Scaling laws for drag of a compliant body in an incompressible viscous flow

Journal of Fluid Mechanics

Volumn 607, Issue , 2008, Pages 387-400

  Zhu, Luoding ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DRAG; REYNOLDS NUMBER; SCALING LAWS; VISCOUS FLOW;

COMPLIANT BODIES; FLOW SPEED; HIGH REYNOLDS NUMBER; IMMERSED BOUNDARY; INCOMPRESSIBLE VISCOUS FLOWS; POWER-LAW; SOAP FILMS;

INCOMPRESSIBLE FLOW;

DRAG; FLOW VELOCITY; INCOMPRESSIBLE FLOW; POWER LAW; REYNOLDS NUMBER; VISCOUS FLOW;

EID: 47149097906     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008002103     Document Type: Article

References (61)

1. ALBEN, S. 2004 Drag reduction by self-similar bending and a transition to forward flight by a symmetry breaking instability. PhD thesis, Courant Institute of Mathematical Sciences, New York University.
2. ALBEN, S., SHELLEY, S. & ZHANG, J. 2002 Drag reduction Trough self-similar bending of a flexible body. Nature 420, 479-481.
3. ALBEN, S., SHELLEY, S. & ZHANG, J. 2004 How flexibility induces streamlining in two-dimensional flow. Phys. Fluids 16, 1694-1713.
4. ATZBERGER, P. J., KRAMER, P. R. & PESKIN, C. S. 2006 A stochastic immersed boundary method for biological fluid dynamics at microscopic length scale. J. Comput. Phys. 224, 1255-1292.
5. BARRETT, D. S., TRIANTAFYLLOU, M. S., YUE, D. K. R, GROSENBAUGH, M. A. & WOLFGANG, M. J. 1999 Drag reduction in fish-like locomotion. J. Fluid Mech. 392, 183-212.
6. BATCHELOR, G. K. 1967 An introduction to Fluid Dynamics. Cambridge University Press.
7. BUSHNELL, D. M. & MOORE, K. J. 1991 Drag reduction in Nature. Annu. Rev. Fluid Mech. 23, 65-79.
8. CORTEZ, R. & MINION,T, M. 2000 The blob projection method for immersed boundary problems. J. Comput. Phys. 161, 428-453.
9. COTTET, G. H. & MAITRE, E. 2004 A level set formulation of immersed boundary methods for fluid-structure interaction problems. C.R. Acad. Sci. Paris I 338, 5881-586.
10. COTTET, G. H. & MATTRE, E. 2006 A level set method for fluid-structure interactions with immersed interfaces. Math. Models Meth. Appl. Sci. 16, 415-438.
11. DENNY, M. W. 1994 Extreme drag forces and the survival of wind and water-swept organisms. J. Expl Biol. 195, 97-115.
12. DONEA, J., GIULIANI S. & HALLEUX, J. P. 1982 An Arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid structure interactions. Comput. Meth. Appl. Mech. Engng 33, 689-723.
13. FAUCI, L. J. & FOGELSON, A. L. 1993 Truncated Newton methods and the modeling of complex elastic structures. Pure Appl. Maths 46 787-818.
14. FAUCI, L. J. & PESKIN, C. S. 1988 A computational model ot aquatic animal locomotion. J. Comput. Phys. 77, 85-108.
15. FISH, F. E. 1998 Imaginative solutions by marine organisms for drag reduction. In Proc. Intl Symp. on Seawater Drag Reduction, Newport, Rhode Island (ed. J. C. S. Meng), pp. 443-450.
16. FOGELSON, A. L. 1992 Continuum models of platelet aggregation: Formulation and mechanical properties. SIAM J. Appl. Maths 52 1089-1110.
17. GLOWINSKI, R., PAN, T., HESLA, T., JOSEPH, D. & PERIAUX, J. 2001 A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow. J. Comput. Phys. 169, 363-426.
18. GLOWINTSKI, R., PAN, T. & PERIAUX, J. 1994a A fictitiou s domain method fbor Dirichiet problem and applications. Comput. Meth. Appl. Mech. Engng 111, 283-303.
19. GLOWINTSKI, R., PAN, T. & PERIAUX, J. 1994b A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Comput. Meth. Appl. Mech. Engng 112 133-148.
20. GRIFFITH, B. E. & PESKIN, C. S. 2005 On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficient smooth problems. J. Comput. Phys. 208, 75-105.
21. HUGHES, T. J. R., LIU, W. & ZIMMERMAN, T. K. 1981. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Meth. Appl. Mech. Engng 29, 329-349.
22. HOU, T. Y., LI, Z. L., OSHER, S., ZHAO, H. K. 1997 A hybrid method for moving interface problems with application to the Hele-Shaw flow. J. Comput. Phys. 134, 236-252.
23. Kim, Y. & PESKIN, C. S. 2007 Penalty immersed boundary method for an elastic boundary with mass. Phys. Fluids 19, 053103.
24. KOEHL, M. A. R. 1984 How do benthic organisms withstand moving water?. Am. Zool. 24, 57-70.
25. KOEHL, M. A. R., HUNTER, T. & JED, J. 1991 How do body flexibility and length affect hydrodynamic-force, on sessile organisms in waves versus in currents. Am. Zool. 31, A60-A60.
26. LAI, M. C. & PESKIN, C. S. 2000 An immersed boundary method with formal second order accuracy and reduced numerical viscosity. J. Comput. Phys. 160, 705-719.
