Transient Schemes for Capturing Interfaces of Free-Surface Flows

REFERENCES

• J. Ha , P. W. Cleary , V. Alguine , and T. Nguyen , Simulation of Die Filling in Gravity Die Casting Using SPH and MAGMA Soft, in Proceedings of the Second International Conference on CFD in the Minerals and Process Industries, Melbourne, Australia, 1999.
   Google Scholar
• P. W. Cleary and J. Ha , Three-Dimensional Modeling of High Pressure Dies Casting, J. Cast Metals Res. , vol. 12, pp. 357–365, 2000.
   Web of Science ®Google Scholar
• M. Darwish and F. Moukalled , Convective Schemes for Capturing Interfaces of Free-Surface Flows on Unstructured Grids , Numer. Heat Transfer B , vol. 49 , pp. 19 – 42 , 2006 .
   Web of Science ®Google Scholar
• D. L. Youngs , An Interface Tracking Method for a 3D Eulerian Hydrodynamics Code, Tech. Rep. 44/92/35, Atomic Weapons Research Establishment, Harwell, UK, 1984.
   Google Scholar
• E. G. Puckett , A Volume of Fluid Interface Tracking Algorithm with Applications to Computing Shock Wave Rarefraction, in Proceedings of the Fourth International Symposium on Computational Fluid Dynamics, University of California at Davis, CA, 9–12 September, pp. 933–938, 1991.
   Google Scholar
• S. O. Unverdi and G. Tryggvason , A Front Tracking Method for Viscous, Incompressible Multi-fluid Flow , J. Comput. Phys. , vol. 100 , pp. 25 – 37 , 1992 .
   Web of Science ®Google Scholar
• W. F. Noh and P. Woodward , (SLIC, Simple Line Interface Calculations) , Lecture Notes Phys. , vol. 59 , pp. 330 – 340 , 1976 .
   Google Scholar
• M. Rudman , Volume Tracking Methods for Interfacial Flow Calculations , Int. J. Numer. Meth. Fluids , vol. 24 , pp. 671 – 691 , 1997 .
   Web of Science ®Google Scholar
• Y. Renardy and M. Renardy , PROST: Parabolic Reconstruction of Surface Tension for the Volume-of-Fluid Method , J. Comput. Phys. , vol. 183 , pp. 400 – 421 , 2002 .
   Web of Science ®Google Scholar
• Q. Chen , Y. Zhang , and M. Yang , An Interfacial Tracking Model for Convection-Controlled Melting Problems , Numer. Heat Transfer B , vol. 59 , pp. 209 – 225 , 2011 .
   Web of Science ®Google Scholar
• D. Z. Guo , D. L. Sun , Z. Y. Li , and W. Q. Tao , Phase Change Heat Transfer Simulation for Boiling Bubbles Arising from A Vapor Film by the Voset Method , Numer. Heat Transfer A , vol. 59 pp. 857 – 881 , 2011 .
   Web of Science ®Google Scholar
• W. Lee , G. Son , and J. J. Jeong , Numerical Analysis of Bubble Growth And Departure From A Microcavity , Numer. Heat Transfer, B , vol. 58 , no. 5 , pp. 323 – 342 , 2010 .
   Web of Science ®Google Scholar
• B. D. Nichols , C. W. Hirt , and R. S. Hotchkiss , SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free Boundaries , Technical Report LA-8355 , Los Alamos Scientific Laboratory , Los Alamos , NM , 1980 .
   Google Scholar
• B. D. Nichols and C. W. Hirt , Methods for Calculating Multi-Dimensional, Transient Free-Surface Flows Past Bodies, in Proceedings of the First International Conference of Numerical Ship Hydrodynamics, Gaithersburg, ML, October 20–23, 1975.
   Google Scholar
• C. W. Hirt and B. D. Nichols , Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries , J. Comput. Phys. , vol. 39 , pp. 201 – 225 , 1981 .
   Web of Science ®Google Scholar
• F. H. Harlow and A. A. Amsden , Fluid dynamics: A LASA Monograph, LA-4700, Los Alamos National Laboratory, Los Alamos, NM, 1971.
   Google Scholar
• B. Lafaurie , C. Nardone , R. Scardovelli , S. Zaleski , and G. Zanetti , Modeling Merging and Fragmentation in Multiphase Flows with SURFER , J. Comput. Phys. , vol. 113 , pp. 134 – 147 , 1994 .
   Web of Science ®Google Scholar
• V. Maronnier , M. Picasso , and J. Rappaz , Numerical Simulation of Free Surface Flows , J. Comput. Phys. , vol. 155 , pp. 439 – 455 , 1999 .
   Web of Science ®Google Scholar
• D. B. Kothe , M. W. Williams , K. L. Lam , D. R. Korzekwa , P. K. Tubesing , and E. G. Puckett , A Second-Order Accurate, Linearity Preserving Volume Tracking Algorithm for Free-Surface Flows on 3-D Unstructured Meshes, in Proceedings of the 3rd ASME, JSME Joint Fluids Engineering Conference, San Francisco, CA, July 18–22, 1999.
