A sharp interface method for incompressible two-phase flows

Journal of Computational Physics

Volumn 221, Issue 2, 2007, Pages 469-505

  Sussman, M ^a   Smith, K M ^a   Hussaini, M Y ^a   Ohta, M ^a   Zhi Wei, R ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Immiscible fluids; Incompressible flow; Multiphase flows; Navier Stokes equations; Numerical methods

Indexed keywords

DENSITY OF GASES; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; PHASE INTERFACES; TWO PHASE FLOW;

GAS PRESSURES; IMMISCIBLE FLUIDS; IMMISCIBLE TWO-PHASE FLOWS; LARGE DENSITY RATIO; LEVEL SET; NAVIER-STOKES EQUATION; SHARP INTERFACE METHODS; TWO PHASES FLOW; VISCOSITY RATIOS; VOLUME OF FLUID TECHNIQUE;

NUMERICAL METHODS;

EID: 33846504341     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.06.020     Document Type: Article

References (60)

1. I. Aleinov, E.G. Puckett, Computing surface tension with high-order kernels, in: Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Lake Tahoe, CA, 1995.
2. Almgren A.S., Bell J.B., Colella P., Howell L.H., and Welcome M. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142 (1998) 1-46
3. 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. Comp. Phys. 188 (2003) 611
4. Aulisa E., Manservisi S., and Scardovelli R. A surface marker algorithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking. J. Comp. Phys. 197 2 (2004) 555-584
5. Bell J.B., Colella P., and Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 December (1989) 257-283
6. Bell J.B., and Marcus D.L. A second-order projection method for variable-density flows. J. Comput. Phys. 101 (1992) 334-348
7. Bhaga D., and Weber M.E. Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech. 105 (1981) 61-85
8. A. Bourlioux, A coupled level-set volume-of-fluid algorithm for tracking material interfaces, in: Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Lake Tahoe, CA, 1995.
9. Brackbill J.U., Kothe D.B., and Zemach C. A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 335-353
10. Bradford S., and Katopodes N.D. Hydrodynamics of turbid underflows. Part II: aggradation, avulsion and channelization. Journal of Hydraulic Engineering, ASCE 125 10 (1999) 1016-1028
11. Caboussat A., Picasso M., and Rappaz J. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J. Comput. Phys. 203 2 (2005) 626-649
12. Chang Y.C., Hou T.Y., Merriman B., and Osher S. Eulerian capturing methods based on a level set formulation for incompressible fluid interfaces. J. Comput. Phys. 124 (1996) 449-464
13. Chorin A.J. Curvature and solidification. J. Comput. Phys. 57 (1985) 472-490
14. Craft T.J., Kidger J.W., and Launder B.E. Three dimensional modelling of turbulent free-surface jets. In: Rodi W., and Laurence D. (Eds). Engineering Turbulence Modelling and Measurements, vol. 4 (1999), Elsevier, Amsterdam 73-82
15. D.G. Dommermuth, M. Gharib, H. Huang, G.E. Innis, P. Maheo, E.A. Novikov, J.C. Talcott, D.C. Wyatt, Turbulent free-surface flows: a comparison between numerical simulations and experimental measurements, in: Proceedings of the 21st Symposium on Naval Hydro, Trondheim, 1996, pp. 249-265.
16. Enright D., Fedkiw R., Ferziger J., and Mitchell I. A hybrid particle level set method for improved interface capturing. J. Comp. Phys. 183 1 (2002) 83-116
17. D. Enright, S. Marschner, R. Fedkiw, Animation and rendering of complex water surfaces, in: SIGGRAPH 2002, volume ACM TOG 21, 2002, pp. 736-744.
18. Francois M., Cummins S., Dendy E., Kothe D., Sicilian J., and Williams M. A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213 1 (2006) 141-173
19. Gibou F., Fedkiw R., Cheng L.-T., and Kang M. A second order accurate symmetric discretization of the poisson equation on irregular domains. J. Comput. Phys. 176 (2002) 205-227
20. Gueyffier D., Li J., Nadim A., Scardovelli R., and Zaleski S. Volume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys. 152 (1999) 423-456
21. Helenbrook B., Martinelli L., and Law C. A numerical method for solving incompressible flow problems with a surface of discontinuity. Journal of Computational Physics 148 (1999) 366-396
22. J. Helmsen, P. Colella, E.G. Puckett, Non-convex profile evolution in two dimensions using volume of fluids, LBNL Technical Report LBNL-40693, Lawrence Berkeley National Laboratory, 1997.
23. Helsby F.W., and Tuson K.R. Behaviour of air bubbles in aqueous solutions. Research 8 (1955) 270
24. Hieber S., and Koumoutsakos P. A Lagrangian particle level set method. Journal of Computational Physics 210 1 (2005) 342-367
25. Hnat J.G., and Buckmaster J.D. Spherical cap bubbles and skirt formation. Physics of Fluids 19 2 (1976) 182-194
26. Kang M., Fedkiw R., and Liu X.-D. A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 15 (2000) 323-360
27. Lamb H. Hydrodynamics (1932), Dover Publications, New York
