Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Perturbation solution of the coupled Stokes-Darcy problem
Pages: 971 - 990, Volume 15, Issue 4, June 2011

doi:10.3934/dcdsb.2011.15.971      Abstract        References        Full text (527.1K)           Related Articles

Sondes khabthani - Laboratoire d'Ingénierie Mathématique, Ecole Polytechnique de Tunisie, Université de Carthage, B.P. 743 - 2078 La Marsa, Tunisia (email)
Lassaad Elasmi - Laboratoire d'Ingénierie Mathématique, Ecole Polytechnique de Tunisie, Université de Carthage, B.P. 743 - 2078 La Marsa, Tunisia (email)
François Feuillebois - LIMSI, UPR 3251 CNRS, BP 133, Bât. 508,91403 Orsay cedex, France (email)

1 G. Beavers and D. Joseph, Boundary conditions at a naturally permeable wall, J. Fluid Mech., 30 (1967), 197-207.
2 G. S. Beavers, E. M. Sparrow and B. A. Masha, Boundary condition at a porous surface which bounds a fluid flow, AIChE. J., 20 (1974), 596-597.
3 J. R. Blake, A note on the image system for a Stokeslet in a no-slip boundary, Proc. Cambridge Philos. Soc., 70 (1971), 303-310.
4 M. Bonnet, "Boundary Integral Equation Methods for Solids and Fluids," John Willey and Sons LTD, 1995.
5 L. Elasmi, Singularity method for Stokes flow with slip boundary condition, IMA Journal of Applied Math., 73 (2008), 724-739.       
6 L. Elasmi and F. Feuillebois, Integral equation method for creeping flow around a solid body near a porous slab, Q. J. Mech. Appl. Math., 56 (2003), 163-185.       
7 B. Goyeau, D. Lhuillier, D. Gobin and M. G. Velarde, Momentum transport at a fluid-porous interface, Int. J. Heat Mass Transfer, 46 (2003), 4071-4081.
8 J. Happel and H. Brenner, "Low Reynolds Number Hydrodynamics," Kluwer Academic Publishers, Dordrecht, Boston, London, 1991.
9 W. Jäger and A. Mikelić, On the interface boundary condition of Beavers, Joseph and Saffman, SIAM J. Appl. Maths, 60 (2000), 1111-1127.       
10 C. Kunert and J. Harting, Roughness induced boundary slip in microchannel flows, Phys. Rev. Letters, 99 (2007), 1-4.
11 N. Lecoq, R. Anthore, B. Cichocki, P. Szymczak and F. Feuillebois, Drag force on a sphere moving towards a corrugated wall, J. Fluid Mech., 513 (2004), 247-264.
12 A. Niavarani and N. Priezjev, The effective slip length and vortex formation in laminar flow over a rough surface, Phys. Fluids, 21 (2009), 1-10.
13 M. E. O'Neill and B. S. Bhatt, Slow motion of a solid sphere in the presence of a naturally permeable surface, Q. J. Mech. Appl. Math., 44 (1991), 91-104.
14 H. Power and L. C. Wrobel, "Boundary Integral Methods in Fluid Mechanics," Computational Mechanics Publications, 1995.
15 C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flow," Cambridge University Press, 1992.       
16 C. Pozrikidis, "A Practical Guide to Boundary Element Methods with the Software Library Bemlib," CRC Press, 2002.       
17 P. G. Saffman, On the boundary condition at the surface of a porous medium, Stud. Appl. Math., 50 (1971), 93-101.
18 M. Sahraoui and M. Kaviany, Slip and no-slip velocity boundary conditions at interface of porous, plain media, Int. J. Heat Mass Transfer, 35 (1992), 927-943.
19 P. Schmitz, D. Houi and B. Wandelt, Hydrodynamic aspects of crossflow microfiltration. Analysis of particle deposition at the membrane surface, J. Membrane Sci., 71 (1992), 29-40.
20 A. Sellier, Settling motion of interacting solid particles in the vicinity of a plane solid boundary, Compte-Rendus Acad. Sci., 333 (2005), 413-418.
21 O. I. Vinogradova and G. E. Yakubov, Surface roughness and hydrodynamic boundary conditions, Phys. Rev. E., 73 (2006), 1-4.

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