Modeling slender bodies with the method of regularized Stokeslets

Journal of Computational Physics

Volumn 230, Issue 10, 2011, Pages 3929-3947

  Bouzarth, Elizabeth L ^a   Minion, Michael L ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

Immersed boundary; Regularized Stokeslets; Stokes flow

Indexed keywords

BODIES OF REVOLUTION; FLOW OF FLUIDS;

CENTERLINES; DISCRETIZATIONS; IMMERSED BOUNDARY; MATHEMATICAL STRUCTURE; REGULARIZED STOKESLET; SLENDER BODIES; STOKES EQUATIONS; STOKES FLOWS; STOKESLET; THREE-DIMENSIONAL OBJECT;

NUMERICAL METHODS;

EID: 79952899038     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.02.017     Document Type: Article

References (25)

1. Greengard L., Kropinski M.C. Integral equation methods for Stokes flow in doubly-periodic domains. J. Eng. Math. 2004, 48(2):157-170. .
2. Wang H., Lei T., Li J., Huang J., Yao Z. A parallel fast multipole accelerated integral equation scheme for 3D Stokes equations. Int. J. Numer. Methods Eng. 2007, 70(7):812-839. .
3. Wang X., Kanapka J., Ye W., Aluru N.R., White J. Algorithms in FastStokes and its application to micromachined device simulation. J. Eng. Math. 2006, 25(2):248-257.
4. Cortez R. The method of regularized Stokeslets. SIAM J. Sci. Comput. 2001, 23(4):1204-1225.
5. Cortez R., Fauci L., Medovikov A. The method of regularized Stokeslets in three dimensions: analysis, validation, and application to helical swimming. Phys. Fluids 2005, 17(3):031504.1-031504.14.
6. Peskin C. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 1972, 10:252-271.
7. LeVeque R., Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 1994, 31(4):1019-1044.
8. Okada Y., Takeda S., Tanaka Y., Belmonte J.-C., Hirokawa N. Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination. Cell 2005, 121:633-644.
9. Flores H., Lobaton E., Mndez-Diez S., Tlupova S., Cortez R. A study of bacterial flagellar bundling. Bull. Math. Biol. 2005, 67:137-168.
10. Dillon R.H., Fauci L.J., Omoto C., Yang X. Fluid dynamic models of flagellar and ciliary beating. Annal. New York Acad. Sci. 2007, 1101:494-505.
11. L.A. Miller, A. Santhanakrishnan, J.G. Cox, K.M. Leiderman, Three-dimensional flow through simplified models of the endothelial surface layer, J. Theor. Biol., submitted for publication.
12. E.L. Bouzarth, Regularized Singularities and Spectral Deferred Correction Methods: A Mathematical Study of Numerically Modeling Stokes Fluid Flow, Ph.D. Thesis, The University of North Carolina at Chapel Hill, 2008. http://dc.lib.unc.edu/u?/etd,1917.
13. Ainley J., Durkin S., Embid R., Boindala P., Cortez R. The method of images for regularized Stokeslets. J. Comput. Phys. 2008, 227:4600-4616.
14. Cummins B., Gedeon T., Klapper I., Cortez R. Interaction between arthropod filiform hairs in a fluid environment. J. Theor. Biol. 2007, 266-280.
15. Bouzarth E.L., Minion M.L. A multirate integrator for regularized Stokeslets. J. Comput. Phys. 2010, 229:4208-4224.
16. Batchelor G.K. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 1970, 44.
17. J.M. Burgers, On the motion of small particles of elongated form suspended in a viscous liquid, in: Second Report of Viscosity and Plasticity, Kon. Ned. Akad. Wet., Verhand. (Eerste Sectie), 1938, p. 16 (Chapter iii).
18. Taylor G.I. Motion of axisymmetric bodies in viscous fluids. Problems of Hydrodynamics and Continuum Mechanics 1969, 718-724. SIAM.
19. Camassa R., Leiterman T.J., McLaughlin R.M. Trajectory and flow properties for a rod spinning in a viscous fluid. Part 1: An exact solution. J. Fluid Mech. 2008, 612:153-200.
20. T.J. Leiterman, Exact and Asymptotic Low Reynolds, Time-varying Solutions for Spinning Rods with a Comparison to Experiments on the Micro and Macroscale, Ph.D. Thesis, The University of North Carolina at Chapel Hill, 2006.http://dc.lib.unc.edu/u?/etd,397.
21. Pozrikidis C. Boundary Integral and Singularity Methods for Linearized Viscous Flow 1992, Cambridge University Press.
22. Pozrikidis C. Introduction to Theoretical and Computational Fluid Dynamics 1997, Oxford University Press.
23. Smith D.J. A boundary element regularized Stokeslet method applied to cilia- and flagella-driven flow. Proc. R. Soc. A. 2009, 465:3605-3626.
24. Yokoyama T. Motor or sensor: a new aspect of primary cilia function. Anatom. Sci. Int. 2004, 47-54.
25. Chwang A.T., Wu T.Y. Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 1975, 67:787-815.