27. LEVEQUE, R. J. & LI, Z. L. 1994 The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31, 1019-1044.
28. LEVEQUE, R. J. & Li, Z. L. 1997 Immersed interface methods for Stokes flows with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18, 709-735.
29. LI, Z. L. 2006 The Immersed interface Method - Numerical Solutions of PDEs involving intertaces and irregular Domains. SIAM, Philadelphia.
30. LI, Z. L. & LAI, M. C. 2001. Immersed interface methods for Navier-Stokes equations with singular forces. J. Comput. Phys. 171, 822-842.
31. LIU, W. K., KIM, D. K. & TANG, S. 2007 Mathematical foundations of the immersed finite element method. Comput. Mech. 39, 211-222.
32. MITTAL, R. & LACCARINO, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239-261.
33. MORI, Y. & PESKIN, C. S. 2006 Implicit second-order immersed boundary method with boundary mass. J. Comput. Phys. (submitted).
34. PESKIN, C. S. 1977 Flow patterns around heart valves: A numerical method. J. Comput. Phys. 25, 220-252.
35. PESKIN, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479-517.
36. PESKIN, C. S. & MCQUEEN, D. M. 1993 Computational biofluid dynamics. Contemp. Maths 141, 161-186.
37. PESKIN, C. S. & MCQUEEN, D. M. 1996 Fluid dynamics of the heart and its valves. In Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology (ed. H. G. Othmer, F. R. Adler, M. A. Lewis & J. C. Dallon), P. 309. Prentice-Hall.
38. PESKIN, C. S. & PRIDNTZ, B. F. 1993 Improved volume conservation in the computation of flows with immersed elastic boundaries. J. Comput. Phys. 105, 33-46.
39. ROMA, A. M., PESKIN, C. S. & BERGER, M. 1999 An adaptive version of the immersed boundary method. J. Comput. Phys. 153, 509-534.
40. SCHOUVEILER, L. & BOUNDAOUD, A. 2006 The rolling up of sheets in a steady flow. J. Fluid Mech. 563, 71-80.
41. STEINBURG, V. 2002 Bend and survive. Nature 420, 473-473.
42. SULSKY, D., CHEN, Z. & SCHREYER, H. L. 1994 A particle method for history-dependent materials. Comput. Mech. Appl. Mech. Engng 118, 179-197
43. SULSKY, D., ZHOU, S. J. & SCHREYER, H. L. 1995 Application of a particle-in-cell method to solid mechanics. Comput. Phys. Commun. 87, 136-152.
44. TAIRA, K. & COLONIUS, T. 2007 The immersed boundary method: A projection approach. J. Comput. Phys. 225, 2118-2137.
45. TU, C. & PESKIN, C. S. 1992 Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods. SIAM J. Sci. Statist. Comput. 13, 1361-1376.
46. UDAYKUMAR, H. S., SHYY, W., RAO, K M. 1996 A nixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries. Int J. Numer. Meth. Fluids 22, 691-712.
47. VOGEL, S. 1984 Drag and flexibility in sessile organisms. Am. Zool. 24, 37-44.
48. VOGEL, S. 1989 Drag aid reconfiguration of broad leaves in high winds. J. Expl Bot. 40, 941-9480.
49. VOGEL, S. 1996 Life in Moving Fluids - The Physical Biology of Flow. Princeton University Press.
50. WANG, X. 2006 From immersed boundary method to immersed continuum method. Intl J. Multiscale Comput. Engng 4, 127-145.
51. WANG, X. 2007 An iterative matrix-free method in implicit immersed boundary/continuum methods. Computers Struct. 85, 739-7488.
52. WANG, X. & LIU, W. K. 2004 Extended immersed boundary method using FEM and RKPM. Comput. Meth. Appl. Mech. Engng 1193, 1305-1321.
53. WIGGINS, C. H. & GOLDSTEIN, R. E. 1998 Flexive and propulsive dynamics of elastica at low Reynolds number. Phys. Rev. Lett. 80, 3879-3882.
54. WU, T. Y. 1972 Cavity and wake flows. Annu. Rev. Fluid Mech. 4, 243-284.
55. WET, T. Y., WHITNEY, A. K. & LIN, J. D. 1969 Wall effect in cavity flows. Calif. Inst. Technol. Rep. E-111A.5
56. XU, J., LI, Z., LOWENGRUB, J. & ZHAO, H. 2006 A level set method for interfacial flows with surfactant. J. Comput. Phys. 212, 590-616.
57. YE, T., MITTAL, R., UDAYKUMAR, H. S. & SHYY, W. 1999 An accurate Cartesian grid method for viscon, incompressible flow, with complex immersed boundaries. J. Comput. Phys. 156, 209-240.
58. ZHANG, L., GERSTERNBERGER, A., WANG, X. & LIU, W. K. 2004 Immersed finite element method. Comput. Meth. Appl. Mech. Engng 193, 2051-2067.
59. ZHU, L. 2001 Simulation of a flapping flexible filment in a flowing soap film by the immersed boundary method. PhD thesis, Courant Institute of Mathematical Sciences, New York University.
60. ZHU, L. 2007 Viscous How past an elastic fiber tethered at the middle point: Vortex shedding. J. Fluid Mech. 587, 217-234.
61. ZHU, L. & PESKIN, C. S. 2007 Drag of a flexible fiber in a 2D moving viscous fluid. Computers Fluids 36, 398-406.