On linear schemes for a cahn-hilliard diffuse interface model

Journal of Computational Physics

Volumn 234, Issue 1, 2013, Pages 140-171

  Guillen gonzalez F ^a   Tierra, G ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Cahn hilliard; Diffuse interface phase field; Equilibrium solutions; Long time stability; Mixed finite element; Time integration

Indexed keywords

CAHN-HILLIARD; DIFFUSE INTERFACE; DIFFUSE INTERFACE PHASE-FIELD; EQUILIBRIUM SOLUTIONS; INTERFACE PHASE; LONG-TIME STABILITIES; MIXED FINITE ELEMENTS; NUMERICAL SCHEME; PHASE FIELDS; TIME-INTEGRATION;

FINITE ELEMENT METHOD;

EID: 84870538130     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.09.020     Document Type: Article

References (31)

1. H. Abels, Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible Fluids, Habilitation Thesis, .
2. S. Badia, F. Guillén-González, J.V. Gutiérrez-Santacreu, Finite element approximation of nematic liquid crystal flows using a saddle-point structure, Journal of Computational Physics 230 (2011) 1686-1706.
3. J.W. Barrett, J.F. Blowey, H. Garcke, Finite element approximation of the Cahn-Hilliard equation with degenerate mobility, SIAM Journal on Numerical Analysis 37 (1999) 286-318.
4. P.W. Bates, P.C. Fife, The dynamics of nucleation for the Cahn-Hilliard equation, SIAM Journal on Applied Mathematics 53 (1993) 990-1008.
5. R. Becker, X. Feng, A. Prohl, Finite element approximations of the Ericksen-Leslie model for nematic liquid crystal flow, SIAM Journal on Numerical Analysis 46 (2008) 1704-1731.
6. F. Boyer, S. Minjeaud, Numerical schemes for a three component Cahn-Hilliard model, ESAIM: Mathematical Modelling and Numerical Analysis. 45 (2011) 697-738.
7. J.W. Cahn, J.E. Hilliard, Free energy of a non-uniform system. I. Interfacial free energy, The Journal of Chemical Physics 28 (1958) 258-267.
8. H.D. Ceniceros, Tracking fluid interfaces approaching singular events, Boletín de la Sociedad Española de Matemática Aplicada 48 (2009) 31-57.
9. M.I.M. Copetti, C.M. Elliott, Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy, Numerische Mathematik 63 (1992) 39-65.
10. Q. Du, R.A. Nicolaides, Numerical analysis of a continuum model of phase transition, SIAM Journal on Numerical Analysis 28 (1991) 1310-1322.
11. C.M. Elliott, D.A. French, A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation, SIAM Journal on Numerical Analysis 26 (1989) 884-903.
12. C.M. Elliott, D.A. French, Numerical studies of the Cahn-Hilliard equation for phase separation, IMA Journal of Applied Mathematics 38 (1987) 97-128.
13. C.M. Elliott, D.A. French, F.A. Milner, A second order splitting method for the Cahn-Hilliard equation, Numerische Mathematik 54 (1989) 575-590.
14. C.M. Elliott, H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM Journal on Mathematical Analysis 27 (1996) 404-423.
15. C.M. Elliott, Z. Songmu, On the Cahn-Hilliard equation, Archive for Rational Mechanics and Analysis 96 (1986) 339-357.
16. David J. Eyre, An Unconditionally Stable One-Step Scheme for Gradient System, ,unpublished.
17. X. Feng, Fully discrete finite element approximations of the Navier-Stokes-Cahn-Hilliard diffuse interface model for two-phase fluid flows, SIAM Journal on Numerical Analysis 44 (2006) 1049-1072.
18. X. Feng, A. Prohl, Error analysis of a mixed finite element method for the Cahn-Hilliard equation, Numerische Mathematik 99 (2004) 47-84.
19. D. Furihata, A stable and conservative finite difference scheme for the Cahn-Hilliard equation, Numerische Mathematik 87 (2001) 675-699.
20. H. Gomez, V.M. Calo, Y. Bazilevs, Thomas J.R. Hughes, Isogeometric analysis of the Cahn-Hilliard phase-field model, Computer Methods in Applied Mechanics and Engineering 197 (2008) 4333-4352.
21. H. Gomez, Thomas J.R. Hughes, Provably unconditionally stable, second-order time-accurate, Journal of Computational Physics 230 (2011) 5310-5327.
22. Z. Hu, S.M. Wise, C. Wang, J.S. Lowengrub, Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation, Journal of Computational Physics 228 (2009) 5323-5339.
23. 0 finite element schemes for phase field models in two-phase flow computations, Journal of Computational Physics 230 (2011) 7115-7131.
24. D. Kay, V. Styles, E. Suli, Discontinuous Galerkin finite element approximation of the Cahn-Hilliard Equation with convection, SIAM Journal on Numerical Analysis 47 (2009) 2660-2685.
25. J. Kim, K. Kang, J. Lowengrub, Conservative multigrid methods for Cahn-Hilliard fluids, Journal of Computational Physics 193 (2004) 511-543.
26. 0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, Journal of Computational Physics 227 (2007) 1411-1427.
27. A. Novick-Cohen, L.A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica D 10 (1984) 277-298.
28. J. Shen, X. Yang, Numerical approximations of Allen-Cahn and Cahn-Hilliard equations, Discrete and Continuous Dynamical Systems 28 (2010) 1669-1691.
29. J.D. van der Waals, The thermodynamic theory of capillarity flow under the hypothesis of a continuous variation of density, Verhandelingen Koninklijke Nederlandse Akademie van Wetenschappen Amsterdam (Sec 1) 1 (1893) 1-56.
30. S.M. Wise, Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations, Journal of Scientific Computing 44 (1) (2010).
31. S. Zhang, M. Wang, A nonconforming finite element method for the Cahn-Hilliard equation, Journal of Computational Physics 229 (2010) 7361-7372.