Sharp interface tracking using the phase-field equation

Journal of Computational Physics

Volumn 220, Issue 2, 2007, Pages 626-653

  Sun, Y ^a   Beckermann, C ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Curvature; Interface tracking; Interfacial flows; Phase field method

Indexed keywords

NONLINEAR EQUATIONS; NUMERICAL METHODS; PHASE INTERFACES; PHASE TRANSITIONS;

CURVATURE; INTERFACE MOTIONS; INTERFACE TRACKING; INTERFACE TRACKING METHOD; INTERFACIAL FLOWS; PHASE FIELD EQUATION; PHASE FIELD METHODS; PHASE FIELDS; SHARP INTERFACE; ZERO-PHASE;

ADVECTION;

EID: 33845666201     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.05.025     Document Type: Article

References (56)

1. Scardovelli R., and Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Ann. Rev. Fluid Mech. 31 (1999) 567
2. Osher S., and Sethian J.A. Fronts propagating with curvature-dependent speed: algorithm based on Hamilton-Jacobi formations. J. Comput. Phys. 79 (1988) 12
3. Sethian J.A. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Material Science (1999), Cambridge University Press
4. Osher S., and Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces (2002), Springer
5. Rider W.J., and Kothe D.B. Reconstructing volume tracking. J. Comput. Phys. 141 (1998) 112
6. Shu C.-W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439
7. Shu C.-W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes II. J. Comput. Phys. 83 (1989) 32
8. Harten A., Engquist B., Osher S., and Chakravarthy S.R. Uniformly high-order accurate essentially non-oscillatory schemes III. J. Comput. Phys. 131 (1997) 3
9. Pilliod Jr. J.E., and Puckett E.G. Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J. Comput. Phys. 199 (2004) 465
10. Renardy Y., and Renardy M. PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. J. Comput. Phys. 183 (2002) 400
11. Unverdi S.O., and Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100 (1992) 25
12. Aulisa E., Manservisi S., and Scardovelli R. A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows. J. Comput. Phys. 188 (2003) 611
13. Enright D., Fedkiw R., Ferziger J., and Mitchell I. A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183 (2002) 83
14. Anderson D.M., McFadden G.B., and Wheeler A.A. Diffuse-interface methods in fluid mechanics. Ann. Rev. Fluid Mech. 30 (1998) 139
15. Boettinger W.J., Warren J.A., Beckermann C., and Karma A. Phase-field simulation of solidification. Ann. Rev. Mater. Res. 32 (2002) 163
16. Beckermann C., Diepers H.-J., Steinbach I., Karma A., and Tong X. Modeling melt convection in phase-field simulations of solidification. J. Comput. Phys. 154 (1999) 468
17. Tan L., and Zabaras N. A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods. J. Comput. Phys. 211 (2006) 36
18. Olsson E., and Kreiss G. A conservative level set method for two phase flow. J. Comput. Phys. 210 (2005) 225
19. Marella S., Krishnan S., Liu H., and Udaykumar H.S. Sharp interface Cartesian grid method I: an easily implemented technique for 3D moving boundary computations. J. Comput. Phys. 210 (2005) 1
20. Liu H., Krishnan S., Marella S., and Udaykumar H.S. Sharp interface Cartesian grid method II: a technique for simulating droplet interactions with surface of arbitrary shape. J. Comput. Phys. 210 (2005) 32
21. Yang Y., and Udaykumar H.S. Sharp interface Cartesian grid method III: solidification of pure materials and binary solutions. J. Comput. Phys. 210 (2005) 55
22. Folch R., Casademunt J., and Hernández-Machado A. Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach. Phys. Rev. E 60 (1999) 1724
23. Biben T., Misbah C., Leyrat A., and Verdier C. An advected-field approach to the dynamics of fluid interfaces. Europhys. Lett. 63 (2003) 623
24. Biben T., and Misbah C. Tumbling of vesicles under shear flow within an advection-field approach. Phys. Rev. E 67 (2003) 031908
25. Beaucourt J., Rioual F., Seon T., Biben T., and Misbah C. Steady to unsteady dynamics of a vesicle in a flow. Phys. Rev. E 69 (2004) 011906
