An efficient moving mesh spectral method for the phase-field model of two-phase flows

Journal of Computational Physics

Volumn 228, Issue 8, 2009, Pages 2978-2992

  Shen, Jie ^a   Yang, Xiaofeng ^b  

^a PURDUE UNIVERSITY   (United States)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Moving mesh; Phase field; Spectral method; Two phase flow

Indexed keywords

MESH GENERATION; NUMERICAL METHODS; PHASE INTERFACES;

IMPLICIT TREATMENT; MOVING MESH; NON-PERIODIC BOUNDARIES; PERIODIC BOUNDARY CONDITIONS; PHASE FIELD MODELS; PHASE FIELDS; PHASE FUNCTIONS; SEMI-IMPLICIT; SPECTRAL METHODS; TWO PHASES FLOW;

TWO PHASE FLOW;

EID: 61349169522     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.01.009     Document Type: Article

References (26)

1. Allen S.M., and Cahn J.W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. Mater. 27 (1979) 1085-1095
2. Anderson D.M., McFadden G.B., and Wheeler A.A. Diffuse-interface methods in fluid mechanics. Ann. Rev. Fluid. Mech. 30 (1998) 139-165
3. Bernardi C., and Maday Y. Approximations Spectrales de Problèmes aux Limites Elliptiques (1992), Springer-Verlag, Paris
4. Brackbill J.U. An adaptive grid with directional control. J. Comput. Phys. 108 1 (1993) 38-50
5. Cao W., Huang W., and Russell R.D. A study of monitor functions for two-dimensional adaptive mesh generation. SIAM J. Sci. Comput. 20 6 (1999) 1978-1994 (Electronic)
6. Ceniceros H.D., and Hou T.Y. An efficient dynamically adaptive mesh for potentially singular solutions. J. Comput. Phys. 172 (2001) 609-639
7. Chen L.Q. Phase-field models for microstructure evolution. Ann. Rev. Mater. Res. 32 (2002) 113
8. Chen L.Q., and Shen J. Applications of semi-implicit Fourier-spectral method to phase-field equations. Comput. Phys. Commun. 108 (1998) 147-158
9. Di Y., Li R., and Tang T. A general moving mesh framework in 3d and its application for simulating the mixture of multi-phase flows. Commun. Comput. Phys. 3 (2008) 582-602
10. Feng J.J., Liu C., Shen J., and Yue P. An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. IMA Vol. Math. Appl. 140 (2005) 1-26
11. Feng W.M., Yu P., Hu S.Y., Liu Z.K., Du Q., and Chen L.Q. Spectral implementation of an adaptive mesh method for phase-field equation. J. Comput. Phys. 220 (2006) 498-510
12. Feng W.M., Yu P., Hu S.Y., Liu Z.K., Du Q., and Chen L.Q. A Fourier spectral mesh method for the Cahn-Hilliard equation with elasticity. Commun. Comput. Phys. 5 (2009) 582-599
13. Guermond J.L., Minev P., and Shen J. An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195 (2006) 6011-6045
14. Huang W. Practical aspects of formulation and solution of moving mesh partial differential equations. J. Comput. Phys. 171 (2001) 753-775
15. Huang W. Variational mesh adaptation: isotropy and equidistribution. J. Comput. Phys. 174 2 (2001) 903-924
16. Huang W., Ren Y., and Russell R.D. Moving mesh methods based on moving mesh partial differential equations. J. Comput. Phys. 113 2 (1994) 279-290
17. Li R., Tang T., and Zhang P. Moving mesh methods in multiple dimensions based on harmonic maps. J. Comput. Phys. 170 2 (2001) 562-588
18. Liu C., and Shen J. A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Physica D 179 3-4 (2003) 211-228
19. Lowengrub J., and Truskinovsky L. Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Roy. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 1978 (1998) 2617-2654
20. Shen J. Efficient spectral-Galerkin method I. Direct solvers for second- and fourth-order equations by using Legendre polynomials. SIAM J. Sci. Comput. 15 (1994) 1489-1505
21. Shen J. On error estimates of the penalty method for the unsteady Navier-Stokes equations. SIAM J. Numer. Anal. 32 (1995) 386-403
22. Jie Shen, Efficient Chebyshev-Legendre Galerkin methods for elliptic problems, in: A.V. Ilin, R. Scott (Eds.), Proceedings of ICOSAHOM'95, Houston J. Math, 1996, pp. 233-240.
23. Vandeven H. Family of spectral filters for discontinuous problems. J. Sci. Comput. 6 2 (1991) 159-192
24. Winslow A.M. Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. J. Comput. Phys. 1 (1967) 149-172
25. Yang X., Feng J.J., Liu C., and Shen J. Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. J. Comput. Phys. 218 (2006) 417-428
26. Yue P., Feng J.J., Liu C., and Shen J. A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515 (2004) 293-317