Implicit second-order immersed boundary methods with boundary mass

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 25-28, 2008, Pages 2049-2067

  Mori, Yoichiro ^a   Peskin, Charles S ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Boundary with mass; Fluid structure interaction; Immersed boundary method; Implicit method

Indexed keywords

BOUNDARY ELEMENT METHOD; ELASTICITY; FLUID STRUCTURE INTERACTION;

ELASTIC FORCE; IMMERSED BOUNDARY METHOD; IMPLICIT METHOD;

COMPUTATIONAL FLUID DYNAMICS;

BOUNDARY ELEMENT METHOD; COMPUTATIONAL FLUID DYNAMICS; ELASTICITY; FLUID STRUCTURE INTERACTION;

EID: 41849088118     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.05.028     Document Type: Article

References (38)

1. McQueen D.M., and Peskin C.S. Heart simulation by an immersed boundary method with formal second order accuracy and reduced numerical viscosity. Mechanics for a New Millennium, Proceedings of the International Conference on Theoretical and Applied Mechanics (ICTAM) 2000 (2001), Kluwer Academic Publishers
2. Beyer R.P. A computational model of the cochlea using the immersed boundary method. J. Comput. Phys. 98 (1992) 145-162
3. E. Givelberg, Modeling elastic shells immersed in fluid, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1997.
4. Fauci L.J., and Fogelson A.L. Truncated Newton methods and the modeling of complex immersed elastic structures. Comm. Pure Appl. Math. 46 (1993) 787-816
5. Wang N.T., and Fogelson A.L. Computational methods or continuum models of platelet aggregation. J. Comput. Phys. 151 2 (1999) 649-675
6. H. Yu, Three-dimensional computational modeling and simulation of platelet aggregation on parallel computers, Ph.D. thesis, University of Utah, 2000.
7. Fauci L.J., and Peskin C.S. A computational model of aquatic animal locomotion. J. Comput. Phys. 77 (1988) 85-108
8. Fauci L.J. Interaction of oscillating filaments - a computational study. J. Comput. Phys. 86 (1990) 294-313
9. Hopkins M., and Fauci L.J. A computational model of the collective fluid dynamics of motile microorganisms. J. Fluid Mech. 455 (2002) 149-174
10. Cortez R., Cowen N., Dillon R., and Fauci L.J. Simulation of swimming organisms: coupling internal mechanics with external fluid dynamics. Comput. Sci. Engrg. 6 3 (2004) 38-45
11. Miller L.A., and Peskin C.S. When vortices stick: an aerodynamic transition in tiny insects. J. Exp. Biol. 207 (2004) 3073-3088
12. Miller L.A., and Peskin C.S. A computational fluid dynamics of 'clap and fling' in small insects. J. Exp. Biol. 208 (2005) 195-212
13. Fogelson A.L., and Peskin C.S. A fast numerical method for solving three-dimensional Stokes' equations in the presence of suspended particles. J. Comput. Phys. 79 (1988) 50-69
14. Stockie J.M., and Green S.I. Simulating the motion of flexible pulp fibres using the immersed boundary method. J. Comput. Phys. 147 (1998) 147-165
15. Jung E.N., and Peskin C.S. Two-dimensional simulations of valveless pumping using the immersed boundary method. SIAM J. Sci. Comput. 23 (2001) 19-45
16. Rosar M.E., and Peskin C.S. Fluid flow in collapsible elastic tubes: a three-dimensional numerical method. New York J. Math. 7 (2001) 281-302
17. Lim S., and Peskin C.S. Simulations of the whirling instability by the immersed boundary method. SIAM J. Sci. Comput. 25 (2004) 2066-2083
18. Cortez R., Peskin C.S., Stockie J., and Varela D. Parametric resonance in immersed elastic boundaries. SIAM J. Appl. Math. 65 (2004) 494-520
19. Peskin C.S. The immersed boundary method. Acta Numer. 11 (2002) 479-517
20. 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
21. Tu C., and Peskin C.S. 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
22. Mayo A.A., and Peskin C.S. An implicit numerical method for fluid dynamics problems with immersed elastic boundaries. Fluid Dynamics in Biology: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference of Biofluid dynamics. Contemporary Mathematics vol. 141 (1993), AMS 261-277
23. Newren E.P., Fogelson A., Guy R., and Kirby R. Unconditionally stable discretizations of the immersed boundary equations. J. Comput. Phys. 222 (2007) 702-719
24. Wang X. From immersed boundary method to immersed continuum method. Int. J. Multiscale Comput. Engrg. 4 (2006) 127-145
25. D. Boffi, L. Gastaldi, L. Heltai, Stability results for the finite element approach to the immersed boundary method, in: K.J. Bathe (Ed.), Proceeding of the Third M.I.T Conference on Computational Fluid and Solid Mechanics, 2005, pp. 93-96.
26. L. Heltai, The finite element immersed boundary method, Ph.D. thesis, Università di Pavia, Dipartimento di Matematica "F. Casorati", submitted.
27. Griffith B.E., and Peskin C.S. On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems. J. Comput. Phys. 208 (2005) 75-105
28. Zhu L., and Peskin C.S. Simulation of a flexible flapping filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 79 2 (2002) 452-468
29. Y. Kim, The penalty immersed boundary method and its application to aerodynamics, Ph.D. thesis, New York University, 2003.
30. Kim Y., Zhu L., Wang X., and Peskin C. On various techniques for computer simulation of boundaries with mass. In: Bathe K. (Ed). Computational Fluid and Solid Mechanics 2003 (2003), Elsevier Science Ltd. 1746-1750
31. Lai M.-C., and Peskin C.S. An immersed boundary method with formal second order accuracy and reduce numerical viscosity. J. Comput. Phys. 160 2 (2000) 705-719
32. Chorin A.J. Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (1968) 745-762
33. Chorin A.J. On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comput. 23 (1969) 341-353
34. Saad Y. Iterative Methods for Sparse Linear Systems. second ed. (2003), SIAM
35. van der Vorst H.A. Iterative Krylov methods for large linear systems. Cambridge Monographs on Applied and Computational Mathematics vol. 13 (2003), Cambridge University Press
36. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7 (1986) 856-869
37. van der Vorst H.A. Bi-CGSTAB: a fast smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Statist. Comput. 13 (1992) 631-644
38. Sonneveld P. CGS, a fast lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 10 (1989) 36-52