Evaluation of interfacial fluid dynamical stresses using the immersed boundary method

Discrete and Continuous Dynamical Systems - Series B

Volumn 11, Issue 2, 2009, Pages 519-540

  Williams, Harvey A R ^a   Fauci, Lisa J ^b   Gaver III, Donald P ^b  

^a SCHLUMBERGER   (United States)

^b Tulane University   (United States)

Author keywords

Immersed boundary; Interfacial stress

Indexed keywords

EID: 60949095005     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2009.11.519     Document Type: Article

References (31)

1. K. M. Arthurs, L. C. Moore, C. S. Peskin, E. B. Pitman and H. E. Layton, Modeling arteriolar flow and mass transport using the immersed boundary method, J. Comp. Phys., 147 (1998), 402-440.
2. J. B. Bell, P. Colellaand H. M. Glatz, A second-order projection method for the incompressible Navier-Stokes equations, J. Comp. Phys., 85 (1989), 257-283.
3. R. P. Beyer and R. J. LeVeque, Analysis of a one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal., 29 (1992), 332-364.
4. D. C. Bottino, Modeling viscoelastic networks and cell deformation in the context of the immersed boundary method, J. Comp. Phys., 147 (1998), 86-113.
5. A. J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp., 22 (1968), 745-762.
6. R. Cortez, L. Fauci and A. Medovikov, The method of regularized stokeslets in three dimensions: analysis, validation, and application to helical swimming, Phys. Fluids., 17 (2005) 031504.
7. R. Dillon, L. Fauci, A. Fogelson and D. P. Gaver, Modeling biofilm processes using the immersed boundary method, J. Comp. Phys., 129 (1996), 57-73.
8. C. D. Eggleton and A. S. Popel, Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids, 10 (1998), 1834-1845.
9. L. Fauci, Peristaltic pumping of solid particles, Computers and Fluids, 21 (1992), 583-598.
10. L. Fauci and A. Fogelson, Truncated newton methods and the modeling of complex immersed elastic structures, Comm. Pure Appl. Math., 46 (1993), 787-818.
11. A. Fogelson, A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting, J. Comp. Phys., 56 (1984), 111-134.
12. D. P. Gaver and S. M. Kute, A theoretical model study of the influence of fluid stresses on a cell adhering to a microchannel wall, Biophys. J., 75 (1998), 721-733.
13. D. P. Gaver, D. Halpern, O. E. Jensen and J. B. Grotberg, The steady motion of a semi-infinite bubble through a flexible-walled channel, J. Fluid Mech., 319 (1996), 25-65.
14. D. Goldstein, R. Handler and L. Sirovich, Direct numerical simulation of turbulent flow over a modeled riblet covered surface, J. Fluid Mech., 302 (1995), 333-376.
15. B. E. Griffith, R. D. Hornung, D. M. McQueen and C. S. Peskin, An adaptive, formally second order accurate version of the immersed boundary method, J. Comp. Phys., 223 (2007), 10-49.
16. H. Haj-Hariri and Q. Shi, Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers, Phys. Fluids, 9 (1997), 845-855.
17. D. N. Ku, D. P. Giddens, C. K. Zairns and S. Glagov, Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plague location and low and oscillating shear stress, Arteriosclerosis, 5 (1985), 293-302.
18. O. A. Ladyzhenskaya, (1969) The mathematical theory of viscous incompressible flow, New York: Gordon & Breach.
19. M. C. Lai and C. S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comp. Phys., 160 (2000), 705-719.
20. R. Mittal and G. Iaccarino, Immersed boundary methods, Ann. Rev. Fluid Mech., 37 (2005), 239.
21. E. P. Newren, A. L. Fogelson, R. D. Guy and R. M. Kirby, Unconditionally stable discretizations of the immersed boundary equations, J. Comp. Phys., 222 (2007), 702-719.
22. C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comp. Phys., 25 (1977), 220-252.
23. C. S. Peskin, The immersed boundary method, Acta Numer., 11 (2002), 479.
24. C. S. Peskin and D. M. McQueen, A three-dimensional computational method for blood-flow in the heart 1. Immersed elastic fibers in a viscous incompressible fluid, J. Comp. Phys., 81 (1989), 372-405.
25. C. S. Peskin and B. F. Printz, Improved volume conservation in the computation of flows with immersed elastic boundaries, J. Comp. Phys., 105 (1993), 33-46.
26. C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flows," Cambridge: Cambridge University Press, 1992.
27. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Numerical Recipes in Fortran - The Art of Scientific Computing," Cambridge: Cambridge University Press, 2nd Edition, 1992.
28. A. H. Shapiro, M. Y. Jaffrin and S. L. Weinberg, Peristaltic pumping with long wavelengths at low Reynolds number, J. Fluid Mech., 37 (1969), 799-825.
29. J. M. Stockie and B. R. Wetton, Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes, J. Comp. Phys., 154 (1999), 41-64.
30. 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. Stat. Comp., 13 (1992), 1361-1376.
31. L. Zhang, A. Gerstenberger, X. Wang and W. K. Liu, Immersed finite element method, Comp. Methods in Appl. Mech. and Engr., 193 (2004), 2051-2067.