A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D

Journal of Computational Physics

Volumn 228, Issue 7, 2009, Pages 2334-2353

  Veerapaneni, Shravan K ^a   Gueyffier, Denis ^b   Zorin, Denis ^b   Biros, George ^c  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

Fast summation methods; Fluid membranes; Inextensible vesicles; Integral equations; Moving boundaries; Numerical methods; Particulate flows

Indexed keywords

COMPUTATIONAL COMPLEXITY; INTEGRODIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; PARALLEL PROCESSING SYSTEMS; STABILITY;

BOUNDARY INTEGRAL METHODS; FAST SUMMATION; FAST SUMMATION METHOD; FLUID MEMBRANE; INEXTENSIBLE VESICLE; MOVING BOUNDARIES; PARTICULATE FLOWS; STABILITY CONSTRAINTS; TIME STEP; VISCOUS FLUIDS;

NUMERICAL METHODS;

EID: 60049101665     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.11.036     Document Type: Article

References (44)

1. Alpert B.K. Hybrid Gauss-trapezoidal quadrature rules. SIAM Journal on Scientific Computing 20 (1999) 1551-1584
2. Ascher U.M., and Petzold L.R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (1998), Society for Industrial and Applied Mathematics, Philadelphia, PA, USA
3. Ascher U.M., Ruuth S.J., and Wetton B.T.R. Implicit-explicit methods for time-dependent partial differential equations. SIAM Journal on Numerical Analysis 32 (1995) 797-823
4. Beale J.T., Hou T.Y., and Lowengrub J. Convergence of a boundary integral method for water waves. Siam Journal On Numerical Analysis 33 (1996) 1797-1843
5. Biros G., Ying L., and Zorin D. A fast solver for the stokes equations with distributed forces in complex geometries. Journal of Computational Physics 194 (2004) 317-348
6. Pozrikidis C. Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. Journal of Fluid Mechanics 440 (2001) 269-291
7. Cheng H., and Greengard L. On the numerical evaluation of electrostatic fields in dense random dispersions of cylinders. Journal of Computational Physics 136 (1997) 629-639
8. de Haas K.H., Blom C., van den Ende D., Duits M.H.G., and Mellema J. Deformation of giant lipid bilayer vesicles in shear flow. Physical Review E 56 (1997) 7132-7137
9. Dimitrakopoulos P. Interfacial dynamics in Stokes flow via a three-dimensional fully-implicit interfacial spectral boundary element algorithm. Journal Of Computational Physics 225 (2007) 408-426
10. Du Q., Liu C., and Wang X. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. Journal of Computational Physics 198 (2004) 450-468
11. Du Q., Liu C., and Wang X. Simulating the deformation of vesicle membranes under elastic bending energy in three-dimensions. Journal of Computational Physics 212 (2006) 757-777
12. Sackmann E. Supported membranes: scientific and practical applications. Science 271 (1996) 43-48
13. Feng F., and Klug W.S. Finite element modeling of lipid bilayer membranes. Journal of Computational Physics 220 (2006) 394-408
14. Greengard L. The Rapid Evaluation of Potential Fields in Particle Systems (1988), MIT Press, Cambridge, Mass
15. Hairer E., and Wanner G. Solving Ordinary Differential Equations II (1980), Springer-Verlag
16. Hou T.Y., Lowengrub J.S., and Shelley M.J. Removing the stiffness from interfacial flows with surface tension. Journal of Computational Physics 114 (1994) 312-338
17. Acrivos A., and Youngren G.K. Stokes flow past a particle of arbitrary shape: a numerical method of solution. Journal of Fluid Mechanics 69 (1975) 377-403
18. Kantsler V., and Steinberg V. Orientation and dynamics of a vesicle in tank-treading motion in shear flow. Physical Review Letters 95 (2005)
