Efficient implementation of THINC scheme: A simple and practical smoothed VOF algorithm

Journal of Computational Physics

Volumn 226, Issue 2, 2007, Pages 1985-2002

  Yokoi, Kensuke ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CHIBA UNIVERSITY   (Japan)

Author keywords

Advection scheme; Interface capturing; Multi phase flow; Volume of fluid

Indexed keywords

HYPERBOLIC FUNCTIONS;

ADVECTION SCHEME; EFFICIENT IMPLEMENTATION; INTERFACE CAPTURING SCHEME; INTERFACE-CAPTURING; MULTI DIMENSIONS; MULTI-PHASE FLOWS; SIMPLE++; TANGENT OF HYPERBOLA FOR INTERFACE CAPTURING; VOLUME OF FLUID ALGORITHMS; VOLUME OF FLUIDS;

ADVECTION;

EID: 34548671841     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.06.020     Document Type: Article

References (54)

1. Xiao F., Honma Y., and kono T. A simple algebraic interface capturing scheme using hyperbolic tangent function. Int. J. Numer. Meth. Fluid. 48 (2005) 1023
2. Unverdi S.O., and Tryggvason G. A front tracking method for viscous, incompressible multi-fluid flow. J. Comput. Phys. 100 (1992) 25
3. Glimm J., et al. Front tracking in two and three dimensions. J. Comput. Mech. 7 (1998) 1
4. Osher S., and Sethian J.A. Front propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys. 79 (1988) 12
5. Sussman M., Smereka P., and Osher S. A level set approach for capturing solution to incompressible two-phase flow. J. Comput. Phys. 114 (1994) 146
6. Sussman M., and Smereka P. Axisymmetric free boundary problems. J. Fluid Mech. 341 (1997) 269
7. Sussman M., and Fatemi E. An efficient, interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput. 20 (1999) 1165
8. Sethian J.A. Level Set Methods and Fast Marching Methods (1999), Cambridge University Press
9. 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) 301-337
10. Yokoi K. Numerical method for complex moving boundary problems in a Cartesian fixed grid. Phys. Rev. E 65 (2002) 055701R
11. Enright D., Fedkiw R., Ferziger J., and Mitchell I. A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183 (2002) 83-116
12. Osher S., and Fedkiw R. Level set methods and dynamics implicit surface. Applied Mathematical Sciences vol. 153 (2003), Springer
13. Noh W.F., and Woodward P. SLIC (simple line interface method). Lecture Notes in Physics 24 (1976) 330
14. Hirt C.W., and Nichols B.D. Volume of fluid (VOF) methods for the dynamic of free boundaries. J. Comput. Phys. 39 (1981) 201
15. Youngs D.L. Time-dependent multi-material flow with large fluid distortion. In: Morton K.W., and Baines M.J. (Eds). Numerical Methods for Fluid Dynamics vol. 24 (1982), Academic Press, New York 273-285
16. Lafaurie B., Nardone C., Scardovelli R., Zaleski S., and Zanetti G. Modeling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113 (1994) 134-147
17. Rudman M. Volume-tracking method for interfacial flow calculations'. Int. J. Numer. Meth. Fluids 24 (1997) 679-691
18. Rider W.J., and Kothe D.B. Reconstructing volume tracking. J. Comput. Phys. 141 (1998) 112
19. Scardovelli R., and Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31 (1999) 567-603
20. Li J., Renardy Y., and Renardy M. Numerical simulation of breakup of a viscous drop in simple shear flow with a volume-of-fluid method. Phys. Fluids 12 (2000) 269-282
21. Harvie D.J.E., and Fletcher D.F. A new volume of fluid advection algorithm: the stream scheme. J. Comput. Phys. 162 (2000) 1-32
22. Harvie D.J.E., and Fletcher D.F. A new volume of fluid advection algorithm: the defined donating region scheme. Int. J. Numer. Meth. Fluids 35 (2001) 151-172
23. Renardy Y., and Cristini V. Effect of inertia on drop breakup under shear. Phys. Fluids 13 (2001) 7
24. Renardy Y., Renardy M., and Cristini V. A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio. Eur. J. Mech. B/Fluids 21 (2002) 49
25. Renardy Y., Cristini V., and Li J. Drop fragment distribution under shear with inertia. Int. J. Multiphase Flow 28 (2002) 1125-1147
