A level set method for fluid-structure interactions with immersed surfaces

Mathematical Models and Methods in Applied Sciences

Volumn 16, Issue 3, 2006, Pages 415-438

  Cottet, Georges Henri ^a   Maitre, Emmanuel ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

Fluid structure; Immersed boundary method; Level set

Indexed keywords

EID: 33645003099     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202506001212     Document Type: Article

References (19)

1. Y. C. Chang, T. Y. Hon, B. Merriman and S. Osher, A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. Comp. Phys. 124 (1996) 449-464.
2. G.-H. Cottet, Multi-physics and particle methods, in Computational Fluid and Solid Mechanics, ed. K. J. Bathe (Elsevier, 2003), pp. 1296-1298.
3. G.-H. Cottet and E. Maitre, A level set formulation of immersed boundary methods for fluid-structure interaction problems, C. R. Acad. Sci. Paris. Ser. I 338 (2004) 581-586.
4. J. Donea, S. Giuliani and J. P. Halleux, An arbitrary, Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Comput. Meth. Appl. Mech. Eng. 33 (1982) 689.
5. L. C. Evans and R. Gariepy, Measure Theory and Fine Properties of Functions (CRC Press, 1992).
6. D. Enright, R. Fedkiw, J. Ferziger and I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 183 (2002) 83-116.
7. C. Grandmont and Y. Maday, Existence for an unsteady fluid-structure interaction problem, Math. Meth. Anal. Numer. 34 (2000) 609-636.
8. S. Hieber and P. Koumoutsakos, A Lagrangian particle level set method, submitted.
9. G. Jiang and D. Peng, Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput. 21 (2000) 2126-2143.
10. J. Kim and P. Moin, Application of a fractional-step method to solve incompressible Navier-Stokes equations. J. Comput. Phys. 59 (1985) 323-360.
11. L. Lee and R. J. Leveque, An immersed interface method for incompressible Navier-Stokes equations, SIAM J. Sci. Comput. 25 (2003) 832-856.
12. R. J. LeVeque and Z. Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, SIAM J. Sci. Comput. 18(3) (1997) 709-735.
13. S, Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer-Verlag, 2002).
14. C. S. Peskin. Numerical analysis of blood flow in the heart, J. Comp. Phys. 25 (1977) 220-252.
15. C. S. Peskin, The immersed boundary method, Acta Numer 11 (2002) 479-517.
16. S. Peskin and B. F. Printz, Improved volume conservation in the computation of flows with immersed boundaries, J. Comput. Phys. 105 (1993) 33-46.
17. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE Report No. 97-65, techreports.larc.nasa.gov/icase/1997/icase-1997-65.pdf.
18. P. Le Tallec and J. Mouro, Fluid structure interaction with large structural displace-ments, Comput. Meth. Appl. Mech. Engrg. 190 (2001) 3039-3067.
19. C. Tu and C. S. Peskin, Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods, SIAM J. Sci. Statist. Comput. 13 (1992) 1361-1376.