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• D. B. Kothe and R. C. Mjolsness , RIPPLE: A New Model for Incompressible Flows with Free Surfaces , AIAA J. , vol. 30 , pp. 2694 – 2700 , 1992 .
   Google Scholar
• O. Ubbink and R. Issa , A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes , J. Comput. Phys. , vol. 153 , pp. 26 – 50 , 1999 .
   Web of Science ®Google Scholar
• Y. Suh , W. Lee , and G. Son , Bubble Dynamics, Flow, and Heat Transfer During Flow Boiling in Parallel Microchannels, Numer. Heat Transfer A , vol. 54, pp. 390–405, 2008.
   Web of Science ®Google Scholar
• J. D. Faires and R. L. Burden , Numerical Methods , PWS , Boston , pp. 152 – 153 , 1993 .
   Google Scholar
• J. Crank and P. Nicolson , A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat-Conduction Type , Proc. Cambr. Phil. Soc. , vol. 43 , pp. 50 – 67 , 1947 .
   Web of Science ®Google Scholar
• W. Shyy , A Study of Finite Difference Approximations to Steady State Convection Dominated Flows , J. Comput. Phys. , vol. 57 , pp. 415 – 438 , 1985 .
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere , New York , 1981 .
   Google Scholar
• P. H. Gaskell and A. K. C. Lau , Curvature Compensated Convective Transport: SMART, a New Boundedness Preserving Transport Algorithm , Int. J. Numer. Meth. Fluids , vol. 8 , pp. 617 – 641 , 1988 .
   Web of Science ®Google Scholar
• B. P. Leonard , A Stable and Accurate Convective Modeling Procedure Based on Quadratic Interpolation , Comput. Meth. Appl. Mech. Eng. , vol. 19 , pp. 59 – 98 , 1979 .
   Web of Science ®Google Scholar
• C. T. DeGroot and A. G. Straatman , A Finite-Volume Model for Fluid Flow and Nonequilibrium Heat Transfer in Conjugate Fluid Porous Domains Using General Unstructured Grids , Numer. Heat Transfer B , vol. 60 , pp. 252 – 277 , 2011 .
   Web of Science ®Google Scholar
• B. Hunter and Z. Guo , Comparison of the Discrete-Ordinates Method and the Finite-Volume Method for Steady-State and Ultrafast Radiative Transfer Analysis in Cylindrical Coordinates , Numer. Heat Transfer B , vol. 59 , pp. 339 – 359 , 2011 .
   Web of Science ®Google Scholar
• L. Sun , S. R. Mathur , and J. Y. Murthy , An Unstructured Finite-Volume Method for Incompressible Flows with Complex Immersed Boundaries , Numer. Heat Transfer B , vol. 58 , pp. 217 – 241 , 2010 .
   Web of Science ®Google Scholar
• S.-K. Choi and C.-L. Lin , A Simple Finite-Volume Formulation of the Lattice Boltzmann Method for Laminar and Turbulent Flows , Numer. Heat Transfer B , vol. 58 , pp. 242 – 261 , 2010 .
   Web of Science ®Google Scholar
• M. M. Larmaei , J. Behzadi , and T.-F. Mahdi , Treatment of Checkerboard Pressure in the Collocated Unstructured Finite-Volume Scheme , Numer. Heat Transfer B , vol. 58 , pp. 121 – 144 , 2010 .
   Web of Science ®Google Scholar
• F. Juretic and A. D. Gosman , Error Analysis of the Finite-Volume Method with Respect to Mesh Type , Numer. Heat Transfer B , vol. 57 , pp. 414 – 439 , 2010 .
   Web of Science ®Google Scholar
• C. Kim , M. Y. Kim , M. J. Yu , and S. C. Mishra , Unstructured Polygonal Finite-Volume Solutions of Radiative Heat Transfer in a Complex Axisymmetric Enclosure , Numer. Heat Transfer B , vol. 57 , pp. 227 – 239 , 2010 .
   Web of Science ®Google Scholar
• N. O. Moraga , S. Del , C. Ramirez , M. J. Godoy , and P. D. Ticchione , Study of Convective Non-Newtonian Alloy Solidification in Molds by the PSIMPLER/Finite-Volume Method , Numer. Heat Transfer A , vol. 57 , pp. 936 – 953 , 2010 .
   Web of Science ®Google Scholar
• K. Guedri , M. Ammar Abbassi , M. Naceur Borjini , K. Halouani , and R. Said , Application of the Finite-Volume Method to Study the Effects of Baffles on Radiative Heat Transfer in Complex Enclosures , Numer. Heat Transfer A , vol. 55 , pp. 780 – 806 , 2009 .
