Free Access
Issue
ESAIM: M2AN
Volume 51, Number 5, September-October 2017
Page(s) 1691 - 1731
DOI https://doi.org/10.1051/m2an/2016073
Published online 20 October 2017
  1. H. Abels, On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities. Arch. Ration. Mech. Anal. 194 (2009) 463–506. [CrossRef]
  2. H. Abels and E. Feireisl, On a diffuse interface model for a two-phase flow of compressible viscous fluids. Indiana Univ. Math. J. 57 (2008) 659–698. [CrossRef]
  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]
  4. B. Andreianov, M. Bendahmane, F. Hubert and S. Krell, On 3D DDFV discretization of gradient and divergence operators. I. meshing, operators and discrete duality. IMA J. Numer. Anal. 32 (2012) 1574–1603. [CrossRef]
  5. B. Andreianov, F. Boyer and F. Hubert, Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Numer. Methods Partial Differ. Equ. 23 (2007) 145–195. [CrossRef] [MathSciNet]
  6. M. Bessemoulin-Chatard, C. Chainais-Hillairet and F. Filbet. On discrete functional inequalities for some finite volume schemes. IMA J. Numer. Anal. 35 (2015) 1125–1149. [CrossRef] [MathSciNet]
  7. F. Boyer, A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 31 (2002) 41–68. [CrossRef]
  8. F. Boyer, F. Hubert and S. Krell, Nonoverlapping Schwarz algorithm for solving two-dimensional m-DDFV schemes. IMA J. Numer. Anal. 30 (2010) 1062–1100. [CrossRef]
  9. F. Boyer, S. Krell and F. Nabet, Inf-sup stability of the discrete duality finite volume method for the 2D stokes problem. Math. Comput. 84 (2015) 2705–2742. [CrossRef]
  10. F. Boyer, C. Lapuerta, S. Minjeaud, B. Piar and M. Quintard, Cahn−Hilliard/Navier−Stokes model for the simulation of three-phase flows. Trans. Porous Media 82 (2010) 463–483. [CrossRef] [MathSciNet]
  11. F. Boyer and S. Minjeaud, Numerical schemes for a three component Cahn−Hilliard model. ESAIM: M2AN 45 (2011) 697–738. [CrossRef] [EDP Sciences]
  12. A. Carlson, M. Do Quang and G. Amberg, Dissipation in rapid dynamic wetting. J. Fluid Mech. 682 (2011) 213–240. [CrossRef]
  13. L. Cherfils, M. Petcu and M. Pierre, A numerical analysis of the Cahn−Hilliard equation with dynamic boundary conditions. Discrete Contin. Dyn. Syst. 27 (2010) 1511–1533. [CrossRef] [MathSciNet]
  14. R. Chill, E. Fašangováand J. Prüss, Convergence to steady state of solutions of the Cahn−Hilliard and Caginalp equations with dynamic boundary conditions. Math. Nachr. 279 (2006) 1448–1462. [CrossRef]
  15. K. Domelevo and P. Omnes. A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. M2AN: M2AN 39 (2005) 1203–1249. [CrossRef] [EDP Sciences]
  16. S. Dong, On imposing dynamic contact-angle boundary conditions for wall-bounded liquid-gas flows. Comput. Methods Appl. Mech. Engrg. 247/248 (2012) 179–200. [CrossRef]
  17. S. Dong, An outflow boundary condition and algorithm for incompressible two-phase flows with phase field approach. J. Comput. Phys. 266 (2014) 47–73. [CrossRef]
  18. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods. In Handbook of numerical analysis, Vol. VII. Edited by Ph. Ciarlet and J.L. Lions. North-Holland, Amsterdam (2000) 715–1022.
  19. R. Eymard, G. Henry, R. Herbin, F. Hubert, R. Klofkorn and G. Manzini, 3d benchmark on discretization schemes for anisotropic diffusion problems on general grids. In Proc. of Finite Volumes for Complex Applications, Vol. VI. Springer (2011) 895–930.
  20. H.P. Fischer, P. Maass and W. Dieterich, Novel surface modes in spinodal decomposition. Phys. Rev. Lett. 79 (1997) 893–896. [CrossRef]
  21. H.P. Fischer, P. Maass and W. Dieterich, Diverging time and length scales of spinodal decomposition modes in thin films. EPL Europhys. Lett. 42 (1998) 49–54. [CrossRef] [EDP Sciences]
  22. T. Goudon and S. Krell, A DDFV Scheme for Incompressible Navier−Stokes equations with variable density. In Proc. of Finite Volumes for Complex Applications VII, edited by J. Fuhrmann, M. Ohlberger and C. Rohde. In Vol. 77 and 78. Springer Proceedings in Mathematics and Statistics. Springer, Berlin, Allemagne (2014).
