Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement

International Journal for Numerical Methods in Fluids

Volumn 45, Issue 9, 2004, Pages 921-944

  Kohno, Haruhiko ^a   Tanahashi, Takahiko ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Adaptive mesh refinement; GSMAC; Level set method; Marangoni effect; Moving free surface; Surface tension

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; INTERPOLATION;

ADAPTIVE MESH REFINEMENT; MARANGONI EFFECT;

NUMERICAL ANALYSIS;

MARANGONI EFFECT;

EID: 3242714276     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.715     Document Type: Article

References (36)

1. Cröll A, Kaiser Th, Schweizer M, Danilewsky AN, Lauer S, Tegetmeier A, Benz KW. Floating-zone and floating-solution-zone growth of GaSb under microgravity. Journal of Crystal Growth 1998; 191:365-376.
2. Davidson PA. An Introduction to Magnetohydrodynamics (1st edn). Cambridge University Press: Cambridge, 2001; 387-404.
3. Floryan JM, Rasmussen H. Numerical methods for viscous flows with moving boundaries. Applied Mechanics Reviews 1989; 42:323-341.
4. Harlow FH, Welch JE. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids 1965; 8:2182-2189.
5. Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 1981; 39:201-225.
6. Nichols BD, Hirt CW, Hotchkiss RS. SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries. Los Alamos Scientific Laboratory Report, LA-8355, 1980.
7. Jeong JH, Yang DY. Finite element analysis of transient fluid flow with free surface using VOF (Volume-of-Fluid) method and adaptive grid. International Journal for Numerical Methods in Fluids 1998; 26:1127-1154.
8. Kim MS, Lee WI. A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: new free surface-tracking algorithm and its verification. International Journal for Numerical Methods in Fluids 2003; 42:765-790.
9. Osher S, Sethian JA. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 1988; 79:12-49.
10. Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics 1994; 114:146-159.
11. Chang YC, Hou TY. Merriman B, Osher S. A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. Journal of Computational Physics 1996; 124:449-464.
12. Himeno T, Watanabe T, Konno A. Numerical analysis for propellant management in liquid rocket tank. AIAA 2001; 01:3822.
13. Iafrati A, Mascio AD, Campana EF. A level set technique applied to unsteady free surface flows. International Journal for Numerical Methods in Fluids 2001; 35:281-297.
14. Tezduyar T, Aliabadi S, Behr M. Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Computer Methods in Applied Mechanics and Engineering 1998; 155: 235-248.
15. Sochnikov V, Efrima S. Level set calculations of the evolution of boundaries on a dynamically adaptive grid. International Journal for Numerical Methods in Engineering 2003; 56:1913-1929.
16. Hirt CW, Amsden AA, Cook JL. An arbitrary Lagrangian-Eulerian computing method for all speeds. Journal of Computational Physics 1974; 14:227-253.
17. Ramaswamy B, Kawahara M. Arbitrary Lagrangian-Eulerian finite element method for unsteady, convective, incompressible viscous free surface fluid flow. International Journal for Numerical Methods in Fluids 1987; 7: 1053-1075.
18. Jung CH, Minowa T, Tanahashi T. Numerical analysis of molten metal under magnetic field using ALE method. JSME International Journal Series A 2002; 45:153-160.
19. Metzger J, Schwabe D. Coupled buoyant and thermocapillary convection. PhysicoChemical Hydrodynamics 1988; 10:263-282.
20. Lan CW, Kou S. Heat transfer, fluid flow and interface shapes in floating-zone crystal growth. Journal of Crystal Growth 1991; 108:351-366.
21. Frank S, Schwabe D. Temporal and spatial elements of thermocapillary convection in floating zones. Experiments in Fluids 1997; 23:234-251.
22. Zeng Z, Mizuseki H, Higashino K, Kawazoe Y. Direct numerical simulation of oscillatory Marangoni convection in cylindrical liquid bridges. Journal of Crystal Growth 1999; 204:395-404.
23. Sumiji M, Nakamura S, Azami T, Hibiya T. Optical observation of solid-melt interface fluctuation due to Marangoni flow in a silicon liquid bridge. Journal of Crystal Growth 2001; 223:503-511.
24. Imaishi N, Yasuhiro S, Akiyama Y. Yoda S. Numerical simulation of oscillatory Marangoni flow in half-zone liquid bridge of low Prandtl number. Journal of Crystal Growth 2001; 230:164-171.
25. Tanahashi T, Okanaga H, Saito T. GSMAC finite element method for unsteady incompressible Navier Stokes equations at high Reynolds numbers. International Journal for Numerical Methods in Fluids 1990; 11: 479-499.
26. Tanahashi T, Oki Y, Henjes K. An application of GSMAC-FEM to electrically conducting fluid flows driven by Lorentz force. International Journal of Computational Fluid Dynamics 1993; 1:233-248.
27. Fujieda T, Tanahashi T. Finite element analysis of visco-elastic flow under high shear rate using the GSMAC-method. International Journal of Computational Fluid Dynamics 2000; 13:203-210.
28. Fujieda T, Wada S, Tanahashi T. Unified solution algorithm for solids and fluids. JSME International Journal Series B 2001; 44:179-187.
29. Yabe T, Wang PY. Unified numerical procedure for compressible and incompressible fluid. Journal of the Physical Society of Japan 1991; 60:2105-2108.
30. Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. Journal of Computational Physics 1992; 100:335-354.
31. Hirt CW, Nichols BD, Romero NC. SOLA: a numerical solution algorithm for transient fluid flow. Los Alamos Scientific Laboratory Report, LA-5852, 1975.
32. Makihara T, Kakuta Y, Tanahashi T. The GSMAC-CIP method. Computational Fluid Dynamics Journal 1999; 8:19-25.
33. Makihara T, Shibata E, Tanahashi T. Application of the GSMAC-CIP method to incompressible Navier-Stokes equations at high Reynolds numbers. International Journal of Computational Fluid Dynamics 1999; 12: 301-314.
34. Zienkiewicz OC, Taylor RL. The Finite Element Method-Volume 3 Fluid Dynamics (5th edn). Butterworth-Heinemann: London, 2000; 169-217.
35. Koshizuka S, Oka Y. Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nuclear Science and Engineering 1996; 123:421-434.
36. Kohno H, Tanahashi T. An application of GSMAC-FEM to coupled natural and Marangoni convection in a square cavity. International Journal of Computational Fluid Dynamics, submitted.