Mixed element FEM level set method for numerical simulation of immiscible fluids

Journal of Computational Physics

Volumn 231, Issue 6, 2012, Pages 2449-2465

  Hysing, S ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Finite element method; Immiscible multiphase fluid flow; Level set method; Numerical simulation

Indexed keywords

DROP BREAKUP; FLOW OF FLUIDS; LEVEL MEASUREMENT; NUMERICAL METHODS; NUMERICAL MODELS;

BUBBLE TEST; ELEMENT LEVEL; IMMISCIBLE FLUID FLOWS; IMMISCIBLE FLUIDS; IMMISCIBLE/MULTIPHASE FLUID FLOW; LEVEL SET; LEVEL SET METHOD; MIXED ELEMENT; MULTI-PHASE FLUID FLOW; TEST CASE;

FINITE ELEMENT METHOD;

EID: 84856223935     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.11.035     Document Type: Article

References (29)

1. Brackbill J.U., Kothe D.B., Zemach C. A continuum method for modeling surface tension. J. Comput. Phys. 1992, 100:335-354. 10.1016/0021-9991(92)90240-Y.
2. Bristeau M.O., Glowinski R., Periaux J. Numerical methods for the Navier-Stokes equations. Applications to the simulation of compressible and incompressible viscous flows. Comput. Phys. Rep. 1987, 6:73-187. 10.1016/0167-7977(87)90011-6.
3. Brooks A.N., Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 1982, 32:199-259. 10.1016/0045-7825(82)90071-8.
4. Hackbusch W. Multi-Grid Methods and Applications. Springer Series in Computational Mathematics 1985, Springer-Verlag, ISBN:0-387-12761-5.
5. Harlow F.H., Welch J.E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 1965, 8:2182-2189. 10.1063/1.1761178.
6. Hirt C.W., Nichols B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 1981, 39:201-225. 10.1016/0021-9991(81)90145-5.
7. Hinton E., Rock T., Zienkiewicz O.C. A note on mass lumping and related processes in the finite element method. Earthq. Eng. Struct. D. 1976, 4:245-249. 10.1002/eqe.4290040305.
8. Hughes T.J.R., Brooks A. A multidimensional upwind scheme with no crosswind diffusion in Finite Element Methods for Convection Dominated Flows. AMD 1979, Vol. 34:19-35. ASME, New York.
9. Hysing S., Turek S. The Eikonal equation: Numerical efficiency vs. algorithmic complexity on quadrilateral grids. Proceedings of Algoritmy 2005, 22-31. Slovak University of Bratislava, Bratislava, ISBN: 80-227-2192-1.
10. Hysing S. A new implicit surface tension implementation for interfacial flows. Int. J. Num. Meth. Fluids 2006, 51:659-672. 10.1002/fld.1147.
11. S. Hysing, Numerical Simulation of Immiscible Fluids with FEM Level Set Techniques, PhD Thesis, University of Dortmund, Institute of Applied Mathematics, Dortmund, 2007.
12. Hysing S., Turek S., Kuzmin D., Parolini N., Burman E., Ganesan S., Tobiska L. Quantitative benchmark computations of two-dimensional bubble dynamics. Int. J. Num. Meth. Fluids 2009, 60:1259-1288. 10.1002/fld.1934.
13. Rising bubble benchmark reference data: http://www.featflow.de/en/benchmarks/cfdbenchmarking/bubble.html.
14. Kuzmin D. A high-resolution finite element scheme for convection-dominated transport. Communications in Numerical Methods in Engineering 2000, 16:215-223. 10.1002/(SICI)1099-0887(200003)16:3<215::AID-CNM326>3.0.CO;2- 1.
15. Kuzmin D. On the design of general-purpose flux limiters for finite element schemes. I. Scalar convection. J. Comput. Phys. 2006, 219:513-531. 10.1016/j.jcp.2006.03.034.
16. Kuzmin D., Turek S. High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter. J. Comput. Phys. 2004, 198:131-158. 10.1016/j.jcp.2004.01.015.
17. Kuzmin D., Löhner R., Turek S. Flux-Corrected Transport: Principles, Algorithms, and Applications. Scientific Computation 2005, Springer, ISBN: 978-3-540-23730-3.
18. Osher S.J., Fedkiw R.P. Level Set Methods and Dynamic Implicit Surfaces. Applied Mathematical Sciences 2002, vol. 153. Springer, ISBN: 978-0-387-95482-0.
19. Osher S.J., Sethian S.A. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 1988, 79:12-49. 10.1016/0021-9991(88)90002-2.
20. Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 1977, 25:220-252. 10.1016/0021-9991(77)90100-0.
21. W.J. Rider, D.B. Kothe, Stretching and tearing interface tracking methods, in the proceeding of the 12th AIAA Computational Fluid Dynamics Conference, AIAA 95-1717, 1995.
22. Sethian J.A. A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 1996, 93:1591-1595. 10.1073/pnas.93.4.1591.
23. Turek S., Rannacher R. A simple nonconforming quadrilateral Stokes element. Num. Meth. Part. D.E. 1992, 8:97-111. 10.1002/num.1690080202.
24. Turek S. On discrete projection methods for the incompressible Navier-Stokes equations: an algorithmical approach. Comput. Methods Appl. Mech. Eng. 1997, 143:271-288. 10.1016/S0045-7825(96)01155-3.
25. Turek S. Efficient Solvers for Incompressible Flow Problems, An Algorithmic and Computational Approach. Lecture Notes in Computational Science and Engineering 1999, Vol. 6. Springer-Verlag, ISBN: 3-540-65433-X.
26. Unverdi S.O., Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 1992, 100:25-37. 10.1016/0021-9991(92)90307-K.
27. Zhang Z. Polynomial preserving gradient recovery and a posteriori estimate for bilinear element on irregular quadrilaterals. Int. J. Num. Anal. Mod. 2004, 1(1):1-24.
28. Zienkiewicz O.C., Zhu J.Z. The superconvergent patch recovery and a posteriori error estimators. part 1: The recovery technique. Int. J. Num. Meth. Eng. 1992, 33:1331-1364. 10.1002/nme.1620330702.
29. FeatFlow CFD benchmark repository: http://www.featflow.de/en/benchmarks/cfdbenchmarking.html.