Free Access
Volume 49, Number 1, January-February 2015
Page(s) 275 - 301
Published online 30 January 2015
  1. H. Abels, Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities. Commun. Math. Phys. 289 (2009) 45–73. [CrossRef] [Google Scholar]
  2. H. Abels, Strong well-posedness of a diffuse interface model for a viscous, quasi-incompressible two-phase flow. SIAM J. Math. Anal. 44 (2012) 316–340. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Abels, H. Garcke and G. Grün, Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Math. Models Methods Appl. Sci. 22 (2012) 1150013, 40. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Aki, J. Daube, W. Dreyer, J. Giesselmann, M. Kränkel and C. Kraus, A diffuse interface model for quasi-incompressible flows: Sharp interface limits and numerics. ESAIM: Proc. 38 (2012) 54–77. [CrossRef] [EDP Sciences] [Google Scholar]
  5. G.L. Aki, W. Dreyer, J. Giesselmann and C. Kraus, A quasi-incompressible diffuse interface model with phase transition. Math. Models Methods Appl. Sci. 24 (2014) 827–861. [CrossRef] [Google Scholar]
  6. S. Aland, J. Lowengrub and A. Voigt, Two-phase flow in complex geometries: a diffuse domain approach. CMES Comput. Model. Eng. Sci. 57 (2010) 77–107. [MathSciNet] [Google Scholar]
  7. J.W. Barrett, H. Garcke and R. Nürnberg, Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow. Comput. Methods Appl. Mech. Engrg. 267 (2013) 511–530. [Google Scholar]
  8. J.U. Brackbill, D.B. Kothe and C. Zemach, A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 335–354. [CrossRef] [MathSciNet] [Google Scholar]
  9. F. Boyer, Mathematical study of multi-phase flow under shear through order parameter formulation. Asymptotic Anal. 20 (1999) 175–212. [Google Scholar]
  10. Ph.G. Ciarlet, The finite element method for elliptic problems. Stud. Math. Appl., Vol. 4. North-Holland Publishing Co., Amsterdam (1978). [Google Scholar]
  11. H. Ding, P.D.M. Spelt and Chang Shu, Diffuse interface model for incompressible two-phase flows with large density ratios, J. Comput. Phys. 226 (2007) 2078–2095. [CrossRef] [Google Scholar]
  12. S. Dong and J. Shen, A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. J. Comput. Phys. 231 (2012) 5788–5804. [CrossRef] [Google Scholar]
  13. L.C. Evans, Partial differential equations, vol. 19 of Grad. Stud. Math. AMS, Providence, RI (1998). [Google Scholar]
  14. J. Giesselmann, Ch. Makridakis and T. Pryer, Energy consistent dg methods for the navier-stokes-korteweg system, Math. Comput. 83 (2014) 2071–2099. [CrossRef] [Google Scholar]
  15. G. Grün, On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities, SIAM J. Numer. Anal. 51 (2013) 3036–3061. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Grün and M. Rumpf, Nonnegativity preserving convergent schemes for the thin film equation, Numer. Math. 87 (2000) 113–152. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Grün and F. Klingbeil, Two-phase flow with mass density contrast: Stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface model. J. Comput. Phys. 257 (2014) A(0):708–725. [Google Scholar]
  18. Z. Guo, Ping Lin and J.S. Lowengrub, A numerical method for the quasi-incompressible cahn-hilliard-navier-stokes equations for variable density flows with a discrete energy law (2014). [Google Scholar]
  19. M.E. Gurtin, D. Polignone and J. Vinals, Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci. 6 (1996) 815–831. [CrossRef] [MathSciNet] [Google Scholar]
  20. P.C. Hohenberg and B.I. Halperin, Theory of dynamic critical phenomena. Rev. Mod. Phys. 49 (1977) 435–479. [CrossRef] [Google Scholar]
  21. Chun Liu and Jie Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Phys. D 179 (2003) 211–228. [Google Scholar]
  22. A. Logg and G.N. Wells, DOLFIN: automated finite element computing. ACM Trans. Math. Software 37 (2010) 20, 28. [CrossRef] [MathSciNet] [Google Scholar]
  23. J.S. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1998) 2617–2654. [Google Scholar]
  24. N.C. Owen, J. Rubinstein and P. Sternberg, Minimizers and gradient flows for singularly perturbed bi–stable potentials with a Dirichlet condition. Proc. R. Soc. Lond., Ser. A 429 (1990) 505–532. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Sussman, P. Smereka and S. Osher, A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1994) 146–159. [Google Scholar]
  26. P. Sternberg, The effect of a singular perturbation on nonconvex variational problems. Arch. Ration. Mech. Anal. 101 (1988) 209–260. [Google Scholar]
  27. R. Scardovelli and S. Zaleski, Direct numerical simulation of free-surface and interfacial flow. In vol. 31 of Annual review of fluid mechanics. Annual Reviews, Palo Alto, CA (1999) 567–603. [Google Scholar]
  28. J. Shen and X. Yang, A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. SIAM J. Sci. Comput. 32 (2010) 1159–1179. [CrossRef] [Google Scholar]
  29. S. Vincent and J.-P. Caltagirone, A one-cell local multigrid method for solving unsteady incompressible multiphase flows. J. Comput. Phys. 163 (2000) 172–215. [CrossRef] [MathSciNet] [Google Scholar]
  30. Zh. Zhang and H. Tang, An adaptive phase field method for the mixture of two incompressible fluids. Comput. Fluids 36 (2007) 1307–1318. [CrossRef] [Google Scholar]

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