On a diphasic low Mach number system

 Access to full text

 Full (PDF)

1. [1] R. Abgrall, R. Saurel, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 425–467 (1999). Zbl0937.76053
2. [2] 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. Paris Ser. I 331 (2000) 1017–1022. Zbl1010.76055
3. [3] 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. Zbl1169.76407
4. [4] Y.-H. Choi, C.L. Merkle, The Application of Preconditioning in Viscous Flows. J. Comput. Phys. 105 (1993) 207–223. Zbl0768.76032
5. [5] A.J. Chorin and J.E. Mardsen, A Mathematical Introduction to Fluid Mechanics. Springer-Verlag (1979). Zbl0417.76002
6. [6] S. Dellacherie, On relaxation schemes for the multicomponent Euler system. ESAIM: M2AN 37 (2003) 909–936. Zbl1070.76037
7. [7] S. Dellacherie, Dérivation du système diphasique bas Mach. Simulation numérique en géométrie monodimensionnelle. CEA report, ref. CEA-R-6046 (2004). 
8. [8] S. Dellacherie and A. Vincent, Zero Mach Number Diphasic Equations for the Simulation of Water-Vapor High Pressure Flows, in Proc. of the 11$\text{th}$ conference of the CFD Society of Canada, Vancouver (2003) 248–255. 
9. [9] P. Embid, Well-posedness of the nonlinear equations for zero Mach number combustion. Comm. Partial Differential Equations 12 (1987) 1227–1283. Zbl0632.76075
10. [10] D. Gueyffier, J. Li, A. Nadim, R. Scardovelli and S. Zaleski, Volume-of-Fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys. 152 (1999) 423–456. Zbl0954.76063
11. [11] H. Guillard and A. Murrone, On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes. Comput. Fluids 33 (2004) 655–675. Zbl1049.76040
12. [12] H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low Mach number limit. Comput. Fluids 28 (1999) 63–86. Zbl0963.76062
13. [13] F.H. Harlow and J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free interface. Phys. Fluids 8 (1965) 2182–2189. Zbl1180.76043
14. [14] D. Jamet, O. Lebaigue, N. Coutris and J.M. Delhaye, The second gradient method for the direct numerical simulation of liquid-vapor flows with phase change. J. Comput. Phys. 169 (2001) 624–651. Zbl1047.76098
15. [15] D. Juric and G. Tryggvason, Computations of boiling flows. Int. J. Multiphase Flow 24 (1998) 387–410. Zbl1121.76455
16. [16] S. Kokh, Aspects numériques et théoriques de la modélisation des écoulements diphasiques compressibles par des méthodes de capture d’interface. Ph.D. thesis of Paris VI University (2001). 
17. [17] B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski and G. Zanetti, Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113 (1994) 134–147. Zbl0809.76064
18. [18] F. Lagoutière, Modélisation mathématique et résolution numérique de problèmes de fluides compressibles à plusieurs constituants. Ph.D. thesis of Paris VI University (2000). 
19. [19] D. Lakehal, M. Meier and M. Fulgosi, Interface tracking towards the direct numerical simulation of heat and mass transfer in multiphase flow. Internat. J. Heat Fluid Flow 23 (2002) 242–257. 
20. [20] J.M. Le Corre, E. Hervieu, M. Ishii and J.M. Delhaye, Benchmarking and improvements of measurement techniques for local time-averaged two-phase flow parameters. Fourth International Conference on Multiphase Flows (ICMF 2001), New-Orleans, USA (2001). 
21. [21] A. Majda, Equations for low mach number combustion. Center of Pure and Applied Mathematics, University of California at Berkeley, report No. 112 (1982). 
22. [22] A. Majda and J.A. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Tech. 42 (1985) 185–205. 
23. [23] W. Mulder, S. Osher and J.A. Sethian, Computing interface motion in compressible gas dynamics. J. Comput. Phys. 100 (1992) 209–228. Zbl0758.76044
24. [24] S. Osher, M. Sussman and P. Smereka, A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1994) 146–159. Zbl0808.76077
25. [25] S. Paolucci, On the filtering of sound from the Navier-Stokes equations. Sandia National Laboratories report SAND82-8257 (1982). 
26. [26] J.A. Sethian, Level Set Methods. Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press (1996). Zbl0859.76004MR1409367
27. [27] K.M. Shyue, A fluid-mixture type algorithm for compressible multicomponent flow with van der Waals equation of state. J. Comput. Phys. 156 (1999) 43–88. Zbl0957.76039
28. [28] G. Tryggvasson and S.O. Unverdi, A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100 (1992) 25–37. Zbl0758.76047
29. [29] E. Turkel, Review of preconditioning methods for fluid dynamics. Appl. Numer. Math. 12 (1993) 257–284. Zbl0770.76048
30. [30] S.W.J. Welch and J. Wilson, A volume of fluid based method for fluid flows with phase change. J. Comput. Phys. 160 (2000) 662–682. Zbl0962.76068