26. Khismatullin D., Renardy Y., and Cristini V. Inertia-induced breakup of highly viscous drops subjected to simple shear. Phys. Fluids 15 (2003) 1351
27. 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) 611-639
28. Lopez J., Hernandez J., Gomez P., and Faura F. A volume of fluid method based on multidimensional advection and spline interface reconstruction. J. Comput. Phys. 195 (2004) 718-742
29. Aulisa E., Manservisi S., Scardovelli R., and Zaleski S. A geometrical area-preserving volume-of-fluid advection method. J. Comput. Phys. 192 (2004) 355-364
30. 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. Comput. Phys. 197 (2004) 555-584
31. Pilliod J.E., and Puckett E.G. Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J. Comput. Phys. 199 (2004) 465-502
32. Cristini V., and Tan Y.C. Theory and numerical simulation of droplet dynamics in complex flows. Lab Chip 4 (2004) 257
33. Lopez J., Hernandez J., Gomez P., and Faura F. An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows. J. Comput. Phys. 208 (2005) 51-74
34. Yang X., James A.J., Lowengrub J., Zheng X., and Cristini V. An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. J. Comput. Phys. 217 2 (2006) 364-394
35. Cristini V., and Renardy Y. Scalings for droplet sizes in shear-driven breakup: non-microfluidic ways to monodisperse emulsions. Fluid Dyn. Mater. Process. 2 2 (2006)
36. E. Aulisa, S. Manservisi, R. Scardovelli, S. Zaleski, Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry, J. Comput. Phys., in press. doi:10.1016/j.jcp.2007.03.015.
37. Fedkiw R., Aslam T., Merriman B., and Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152 (1999) 457-492
38. Yokoi K. Numerical method for moving solid object in flows. Phys. Rev. E 67 (2003) 045701R
39. 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
40. Sussman M., Smith K.M., Hussaini M.Y., Ohta M., and Zhi-Wei R. A sharp interface method for incompressible two-phase flows. J. Comput. Phys. 221 (2007) 469-505
41. Zalesak S.T. Fully multi-dimensional flux corrected transport algorithm for fluid flow. J. Comput. Phys. 31 (1979) 335
42. Bell J.B., Colella P., and Glaz H.M. A second-order projection method of the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257
43. LeVeque R. High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33 (1996) 627-665
44. Tanaka R., Nakamura T., and Yabe T. Constructing exactly conservative scheme in a non-conservative form. Comput. Phys. Commun. 126 (2000) 232
45. Yabe T., Xiao F., and Utsumi T. Constrained interpolation profile method for multiphase analysis. J. Comput. Phys. 169 (2001) 556
46. Xiao F., Yabe T., Peng X., and Kobayashi H. Conservative and oscillation-less atmospheric transport schemes based on rational functions. J. Geophys. Res. 107 (2002) 4609
47. Xiao F., Ikebata A., and Hasegawa T. Numerical simulations of free-interface fluids by a multi integrated moment method. Comp. Struct. 83 (2005) 409-423
48. Xiao F., Akoh R., and Ii S. Unified formulation for compressible and incompressible flows by using multi integrated moments II: multi-dimensional version for compressible and incompressible flows. J. Comput. Phys. 213 (2006) 31-56
49. Daly B.J. Numerical study of the effect of surface tension on interface instability. Phys. Fluids 12 (1969) 1340
50. Brackbill J.U., Kothe D.B., and Zemach C. A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 335
51. Gerlach D., Tomar G., Biswas G., and Durst F. Comparison of volume-of-fluid methods for surface tension-dominant two-phase flows. Int. J. Heat Mass Transfer 49 (2006) 740
52. Bellman R., and Pennington R.H. Effect of surface tension and viscosity on Taylor instability. Quart. Appl. Meth. 12 12 (1954) 151
53. Drazin P.G., and Reid W.H. Hydrodynamic Stability (1967), Cambridge University Press, Cambridge, UK
54. K. Yokoi, A numerical method for free-surface flows and its application to droplet impact on a thin liquid layer, J. Sci. Comp., submitted for publication.