  23. R. Herbin and F. Hubert, Benchmark on discretization schemes for anisotropic diffusion problems on general grids. In Proc. of Finite Volumes for Complex Applications V, Aussois, France. Edited by R. Eymard and J.M. Herard. Hermès (2008).
  24. S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, S. Ganesan and L. Tobiska, Quantitative benchmark computations of two-dimensional bubble dynamics. Int. J. Numer. Methods Fluids 60 (2009) 1259–1288. [CrossRef] [MathSciNet]
  25. D. Jacqmin, Calculation of two-phase Navier−Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1999) 96–127. [CrossRef] [MathSciNet]
  26. D. Jacqmin, Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402 (2000) 57–88. [CrossRef] [MathSciNet]
  27. D. Kay, V. Styles and R. Welford, Finite element approximation of a Cahn–Hilliard–Navier−Stokes system. Interfaces Free Bound. 10 (2008) 15–43. [CrossRef] [MathSciNet]
  28. R. Kenzler, F. Eurich, P. Maass, B. Rinn, J. Schropp, E. Bohl and W. Dieterich, Phase separation in confined geometries: Solving the Cahn–Hilliard equation with generic boundary conditions. Comput. Phys. Commun. 133 (2001) 139–157. [CrossRef]
  29. S. Krell, Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes. Numer. Methods Partial Differ. Equ. 27 (2011) 1666–1706. [CrossRef]
  30. S. Krell and G. Manzini, The discrete duality finite volume method for stokes equations on three-dimensional polyhedral meshes. SIAM J. Numer. Anal. 50 (2012) 808–837. [CrossRef]
  31. C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Physica D 179 (2003) 211–228. [CrossRef] [MathSciNet]
  32. S. Metzger, On numerical schemes for phase-field models for electrowetting with electrolyte solutions. Proc. Appl. Math. Mech. 15 (2015) 715–718. [CrossRef]
  33. S. Minjeaud, An adaptive pressure correction method without spurious velocities for diffuse-interface models of incompressible flows. J. Comput. Phys. 236 (2013) 143–156. [CrossRef]
  34. S. Minjeaud, An unconditionally stable uncoupled scheme for a triphasic Cahn−Hilliard/Navier−Stokes model. Numer. Methods Partial Differ. Equ. 29 (2013) 584–618. [CrossRef]
  35. A. Miranville and S. Zelik, Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions. Math. Methods Appl. Sci. 28 (2005) 709–735. [CrossRef]
  36. F. Nabet, Schémas volumes finis pour des problèmes multiphasiques. Ph.D. thesis, Aix-Marseille université (2014).
  37. F. Nabet, Convergence of a finite-volume scheme for the cahn–hilliard equation with dynamic boundary conditions. IMA J. Numer. Anal. 36 (2015) 1898–1942. [CrossRef]
  38. F. Nabet, An error estimate for a finite-volume scheme for the Cahn−Hilliard equation with dynamic boundary conditions (2016). Preprint hal-01273945 (2016).
  39. J. Prüss, R. Racke and S. Zheng, Maximal regularity and asymptotic behavior of solutions for the Cahn−Hilliard equation with dynamic boundary conditions. Ann. Mat. Pura Appl. 185 (2006) 627–648. [CrossRef]
  40. T. Qian, X.-P. Wang and P. Sheng, A variational approach to moving contact line hydrodynamics. J. Fluid Mech. 564 (2006) 333. [CrossRef] [MathSciNet]
  41. R. Racke and S. Zheng, The Cahn−Hilliard equation with dynamic boundary conditions. Adv. Differ. Equ. 8 (2003) 83–110.
  42. A.J. Salgado, A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines. ESAIM: M2AN 47 (2013) 743–769, 5. [CrossRef] [EDP Sciences]
  43. J. Shen, X. Yang and H. Yu, Efficient energy stable numerical schemes for a phase field moving contact line model. J. Comput. Phys. 284 (2015) 617–630. [CrossRef]
  44. X-.P. Wang, T. Qian and P. Sheng, Moving contact line on chemically patterned surfaces. J. Fluid Mech. 605 (2008) 59–78.
  45. H. Wu and S. Zheng, Convergence to equilibrium for the Cahn−Hilliard equation with dynamic boundary conditions. J. Differ. Equ. 204 (2004) 511–531. [CrossRef]

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