19. Kraus M., Wintz W., Seifert U., and Lipowsky R. Fluid vesicles in shear flow. Physical Review Letters 77 (1996)
20. Kraus M., Wintz W., Seifert U., and Lipowsky R. Fluid vesicles in shear flow. Physical Review Letters 77 (1996) 3685-3688
21. Kropinski M.C.A. Integral equation methods for particle simulations in creeping flows. Computers and Mathematics with Applications 38 (1999) 67-87
22. Kropinski M.C.A. Numerical methods for multiple inviscid interfaces in creeping flows. Journal of Computational Physics 180 (2002) 1-24
23. Kropinski M.C.A. An efficient numerical method for studying interfacial motion in two-dimensional creeping flows. Journal of Computational Physics 171 (2001) 479-508
24. Li X., Barthes-Biesel D., and Helmy A. Large deformations and burst of a capsule freely suspended in an elongational flow. Journal of Fluid Mechanics 187 (1988) 179-196
25. Markvoort A.J., Van Santen R.A., and Hilbers P.A.J. Vesicle shapes from molecular dynamics simulations. Journal of Physical Chemistry B 110 (2006) 22780-22785
26. H. Noguchi, G. Gompper, Shape transitions of fluid vesicles and red blood cells in capillary flows, in: Proceedings of The National Academy of Sciences of The United States of America, vol. 102, 2005, pp. 14159-14164.
27. Power H., and Wrobel L. Boundary integral methods in fluid mechanics (1995), Computational Mechanics Publications
28. Pozrikidis C. The axisymmetric deformation of a red blood cell in uniaxial straining Stokes flow. Journal of Fluid Mechanics 216 (1990) 231-254
29. Pozrikidis C. Boundary Integral and Singularity Methods for Linearized Viscous Flow (1992), Cambridge University Press, Cambridge
30. Pozrikidis C. On the transient motion of ordered suspensions of liquid drops. Journal of Fluid Mechanics 246 (1993) 301-320
31. Pozrikidis C. Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. Journal of Fluid Mechanics 297 (1995) 123-152
32. Pozrikidis C. Interfacial dynamics for stokes flow. Journal of Computational Physics 169 (2001) 250-301
33. Rallison J., and Acrivos A. A numerical study of the deformation and burst of a viscous drop in an extensional flow. Journal of Fluid Mechanics 89 (1978) 191-200
34. Reddy S.C., and Trefethen L.N. Stability of the method of lines. Numerische Mathematik 62 (1992) 235-267
35. Saad Y. Iterative Methods for Sparse Linear Systems. second ed. (2003), SIAM, Philadelpha, PA
36. Seifert U. Adhesion of vesicles in two-dimensions. Physical Review A 43 (1991) 6803-6814
37. Seifert U. Configurations of fluid membranes and vesicles. Advances in Physics 46 (1997) 13-137
38. Stevens M.J. Coarse-grained simulations of lipid bilayers. Journal of Chemical Physics 121 (2004)
39. Sukumaran S., and Seifert U. Influence of shear flow on vesicles near a wall: a numerical study. Physical Review E 64 (2001)
40. Tornberg A.-K., and Greengard L. A fast multipole method for the three-dimensional Stokes equations. Journal of Computational Physics 227 (2008) 1613-1619
41. Tornberg A.-K., and Shelley M. Simulating the dynamics and interactions of flexible fibers in stokes flows. Journal of Computational Physics 196 (2004) 8-40
42. Ying L., Biros G., and Zorin D. A high-order 3D boundary integral equation solver for elliptic pdes in smooth domains. Journal of Computational Physics 219 (2006) 247-275
43. Yuhong Fu G.J.R. Fast solution method for three-dimensional stokesian many-particle problems. Communications in Numerical Methods in Engineering 16 (2000) 145-149
44. Zhou H., and Pozrikidis C. Deformation of liquid capsules with incompressible interfaces in simple shear flow. Journal of Fluid Mechanics 283 (1995) 175-200