Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids

International Journal for Numerical Methods in Fluids

Volumn 44, Issue 10, 2004, Pages 1093-1117

  Greaves, Deborah ^a  

^a University of Bath   (United Kingdom)

Author keywords

Free surface; Interface; Quadtree adaptive grids; Viscous fluid; Volume of fluid method

Indexed keywords

COMPRESSIBILITY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; CONTACTS (FLUID MECHANICS); LAMINAR FLOW; NAVIER STOKES EQUATIONS; VOLUME FRACTION;

FREE SURFACE FLOW; VISCOUS FLUIDS;

VISCOUS FLOW;

FLUID INTERFACE; FREE SURFACE FLOW; LAMINAR FLOW; MATHEMATICAL MODELING; NAVIER-STOKES EQUATIONS; VISCOUS FLUID;

EID: 2142806920     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.687     Document Type: Article

References (40)

1. Ma QW, Wu GX, Eatock Taylor R. Finite element simulation of fully nonlinear interaction between vertical cylinders and steep waves-part 1: methodology and numerical procedure. International Journal for Numerical Methods in Fluids 2001; 36:265-285.
2. Ma QW, Wu GX, Eatock Taylor R. Finite element simulation of fully nonlinear interaction between vertical cylinders and steep waves-part 2: numerical results and validation. International Journal for Numerical Methods in Fluids 2001; 36:287-308.
3. Ferziger JH, Perié M. Computational Methods for Fluid Dynamics. Springer: Berlin, 1996, ISBN 3-540-59434-5.
4. Hyman JM. Numerical methods for tracking interfaces. Physica 1984; 12D:396-407.
5. Monaghan JJ. Simulating free surface flows with SPH. Journal of Computational Physics 1994; 65:179-214.
6. Causon DM. An efficient front tracking algorithm for multi-component fluid calculations with biomedical applications. Zeitscrift fur Angewandte Mathematik und Mechanik 1996; 76(S1):371-372.
7. Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 1981; 39:201-225.
8. Heinrich P. Nonlinear numerical model of landslide-generated water waves. International Journal of Engineering Fluid Mechanics 1991; 4(4):403-416.
9. Tomiyama A, Sou A, Minagawa H, Sakaguchi T. Numerical analysis of a single bubble by VoF method. JSME International Journal Series B 1993; 36:51-56.
10. Ubbink O. Numerical prediction of two fluid systems with sharp interfaces. Ph.D. Thesis, Imperial College of Science. Technology and Medicine, London. 1997.
11. Greaves DM, Borthwick AGL. On the use of adaptive hierarchical meshes for numerical simulation of separated flows. International Journal for Numerical Methods in Fluids 1998; 26:303-322, ISSN 0271-2091.
12. Lafaurie B, Nardone C, Seardovelli R, Zaleski S, Zanetti G. Modelling merging and Fragmentation in multiphase flows with SURFER. Journal of Computational Physics 1994; 113:134-147.
13. Noh WF, Woodward P. SLIC (simple line interface calculations). Lecture Notes in Physics 1976; 59:330-340.
14. Ashgriz N, Poo JY. FLAIR: flux line-segment model for advection and interface reconstruction. Journal of Computational Physics 1991; 93:449-468.
15. Gueyffier D, Li J, Nadim A, Scardovelli R. Zaleski S. Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows. Journal of Computational Physics 1999; 152:423-456.
16. Leonard BP. The ULTIMATE conservative difference scheme applied to steady one-dimensional advection. Computer Methods in Applied Mechanics and Engineering 1991; 98:17-74.
17. Leonard BP. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineerinq 1979; 19:59-98.
18. Samet H. The Design and Analysis of Spatial Data Structures. Addison-Wesley: Reading, MA, 1990.
19. Samet H. Applications of Spatial Data Structures. Addison-Wesley: Reading, MA, 1990.
20. Yerry MA, Shephard MS. A modified quadtree approach to finite element mesh generation. IEEE Computer Graphics and Applications 1983; 3(1):39-46.
21. Messaoud B. Parallel and adaptive algorithms for elliptic partial differential systems. Ph.D. Rensselaer Polytechnic Institute. Troy, New York. 1992.
22. van Dommelen L. Rundensteiner EA. Fast, adaptive summation of point forces in the two-dimensional Poisson equation. Journal of Computational Physics 1989; 83:126-147.
23. Józsa J. Gáspár C. Fast. adaptive approximation of wind-induced horizontal flow patterns in shallow lakes using quadtree-based multigrid method. C.M.W.R., Denver, 1992.
24. Young DP, Melvin RG, Bieterman MB, Johnson FT, Samant SS, Bussoletti JE. A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics. Journal of Computational Physics 1991; 92:1-66.
25. de Zeeuw D. Powell KG. An adaptively refined Cartesian mesh solver for the Euler equations. Journal of Computational Physics 1993; 1104:56-68.
26. Greaves DM, Borthwick AGL. Hierarchical tree-based finite element mesh generation. International Journal for Numerical Methods in Engineering 1999; 45:447-471. ISSN 0029-5981.
27. Hu ZZ, Greaves DM, WU GX. Numerical simulation of fluid flows using an unstructured finite volume method with adaptive tri-tree grids. International Journal for Numerical Methods in Fluids 2002; 39:403-440.
28. Yiu KFC, Greaves DM, Cruz S, Saalehi A, Borthwick AGL. Quadtree grid generation: information handling, boundary fitting and CFD applications. International Journal of Computers and Fluids 1995; 25(8):759-769.
29. Greaves DM. Numerical modelling of laminar separated flows and inviscid steep waves using adaptive hierarchical meshes. D.Phil. Thesis, Oxford University, 1995.
30. Perić M, Kessler R, Scheurer G. Comparison of finite volume numerical methods with staggered and colocated grids. Computers and Fluids 1998; 16(4):389-403.
31. Patanker SV. Numerical Heat Transfer and Fluid Flow. Taylor and Francis, Hemisphere Publishing Corporation: U.S.A., 1980.
32. Rhie CM, Chow WL. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA Journal 1983; 21:1525-1532
33. Ubbink O, Issa RI. A method for capturing sharp fluid interfaces on arbitrary meshes. Journal of Computational Physics 1999; 153:26-50.
34. Rudman M. Volume-tracking methods for interfacial flow calculations. International Journal for Numerical Methods in Fluids 1997; 24:671-691.
35. 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.
36. Jeong JH, Yang DY. Three-dimensional finite element analysis of transient fluid flow with free surface using marker surface method and adaptive grid refinement. International Journal for Numerical Methods in Fluids 1999; 29:657-684.
37. Qian L, Causon DM, Ingram DM, Mingham CG. Cartesian cut cell two-fluid solver for hydraulic flow problems. Journal of Hydraulic Engineering 2003; 129(9):688-696.
38. Martin JC, Moyce WJ. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions of the Royal Society of London 1952; A244:312-324.
39. Koshizuka S, Tamako H, Oka Y. A particle method for incompressible viscous flow with fluid fragmentation. Computational Fluid Dynamics Journal 1995; 4(l):29-46.
40. Wang JP. Viscous free surface flow modelling using interface capturing methods on adaptive grids. D.Phil. Thesis, Oxford University, 2002.