   Web of Science ®Google Scholar
• A. Dalal , V. Eswaran , and G. Biswas , A Finite-Volume Method for Navier-Stokes Equations on Unstructured Meshes , Numer. Heat Transfer B , vol. 54 , pp. 238 – 259 , 2008 .
   Web of Science ®Google Scholar
• M. Y. Kim , S. W. Baek , and S. I. Park , Evaluation of the Finite-Volume Solutions of Radiative Heat Transfer in a Complex Two-Dimensional Enclosure with Unstructured Polygonal Meshes , Numer. Heat Transfer B , vol. 54 , pp. 116 – 137 , 2008 .
   Web of Science ®Google Scholar
• P. Hassanzadeh and G. D. Raithby , Finite-Volume Solution of the Second-Order Radiative Transfer Equation: Accuracy and Solution Cost , Numer. Heat Transfer B , vol. 53 , pp. 374 – 382 , 2008 .
   Web of Science ®Google Scholar
• R. Das , S. C. Mishra , and R. Uppaluri , Multiparameter Estimation in a Transient Conduction-Radiation Problem Using the Lattice Boltzmann Method and the Finite-Volume Method Coupled with the Genetic Algorithms, Numer. Heat Transfer A , vol. 53, pp. 1321–1338, 2008.
   Web of Science ®Google Scholar
• M. Ko and N. K. Anand , Three-Dimensional Combined Convective-Radiative Heat Transfer over a Horizontal Backward-Facing Step—A Finite-Volume Method , Numer. Heat Transfer A , vol. 54 , pp. 109 – 129 , 2008 .
   Web of Science ®Google Scholar
• B. Mondal , S. C. Mishra , P. Asinari , and R. Borchiellini , Analysis of a Localized Fire in a 3-D Tunnel Using a Hybrid Solver: Lattice Boltzmann Method, Finite-Volume Method, and Fully Explicit Upwind Scheme , Numer. Heat Transfer A , vol. 53 , pp. 392 – 417 , 2008 .
   Web of Science ®Google Scholar
• M. S. Darwish and F. Moukalled , Normalized Variable and Space Formulation Methodology for High-Resolution Schemes , Numer. Heat Transfer B , vol. 26 , pp. 79 – 96 , 1994 .
   Web of Science ®Google Scholar
• W. Shyy , A Study of Finite Difference Approximations to Steady State Convection Dominated Flows , J. Comput. Phys. , vol. 57 , pp. 415 – 438 , 1985 .
   Web of Science ®Google Scholar
• S. G. Rubin and P. K. Khosla , Polynomial Interpolation Method for Viscous Flow Calculations , J. Comput. Phys. , vol. 27 , pp. 153 – 168 , 1982 .
   Google Scholar
• J. D. Ramshaw and J. A. Trapp , Numerical Technique for Low Speed Homogeneous Two Phase Flow with a Sharp Interface , J. Comput. Phys. , vol. 21 , pp. 438 – 453 , 1976 .
   Web of Science ®Google Scholar
• W. J. Rider and D. B. Kothe , Stretching and Tearing Interface Tracking Methods, AIAA Paper 95-1717 (Les Almos Natl. Lab. Rep. LA-UR-95–1145), presented at the 12th AIAA CFD Conference, San Diego, CA, June 19–22, 1995.
   Google Scholar
• M. Rudman , Volume-Tracking Methods for Interfacial Flow Calculations , Int. J. Numer. Meth. Fluids , vol. 24 , pp. 671 – 691 , 1997 .
   Web of Science ®Google Scholar
• H. Jasak , Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows, Ph.D. thesis, Imperial College of Science, Technology and Medicine, London, 1996.
   Google Scholar
• B. P. Leonard and H. S. Niknafs , Sharp Monotonic Resolution of Discontinuities without Clipping of Narrow Extrema , Comput. Fluids , vol. 19 , pp. 141 – 154 , 1991 .
   Web of Science ®Google Scholar
• W. J. Rider and D. B. Kothe , Reconstructing Volume Tracking , J. Comput. Phys. , vol. 141 , pp. 112 – 152 , 1998 .
   Web of Science ®Google Scholar
• S. T. Zalesak , Fully Multi-Dimensional Flux Corrected Transport Algorithms for Fluid Flow , J. Comput. Phys. , vol. 31 , pp. 335 – 362 , 1979 .
   Web of Science ®Google Scholar
• J. C. Martin and W. J. Moyce , An Experimental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane , Phil. Trans. Roy. Soc. Lond., Ser. A , vol. 244 , pp. 312 – 324 , 1952 .
   Web of Science ®Google Scholar
• K. Abdolmaleki , K. P. Thiagarajan , and M. T. Morris-Thomas , Simulation of the Dam Break Problem and Impact Flows Using a Navier-Stokes Solver, Proceedings of the 15th Australasian Fluid Mechanics Conference, Paper # AFMC00031, Sydney, Australia, 13–17 December 2004.
   Google Scholar