Free Access
Volume 40, Number 4, July-August 2006
Page(s) 653 - 687
Published online 15 November 2006
  1. N.D. Alikakos, P.W. Bates and X. Chen, Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Arch. Ration. Mech. An. 128 (1994) 165–205. [CrossRef] [MathSciNet]
  2. D.M. Anderson, G.B. McFadden and A.A. Wheeler, Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1998) 139–165. [CrossRef]
  3. J.W. Barrett and J.F. Blowey, Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy and a concentration dependent mobility matrix. Math. Mod. Meth. Appl. S. 9 (1999) 627–663. [CrossRef] [MathSciNet]
  4. J.F. Blowey, M.I.M. Copetti and C.M. Elliott, Numerical analysis of a model for phase separation of a multi-component alloy. IMA J. Numer. Anal. 16 (1996) 111–139. [CrossRef] [MathSciNet]
  5. F. Boyer, Mathematical study of multiphase flow under shear through order parameter formulation. Asymptotic Anal. 20 (1999) 175–212.
  6. F. Boyer, A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 31 (2002) 41–68. [CrossRef]
  7. M.I.M. Copetti, Numerical experiments of phase separation in ternary mixtures. Math. Comput. Simulat. 52 (2000) 41–51. [CrossRef]
  8. C.M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in Mathematical Models for Phase Change Problems, J.F. Rodrigues Ed., Birkhäuser Verlag Basel. Intern. Ser. Numer. Math. 88 (1989).
  9. C.M. Elliott and S. Luckhaus, A generalised diffusion equation for phase separation of a multi-component mixture with interfacial free energy. IMA Preprint Series 887 (1991).
  10. D.J. Eyre, Systems of Cahn-Hilliard equations. SIAM J. Appl. Math. 53 (1993) 1686–1712. [CrossRef] [MathSciNet]
  11. H. Garcke and A. Novick-Cohen, A singular limit for a system of degenerate Cahn-Hilliard equations. Adv. Differ. Equ. 5 (2000) 401–434.
  12. H. Garcke, B. Nestler and B. Stoth, On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Physica D 115 (1998) 87–108. [CrossRef] [MathSciNet]
  13. H. Garcke, B. Nestler and B. Stoth, A multi phase field: numerical simulations of moving phase boundaries and multiple junctions. SIAM J. Appl. Math. 60 (1999) 295–315. [CrossRef] [MathSciNet]
  14. G.A. Greene, J.C. Chen and M.T. Conlin, Onset of entrainment between immiscible liquid layers due to rising gas bubbles. Int. J. Heat Mass Tran. 31 (1988) 1309–1317. [CrossRef]
  15. D. Jacqmin, Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1999) 96–127. [CrossRef] [MathSciNet]
  16. D. Jacqmin, Contact-line dynamics of a diffuse fluid interface. J. Fluid Mechanics 402 (2000) 57–88. [CrossRef] [MathSciNet]
  17. M. Jobelin, C. Lapuerta, J.-C. Latché, P. Angot and B. Piar, A finite element penalty-projection method for incompressible flows. J. Comput. Phys. (2006) (to appear).
  18. J. Kim, Modeling and simulation of multi-component, multi-phase fluid flows. Ph.D. thesis, Univeristy of California, Irvine (2002).
  19. J. Kim, A continuous surface tension force formulation for diffuse-interface models. J. Comput. Phys. 204 (2005) 784–804. [CrossRef] [MathSciNet]
  20. J. Kim and J. Lowengrub, Phase field modeling and simulation of three-phase flows. Interfaces and Free Boundaries 7 (2005) 435–466. [CrossRef] [MathSciNet]
  21. J. Kim, K. Kang and J. Lowengrub, Conservative multigrid methods for ternary Cahn-Hilliard systems. Commu. Math. Sci. 2 (2004) 53–77.
  22. 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]
  23. J.S. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Proc. Royal Soc. London, Ser. A 454 (1998) 2617–2654.
  24. B. Piar, PELICANS: Un outil d'implémentation de solveurs d'équations aux dérivées partielles. Note Technique 2004/33, IRSN (2004).
  25. J.S. Rowlinson and B. Widom, Molecular Theory of Capillarity. Clarendon Press (1982).
  26. K.A. Smith, F.J. Solis and D.L. Chopp, A projection method for motion of triple junctions by level sets. Interfaces and Free Boundaries 4 (2002) 239–261. [MathSciNet]
  27. R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences 68, Springer-Verlag, New York (1997).
  28. P. Yue, J. Feng, C. Liu and J. Shen, A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mechanics 515 (2004) 293–317. [CrossRef] [MathSciNet]

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