Multigrid computations and conservation law treatment of a sharp interface method

Numerical Heat Transfer, Part B: Fundamentals

Volumn 48, Issue 5, 2005, Pages 405-424

  Tai, Cheng Feng ^a   Shyy, Wei ^a,b  

^a UNIVERSITY OF FLORIDA   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; INTERFACES (MATERIALS); PRESSURE EFFECTS;

CARTESIAN GRIDS; FLUID DOMAINS; SHARP INTERFACE METHOD (SIM);

FLUID DYNAMICS;

EID: 27744495804     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407790500272095     Document Type: Article

References (32)

1. W. Shyy, H. S. Udaykumar, M. M. Rao, and R. W. Smith, Computational Fluid Dynamics with Moving Boundaries, Taylor & Francis, Washington, DC, 1996.
2. C. W. Hirt and B. D. Nichols, Volume of Fluid (VOF) Method for Thermodynamics of Free Boundaries, J. Comput. Phys., vol. 39, pp. 201-225, 1981.
3. M. Ni, M. Abdou, and S. Komori, A Variable-Density Projection Method for Interfacial Flows, Numer. Heat Transfer B, vol. 44, no. 6, pp. 553-574, 2003.
4. G. Caginalp, Applications of Field Theory to Statistical Mechanics, Springer-Verlag, Berlin, 1984.
5. D. S. Dandy and L. G. Leal, Buoyancy-Driven Motion of a Deformable Drop through a Quiescent Liquid at Intermediate Reynolds Numbers, J. Fluid Mech., vol. 208, pp. 161-192, 1989.
6. J. U. Brackbill, D. B. Kothe, and C. Zemach, A Continuum Method for Modeling Surface Tension, J. Comput. Phys., vol. 100, pp. 335-354, 1992.
7. L. Zheng and H. Zhang, An Adaptive Level Set Method for Moving-Boundary Problems: Application to Droplet Spreading and Solidification, Numer. Heat Transfer B, vol. 37, no. 4, pp. 437-454, 2000.
8. Z. Li and B. Soni, Fast and Accurate Numerical Approaches for Stefan Problems and Crystal Growth, Numer. Heat Transfer B, vol. 35, no. 4, pp. 461-484, 1999.
9. H. Zhang, L. L. Zheng, V. Prasad, and T. Y. Hou, Curvilinear Level Set Formulation for Highly Deformable Free Surface Problems with Application to Solidification, Numer. Heat Transfer B, vol. 34, no. 1, pp. 1-20, 1998.
10. G. Son, Efficient Implementation of a Coupled Level-Set and Volume-of-Fluid Method for Three-Dimensional Incompressible Two-Phase Flows, Numer. Heat Transfer B, vol. 43, no. 6, pp. 549-565, 2003.
11. G. Son, A Coupled Level Set and Volume-of-Fluid Method for the Buoyancy-Driven Motion of Fluid Particles, Numer. Heat Transfer B, vol. 42, no. 6, pp. 523-542, 2002.
12. D. M. Anderson and G. B. McFadden, A Diffuse-Interface Description of Internal Waves in a Near-Critical Fluid, Phys. Fluids, vol. 9, pp. 1870-1879, 1997.
13. C. S. Peskin, Numerical Analysis of Blood Flow in the Heart, J. Comput. Phys., vol. 25, pp. 220-252, 1977.
14. H. C. Kan, H. S. Udaykumar, W. Shyy, and R. Tran-Son-Tay, Hydrodynamics of a Compound Drop with Application to Leukocyte Modeling, Phys. Fluids, vol. 10, no. 4, pp. 760-774, 1998.
15. M. Francois and W. Shyy, Computations of Drop Dynamics with the Immersed Boundary Method, Numer. Heat Transfer B, vol. 44, pp. 101-118, 2003.
16. M. Francois, E. Uzgoren, J. Jackson, and W. Shyy, Multigrid Computations with the Immersed Boundary Technique for Multiphase Flows, Int. J. Numer. Meth. Heat Fluid Flow, vol. 14, pp. 98-115, 2004.
17. M. Francois and W. Shyy, Micro-Scale Drop Dynamics for Heat Transfer Enhancement, Prog. Aerospace Sci., vol. 38, pp. 275-304, 2002.
18. A. Esmaeeli and G. Tryggvason, Computations of Explosive Boiling in Microgravity, J. Sci. Comput., vol. 19, pp. 163-182, 2003.
19. S. Shin and D. Juric, Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking without Connectivity, J. Comput. Phys., vol. 180, pp. 427-470, 2002.
20. K. L. Pan, W. Shyy, and C. K. Law, An Immersed-Boundary Method for the Dynamics of Premixed Flame, Int. J. Heat Mass Transfer, vol. 45, pp. 3503-3516, 2002.
21. H. S. Udaykumar, R. Mittal, and W. Shyy, Computation of Solid-Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids, J. Comput. Phys., vol. 153, pp. 535-574, 1999.
22. H. S. Udaykumar, L. Mao, and R. Mittal, A Finite-Volume Sharp Interface Scheme for Dendritic Growth Simulations: Comparison with Microscopic Solvability Theory, Numer. Heat Transfer B, vol. 42, no. 5, pp. 389-409, 2002.
23. T. Ye, R. Mittal, H. S. Udaykumar, and W. Shyy, An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries, J. Comput. Phys., vol. 156, pp. 209-240, 1999.
24. T. Ye, W. Shyy, and J. N. Chung, A Fixed-Grid, Sharp-Interface Method for Bubble Dynamics and Phase Change, J. Comput. Phys., vol. 174, pp. 781-815, 2001.
25. T. Ye, Direct Numerical Simulation of a Translating Vapor Bubble with Phase Change, Ph.D. thesis, University of Florida, Gainesville, FL, 2001.
26. H. S. Udaykumar, R. Mittal, P. Rampuggoon, and A. Khanna, A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries, J. Comput. Phys., vol. 174, pp. 345-380, 2001.
27. T. Ye, W. Shyy, C. Tai, and J. Chung, Assessment of Sharp- and Continuous-Interface Methods for Drop in Static Equilibrium, Comput. Fluids, vol. 33, pp. 917-926, 2004.
28. J. Chorin, Numerical Solution of the Navier-Stokes Equations, Math. Comput., vol. 22, pp. 745-762, 1968.
29. J. Kim and P. Moin, Application of a Fractional Step Method to Incompressible Navier-Stokes Equations, J. Comput. Phys., vol. 59, pp. 308-323, 1985.
30. Y. Zang, R. L. Street, and J. R. Koseff, A Non-staggered Grid, Fractional Step Method for Time-Dependent Incompressible Navier-Stokes Equations in Curvilinear Coordinates, J. Comput. Phys., vol. 114, pp. 18-33, 1994.
31. W. Shyy, Computational Modeling for Fluid Flow and Interfacial Transport, Elsevier, Amsterdam, 1994.
32. U. Ghia, K. N. Ghia, and C. T. Shin, High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method, J. Comput. Phys., vol. 48, pp. 387-411, 1982.