A 3D immersed interface method for fluid-solid interaction

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 25-28, 2008, Pages 2068-2086

  Xu, Sheng ^a   Wang, Z Jane ^b  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Fluid solid interaction; Immersed boundary method; Immersed interface method; Jump conditions; Singular force

Indexed keywords

FLOW OF SOLIDS; INTERFACES (MATERIALS); INTERPOLATION; LAGRANGE MULTIPLIERS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; POISSON EQUATION;

FLUID-SOLID INTERACTION; IMMERSED BOUNDARY METHOD; IMMERSED INTERFACE METHOD; JUMP CONDITIONS; SINGULAR FORCE;

FLUID STRUCTURE INTERACTION;

FLOW OF SOLIDS; FLUID STRUCTURE INTERACTION; INTERFACES (MATERIALS); INTERPOLATION; LAGRANGE MULTIPLIERS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; POISSON EQUATION;

EID: 41949094817     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.06.012     Document Type: Article

References (34)

1. Attila J. Bergou, Sheng Xu, Z. Jane Wang, Passive wing rotation in dragonfly flight, J. Fluid Mech., accepted for publication.
2. Andreas Berthelsen P. A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions. J. Comput. Phys. 197 (2004) 364-386
3. Beyer R.P., and LeVeque R.J. Analysis of a one-dimensional model for the immersed boundary method. SIAM J. Numer. Anal. 29 2 (1992) 332-364
4. Chong M.S., Perry A.E., and Cantwell B.J. A general classification of three-dimensional flow fields. Phys. Fluids A 2 5 (1990) 765-777
5. Cortez R., and Minion M. The blob projection method for immersed boundary problems. J. Comput. Phys. 161 (2000) 428-453
6. Deng S., Ito K., and Li Z. Three-dimensional elliptic solvers for interface problems and applications. J. Comput. Phys. 184 (2003) 215-243
7. E W., and Liu J.-G. Vorticity boundary condition and related issues for finite difference schemes. J. Comput. Phys. 124 (1996) 368-382
8. Fogelson A.L., and Keener J.P. Immersed interface method for Neumann and related problems in two and three dimensions. SIAM J. Sci. Comput. 22 5 (2000) 1630-1654
9. Johnston H., and Liu J.-G. Finite difference schemes for incompressible flow based on local pressure boundary conditions. J. Comput. Phys. 180 (2002) 120-154
10. Johnston H., and Liu J.-G. Accurate stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term. J. Comput. Phys. 199 (2004) 221-259
11. Johnson T.A., and Patel V.C. Flow past sphere up to a Reynolds number of 300. J. Fluid Mech. 378 (1999) 19-70
12. Lai M.-C., and Peskin C.S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160 (2000) 705-719
13. Le D.V., Khoo B.C., and Peraire J. An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries. J. Comput. Phys. 220 (2006) 109-138
14. Lee L., and LeVeque R.J. An Immersed Interface Method for Incompressible Navier-Stokes Equations. SIAM J. Sci. Comput. 25 3 (2003) 832-856
15. LeVeque R.J., and Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 4 (1994) 1019-1044
16. LeVeque R.J., and Li Z. Immersed interface methods for Stokes flow with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18 3 (1997) 709-735
17. Li Z., and Lai M.-C. The immersed interface method for the Navier-Stokes equations with singular forces. J. Comput. Phys. 171 (2001) 822-842
18. Zhilin Li, Kazufumi Ito, The Immersed Interface Method - Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, SIAM Frontiers in Applied Mathematics, vol. 33, SIAM Publisher, 2006, ISBN: 0-89971-609-8.
19. Linnick M.N., and Fasel H.F. A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J. Comput. Phys. 204 (2005) 157-192
20. Peskin C.S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 (1972) 252-271
21. Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 (1977) 220-252
22. Peskin C.S., and Printz B.F. Improved volume conservation in the computation of flows with immersed elastic boundaries. J. Comput. Phys. 105 (1993) 33-46
23. Peskin C.S. The immersed boundary method. Acta Numer. 11 (2002) 479-517
24. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes in Fortran 77. second ed. (1999), The Art of Scientific Computing pp. 848-852
25. Roma A.M., Peskin C.S., and Berger M.J. An adaptive version of the immersed boundary method. J. Comput. Phys. 153 (1999) 509-534
26. Sheard G.J., Hourigan K., and Thompson M.C. Computations of the drag coefficients for low-Reynolds-number flow past rings. J. Fluid Mech. 526 (2005) 257-275
27. Stockie J.M., and Wetton B.R. Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes. J. Comput. Phys. 154 (1999) 41-64
28. Tu C., and Peskin C.S. Stability and instability in the computation of flows with moving immersed boundaries. SIAM J. Statist. Comput. 13 (1992) 70-83
29. Jane Wang Z. Two dimensional mechanism for insect hovering. Phys. Rev. Lett. 85 10 (2000)
30. Wiegmann A., and Bube K.P. The immersed interface method for nonlinear differential equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 35 1 (1998) 177-200
31. Wiegmann A., and Bube K.P. The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions. SIAM J. Numer. Anal. 37 3 (2000) 827-862
32. Xu S., and Jane Wang Z. Systematic derivation of jump conditions for the immersed interface method in three-dimensional flow simulation. SIAM J. Sci. Comput. 27 6 (2006) 948-1980
33. Xu S., and Jane Wang Z. An immersed interface method for simulating the interaction of a fluid with moving boundaries. J. Comput. Phys. 216 2 (2006) 454-493
34. Zhu L., and Peskin C.S. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 179 (2002) 452-468