26. Steinbach I., Beckermann C., Kauerauf B., Li Q., and Guo J. Three-dimensional modeling of equiaxed dendritic growth on a mesoscopic scale. Acta Mater. 47 (1999) 971
27. Karma A., and Rappel W.-J. Phase-field model for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys. Rev. E 53 (1996) R3017
28. Jacqmin D. Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1999) 96
29. Pismen L.M. Mesoscopic hydrodynamics of contact line motion. Colloid Surf. A 206 (2002) 11
30. 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 (2003) 211
31. Badalassi V.E., Ceniceros H.D., and Banerjee S. Computation of multiphase systems with phase field models. J. Comput. Phys. 190 (2003) 371
32. Yue P., Feng J.J., Liu C., and Shen J. A diffuse-interface method for simulating two-phase flows of complex methods. J. Fluid Mech. 515 (2004) 293
33. Sun Y., and Beckermann C. Phase-field simulation of two-phase micro-flows in a Hele-Shaw cell. In: Mammoli A.A., and Brebbia C.A. (Eds). Computational Methods in Multiphase Flow III (2005), WIT Press, UK 147-157
34. Sun Y., and Beckermann C. Diffuse interface modeling of two-phase flows based on averaging: mass and momentum equations. Physica D 198 (2004) 281
35. Glasner K. Nonlinear preconditioning for diffuse interfaces. J. Comput. Phys. 174 (2001) 695
36. Gómez P., Hernández J., and López J. On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows. Int. J. Numer. Meth. Eng. 63 (2005) 1478
37. Ramirez J.C., and Beckermann C. Examination of binary alloy free dendritic growth theories with a phase-field model. Acta Mater. 53 (2005) 1721
38. Sethian J.A. Curvature and the evolution of fronts. Commun. Math. Phys. 101 (1985) 487
39. Sethian J.A. Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws. J. Diff. Geom. 31 (1990) 131
40. Chopp D.L., and Sethian J.A. Flow under curvature: singularity formation, minimal surfaces, and geodesics. Exp. Math. 2 (1993) 235
41. W.J. Rider, D.B. Kothe, Stretching and tearing interface tracking methods, in: 12th AIAA CFD Conference, AIAA 95-1717, 1995.
42. Rudman M. Volume-tracking methods for interfacial flow calculations. Int. J. Numer. Meth. Fluids 24 (1997) 671
43. Zalesak S.T. Fully multi-dimensional flux corrected transport algorithms for fluid flow. J. Comput. Phys. 33 (1979) 335
44. Bell J.B., Colella P., and Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257
45. Liu X.-D., and Osher S. Convex ENO high order schemes without field-by-field decomposition or staggered grids. J. Comput. Phys. 142 (1998) 304
46. López J., Hernández J., Gómez P., and Faura F. A volume of fluid method based on multidimensional advection and spline interface reconstruction. J. Comput. Phys. 195 (2004) 718
47. Enright D., Losasso F., and Fedkiw R. A fast and accurate semi-Lagrangian particle level set method. Comput. Struct. 83 (2005) 479
48. LeVeque R.J. High-resolution conservation algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33 (1996) 627
49. Sussman M., and Puckett E.G. A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162 (2000) 301
50. Karma A., and Rappel W.-J. Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E 57 (1998) 4323
51. Almgren R.F. Second-order phase field asymptotics for unequal conductivities. SIAM J. Appl. Math. 59 (1999) 2086
52. Kim Y.-T., Provatas N., Goldenfeld N., and Dantzig J. Universal dynamics of phase-field models for dendritic growth. Phys. Rev. E 59 (1999) R2546
53. Echebarria B., Folch R., Karma A., and Plapp M. Quantitative phase-field model of alloy solidification. Phys. Rev. E 70 (2004) 061604
54. Liu X.-D., Osher S., and Chan T. Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115 (1994) 200
55. Jiang G.-S., and Shu C.-W. Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1996) 202
56. Udaykumar H.S., Tran L., Belk D.M., and Vanden K.J. An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces. J. Comput. Phys. 186 (2003) 136