Simulations of the whirling instability by the immersed boundary method

SIAM Journal on Scientific Computing

Volumn 25, Issue 6, 2004, Pages 2066-2083

  Lim, Sookkyung ^a   Peskin, Charles S ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Immersed boundary method; Overwhirling; Twirling; Whirling

Indexed keywords

BUOYANCY; ELASTIC MODULI; NATURAL FREQUENCIES; PARAMETER ESTIMATION; REYNOLDS NUMBER; VISCOSITY;

IMMERSED BOUNDARY METHOD; OVERWHIRLING; ROTATION RATE; TWIRLING;

BOUNDARY ELEMENT METHOD;

EID: 10244245497     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502417477     Document Type: Article

References (29)

1. C. W. WOLGEMUTH, T. R. POWERS, AND R. E. GOLDSTEIN, Twirling and whirling: Viscous dynamics of rotating elastic filaments, Phys. Rev. Lett., 84 (2000), pp. 16-23.
2. J. B. KELLER AND S. I. RUBINOW, Slender-body theory for slow viscous flow, J. Fluid Mech., 75 (1976), pp. 705-714.
3. C. S. PESKIN, Flow patterns around heart valves: A numerical method, J. Comput. Phys., 10 (1972), pp. 252-271.
4. C. S. PESKIN, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), pp. 220-252.
5. C. S. PESKIN AND D. M. MCQUEEN, Fluid dynamics of the heart and its valves, in Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology, H. G. Othmer, F. R. Adler, M. A. Lewis, and J. C. Dallon, eds., Prentice-Hall, Englewood Cliffs, NJ, 1996, pp. 309-337.
6. L. FAUCI AND C. S. PESKIN, A computational model of aquatic animal locomotion, J. Comput. Phys., 77 (1988), pp. 85-108.
7. L. ZHU AND C. S. PESKIN, Simulation of a flaping flexible filament in a flowing soap film by the immersed boundary method, J. Comput. Phys., 179 (2002), pp. 452-468.
8. R. DILLON, L. FAUCI, AND D. GAVER III, A microscale model of bacterial swimming, chemotaxis and substrate transport, J. Theor. Biol., 177 (1995), pp. 325-340.
9. E. JUNG AND C. S. PESKIN, Two-dimensional simulations of valveless pumping using the immersed boundary method, SIAM J. Sci. Comput., 23 (2001), pp. 19-45.
10. E. GIVELBERG, Modelling Elastic Shells Immersed in Fluid, Ph.D. thesis, Mathematics, New York University, 1997; available online at http://www.umi.com/hp/Products/ DisExpress.html, order number 9808292.
11. A. L. FOGELSON, A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting, J. Comput. Phys., 56 (1984), pp. 111-134.
12. C. J. JONES AND S. I. AIZAWA, The bacterial flagellum and flagellar motor: Structure, assembly and function, Adv. Microb. Physiol, 32 (1991), pp. 109-172.
13. C. R. CALLADINE, Change of waveform in bacterial flagella: The role of mechanics at the molecular level, J. Mol. Biol., 118 (1978), pp. 457-479.
14. A. J. CHORIN AND J. E. MARSDEN, A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, New York, 1993.
15. SIR J. LIGHTHILL, Mathematical Biofluiddynamics, Regional Conference Series in Applied Mathematics 17, SIAM, Philadelphia, 1975.
16. S. CHILDRESS, Mechanics of Swimming and Flying, Cambridge Stud. Math. Biol., Cambridge University Press, Cambridge, UK, 1981.
17. S. H. STROGATZ, Nonlinear Dynamics and Chaos, Westview Press, Boulder, CO, 2000.
18. H. KONDOH AND M. YANAGIDA, Structure of straight flagellar filaments from a mutant of E. coli, J. Mol. Biol., 96 (1975), pp. 641-652.
19. N. NANNINGA, Molecular Cytology of E. coli, Academic Press, New York, 1985, pp. 9-37.
20. C. S. PESKIN AND D. M. MCQUEEN, Modeling prosthetic heart valves for numerical analysis of blood flow in the heart, J. Comput. Phys., 37 (1980), pp. 113-132.
21. W. H. PRESS, B. P. FLANNERY, S. A. TEUKOLSKY, AND W. T. VETTERLING, Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 1986, pp. 390-396.
22. M. C. LAI AND C. S. PESKIN, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys., 160 (2000), pp. 705-719.
23. D. M. MCQUEEN AND C. S. PESKIN, Heart simulation by an immersed boundary method with formal second-order accuracy and reduced numerical viscosity, in Proceedings of the ICTAM, 2000.
24. C. S. PESKIN, The immersed boundary method, in Acta Numerica, Cambridge University Press, Cambridge, UK, 2002, pp. 1-39.
25. S. S. ANTMAN, Nonlinear Problems of Elasticity, Springer-Verlag, New York, 1995.
26. I. KELLER, Biological applications of the dynamics of twisted elastic rods, J. Comput. Phys., 125 (1996), pp. 325-337.
27. R. E. GOLDSTEIN, T. R. POWERS. AND C. H. WIGGINS, Viscous nonlinear dynamics of twist and writhe, Phys. Rev. Lett., 80 (1998), pp. 5232-5237.
28. N. S. COWEN, D. M. MCQUEEN, AND C. S. PESKIN, Immersed Boundary General Software Package (IBGSP), available by request from peskin@cims.nyu.edu.
29. D. M. MCQUEEN, hrtmvp-readmenu-57.f, A Three-Dimensional Visualization Program Using Fortran and SGI GL, available by request from mcqueen@cims.nyu.edu.