gas and Liquid/Vapour Two-Phase Systems, Kluwer Academic Publishers, Dordrecht, 1995, p, 405.
12. Ishii M. Thermo-Fluid Dynamic Theory of Two-Phase Flow. 1975.
13. Jacqmin D. An energy approach to the continuum surface tension method. Proceedings of the 34th Aerospace Sciences Meeting and Exhibit. 1996.
14. Jacqmin D. Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 155:1999;1.
15. Jamet D. Etude des potentialites de la théorie du second gradient pour la simulation numérique directe des écoulements liquide-vapeur avec changement de phase. 1998.
16. Jamet D., Lebaigue O., Coutris N., Delhaye J. M. A numerical description of a liquid-vapor interface based on the second gradient theory. Fluid Mech. Res. 22:1997;1.
17. Jasnow D., Viñals J. Coarse-grained description of thermo-capillary flow. Phys. Fluids. 8:1996;660.
18. Juric D. Computations of Phase Change. 1996.
19. Juric D., Tryggvason G. Computations of boiling flows. Int. J. Multiphase Flow. 24:1998;387.
20. Kolev N. I. Fragmentation and coalescence dynamics in multiphase flows. Exp. Thermal Fluid Sci. 6:1993;211.
21. Korteweg D. J. Sur la forme que prennent les équations du mouvement des fluides si l'on tient compte des forces capillaires causées par des variations de densité considérables mais continues et sur la théorie de la capillarité dans l'hypothèse d'une variation continue de la densité Arch. Néerl. Sci. Exactes Nat. 6:1901;1.
22. Lafaurie B., Nardone C., Scardovelli R., Zaleski S., Zanetti G. Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113:1994;134.
23. Maxwell J. C. On the dynamical evidence of the molecular constitution of bodies. Nature. 11:1875;357.
24. McFadden G. B., Wheeler A. A., Braun R. J., Coriell S. R. Phase-field models for anisotropic interfaces. Phys. Rev. E. 48:1993;2016.
25. Nadiga B. T., Zaleski S. Investigations of a two-phase fluid model. Eur. J. Mech. B/Fluids. 15:1996;885.
26. Palermo T. Le phénomène de coalescence. Rev. Inst. Français Pétrole. 46:1991;325.
27. Penrose O., Fife P. C. Thermodynamically consistent models of phase-field type for kinetics of phase transitions. Physica D. 43:1990;44.
28. Poinsot T. J., Lele S. K. Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101:1992;104.
29. Reese J. M., Woods L. C., Thivet F. J. P., Candel S. A second-order description of shock structure. J. Comput. Phys. 117:1995;240.
30. Rocard Y. Thermodynamique. 1967.
31. Rowlinson J. S., Widom B. Molecular Theory of Capillarity. 1982.
32. Seppecher P. Etude d'une modélisation des zones capillaires fluides: Interfaces et lignes de contact. 1987.
33. Seppecher P. Moving contact line in the Cahn-Hilliard theory. Int. J. Eng. Sci. 34:1996;977.
34. Sethian J. A. Level Set Methods. 1996.
35. Thompson K. W. Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68:1987;1.
36. Unverdi S. O., Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100:1992;25.
37. van der Waals, Thermodynamische Theorie der Kapillarität unter Voraussetzung stetiger Dichteanderung, Z. Phys. Chem. 13, 657, 1894. English translation in, J. Stat. Phys. 20, 197, 1979.
38. van der Waals, Thermodynamische Theorie der Kapillarität unter Voraussetzung stetiger Dichteanderung, Z. Phys. Chem. 13, 657, 1894. English translation in, J. Stat. Phys. 20, 197, 1979.
39. Welch S. W. J., Wilson J. A volume of fluid based method for fluid flows with phase change. J. Comput. Phys. 160:2000;662.
40. Wheeler A. A., Murray B. T., Schaefer R. J. Computation of dendrites using a phase field model. Physica D. 66:1993;243.