A least-squares/finite element method for the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line

Journal of Computational Physics

Volumn 230, Issue 12, 2011, Pages 4991-5009

  He, Qiaolin ^a,b   Glowinski, Roland ^b,c   Wang, Xiao Ping ^b  

^a SICHUAN UNIVERSITY   (China)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c University of Houston   (United States)

Author keywords

Cahn Hilliard; Conjugate gradient; Contact line; Least squares; Navier Stokes; Operator splitting

Indexed keywords

LEAST SQUARES APPROXIMATIONS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS;

CAHN-HILLIARD; CAHN-HILLIARD SYSTEMS; CONJUGATE GRADIENT; CONTACT LINES; LEAST SQUARE; LEAST SQUARES FINITE ELEMENT METHODS; NAVIER STOKES; NUMERICAL SOLUTION; OPERATOR-SPLITTING; SYSTEM MODELS;

FINITE ELEMENT METHOD;

EID: 79955646429     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.03.022     Document Type: Article

References (30)

1. Vollmayr-Lee B.P. Fast and accurate coarsening simulation with an unconditionally stable time step. Phys. Rev. E 2003, 68(8):066703.
2. E. Dean, R. Glowinski, T.-W. Pan, A wave equation approach to the numerical simulation of incompressible viscous fluid flow modeled by the Navier-Stokes equations, in: J.A. de Santo (Ed.), Mathematical and Numerical Aspects of Wave Propagation, SIAM, Philadelphia, 1998, pp. 65-74.
3. Dean E., Glowinski R., Trevas D. An approximate factorization/least-squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation. Jpn. J. Ind. Appl. Math. 1996, 13(3):495-517.
4. Di Y., Wang X. Precursor simulations in spreading using a multi-mesh adaptive finite element method. J. Comput. Phys. 2009, 228:1380-1390.
5. Mello E.V.L. Numerical study of the Cahn-Hilliard equations in one, two and three dimensions. Phys. A 2005, 347:429-443.
6. D.J. Eyre, Unconditionally gradient stable time marching the Cahn-Hilliard equation, in: J. Bullard, R. Kalia, M. Stoneham, L.-Q. Chen (Eds.), Computational and Mathematical Models of Microstructural Evolution, The Materials Research Society, 1998a.
7. D.J. Eyre, An unconditionally stable one step scheme for gradient systems, Unpublished article, 1998b.
8. Furihata D. Finite difference schemes for ∂u∂t=∂∂xαδgδu that inherit energy conservation or dissipation property. J. Comput. Phys. 1999, 156:181-205.
9. Furihata D. A stable and conservative finite difference scheme for the Cahn-Hilliard equation. Numer. Math. 2001, 87(4):675-699.
10. Glowinski R. Numerical Methods for Nonlinear Variational Problems 1984, Springer, New York, NY.
11. R. Glowinski, Finite element methods for incompressible viscous flow, in: Handbook of Numerical Analysis, vol. 9, North-Holland, Amsterdam, 2003, pp. 3-1176.
12. Glowinski R., Guidoboni G., Pan T.-W. Wall-driven incompressible viscous flow in a two-dimensional semi-circular cavity. J. Comput. Phys. 2006, 216(1):76-91.
13. Glowinski R., Keller H.B., Reinhart L. Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems. SIAM J. Sci. Stat. Comp. 1985, 4(6):793-832.
14. He Y., Liu Y., Tang T. On large time-stepping methods for the Cahn-Hilliard equation. Appl. Numer. Math. 2007, 57:616-628.
15. Choi J.W., Lee H.G. An unconditionally gradient stable numerical method for solving the Allen-Chan equation. Phys. A 2009, 388:1791-1803.
16. Koplik J., Banavar J.R., Willemsen J.F. Molecular dynamics of poiseuille flow and moving cantact lines. Phys. Rev. Lett. 1988, 60:1282-1285.
17. Koplik J., Banavar J.R., Willemsen J.F. Molecular dynamics of fluid flow at solid surfaces. Phys. Fluids A 1989, 1:781-794.
18. Du Q. Numerical analysis of a continuum model of phase transition. SIAM J. Numer. Anal. 1991, 28(5):1310-1322.
19. Qian T., Wang X., Sheng P. Molecular scale contact line hydrodynamics of immiscible flows. Phys. Rev. E 2003, 68:016306.
20. Qian T., Wang X., Sheng P. Power-law slip profile of the moving contact line in two phase immiscible flows. Phys. Rev. Lett. 2004, 63:094501.
21. Qian T., Wang X., Sheng P. A variational approach to the moving contact line hydrodynamics. J. Fluid Mech. 2006, 564:333-360.
22. Glowinski R. Numerical Methods for Nonlinear Variational Problems 2008, Springer.
23. Shen J., Yang X. A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. SIAM J. Sci. Comput. 2010, 32(3):1159-1179.
24. Wise S.M., Wang C. An energy-stable and convergent finite-difference scheme for the phase field crystal equation. SIAM J. Numer. Anal. 2009, 47(3):2269-2288.
25. Sun Z. A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation. Math. Comp. 1995, 64(212):1463.
26. Thompson P.A., Brinckerhoff W., Robbins M.O. Microscopic studies of static and dynamic contact angles. J. Adhesion Sci. Tech. 1993, 7:535-554.
27. Thompson P.A., Robbins M.O. Simulations of contact-line motion: slip and the dynamic contact angle. Phys. Rev. Lett. 1989, 63:766-769.
28. Wang X., Qian T., Sheng P. Moving contact line on chemically patterned surfaces. J. Fluid Mech. 2008, 605:59-78.
29. Yang X., Feng J., Liu C., Shen J. Numerical simulation of jet pinching-off and drop formation using an energetic phase-field method. J. Comput. Phys. 2006, 218:417-428.
30. Hu Z., Wise S.M. Stable and efficient finite-difference nonlinear-multigrid schemes for the phase filed crystal equation. J. Comput. Phys. 2009, 228:5323-5339.