28. Liu H., Krishnan S., Marella S., and Udaykumar H.S. Sharp interface cartesian grid method II: a technique for simulating droplet interactions with surfaces of arbitrary shape. J. Computational Physics 210 1 (2005) 32-54
29. Lorstad D., and Fuchs L. High-order surface tension VOF-model for 3D bubble flows with high density ratio. Journal of Computational Physics 200 1 (2004) 153-176
30. Marchandise E., Remacle J.-F., and Chevaugeon N. A quadrature-free discontinuous Galerkin method for the level set equation. Journal of Computational Physics 212 1 (2006) 338-357
31. Minion M.L. On the stability of Godunov-projection methods for incompressible flow. J. Comput. Phys. 123 2 (1996) 435-449
32. Nguyen D., Fedkiw R., and Kang M. A boundary condition capturing method for incompressible flame discontinuities. J. Comput. Phys. 172 (2001) 71-98
33. Pilliod J.E., and Puckett E.G. Second-order accurate volume-of-fluid algorithms for tracking material interfaces. Journal of Computational Physics 199 2 (2004) 465-502
34. Poo J.Y., and Ashgriz N. A computational method for determining curvatures. J. Comput. Phys. 84 (1989) 483-491
35. Popinet S., and Zaleski S. A front-tracking algorithm for accurate representation of surface tension. International Journal for Numerical Methods in Fluids 30 6 (1999) 775-793
36. H. Rasmussen, A. Bach, O. Hassager, 3D transient free surface viscoelastic flow, in: XIIth International Workshop on Numerical Methods for Non-Newtonian Flows, Abstracts, June, 2001, Monterray Bay, USA.
37. Renardy Y., and Renardy M. Prost: A parabolic reconstruction of surface tension for the volume-of-fluid method. J. Comput. Phys. 183 2 (2002) 400-421
38. Rudman M. A volume tracking method for interfacial flows with large density variations. Int. J. Numer. Methods Fluids 28 (1998) 357-378
39. Ryskin G., and Leal L.G. Numerical solution of free boundary problems in fluid mechanics. Part 2 buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech. 148 (1984) 19-35
40. Scardovelli R., and Zaleski S. Interface reconstruction with least-square fit and split Eulerian-Lagrangian advection. Int. J. Numer. Meth. Fluids 41 (2003) 251-274
41. Shin S., and Juric D. Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J. Comp. Phys. 180 2 (2002) 427-470
42. Shu C.-W., and Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes, ii. J. Comput. Phys. 83 (1989) 32-78
43. Strain J. Tree methods for moving interfaces. J. Comput. Phys. 151 2 (1999) 616-648
44. Strang G. On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 506-517
45. Sussman M. A second order coupled levelset and volume of fluid method for computing growth and collapse of vapor bubbles. Journal of Computational Physics 187 (2003) 110-136
46. Sussman M. A parallelized, adaptive algorithm for multiphase flows in general geometries. Computers and Structures 83 (2005) 435-444
47. Sussman M., Almgren A., Bell J., Colella P., Howell L., and Welcome M. An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148 (1999) 81-124
48. M. Sussman, D. Dommermuth, The numerical simulation of ship waves using cartesian grid methods, in: Proceedings of the 23rd Symposium on Naval Hydrodynamics, September, 2000, Val-De-Reuel, France.
49. Sussman M., and Hussaini M.Y. A discontinuous spectral element method for the level set equation. J. Scientific Computing 19 (2003) 479-500
50. 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. Comp. Phys. 162 (2000) 301-337
51. Sussman M., Smereka P., and Osher S.J. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1994) 146-159
52. O. Tatebe, The multigrid preconditioned conjugate gradient method, in: 6th Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO, April 4-9, 1993.
53. Unverdi S.O., and Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100 (1992) 25-37
54. van Leer B. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 101-136
55. M. Williams, D. Kothe, E.G. Puckett, Convergence and accuracy of kernel-based continuum surface tension models, in: Proceedings of the 13th U.S. National Congress of Applied Mechanics, Gainesville, FL, June 16-21, 1998.
56. Wu J. Wind-induced drift currents. J. Fluid Mech. 68 (1975) 49-70
57. Yang B., and Prosperetti A. A second-order boundary-fitted projection method for free-surface flow computations. J. Comput. Phys. 213 (2006) 574-590
58. X. Yang, A. James, J. Lowengrub, X. Zheng, V. Cristini, An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids, J. Comput. Phys. (in press), doi:10.1016/j.jcp.2006.01.007.
59. Yang Y., and Tryggvason G. Dissipation of energy by finite amplitude surface waves. Computers and Fluids 27 (1998) 829-845
60. Ye T., Shyy W., and Chung J.N. A fixed-grid, sharp interface method for bubble dynamics and phase change. J. Comp. Phys. 174 (2001) 781-815