Équations aux dérivées partielles, Mécanique des fluides
Equilibrium configuration of a rectangular obstacle immersed in a channel flow
Comptes Rendus. Mathématique, Tome 358 (2020) no. 8, pp. 887-896.

Fluid flows around an obstacle generate vortices which, in turn, generate lift forces on the obstacle. Therefore, even in a perfectly symmetric framework equilibrium positions may be asymmetric. We show that this is not the case for a Poiseuille flow in an unbounded 2D channel, at least for small Reynolds number and flow rate. We consider both the cases of vertically moving obstacles and obstacles rotating around a fixed pin.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/crmath.95
Classification : 35Q30,  35A02,  46E35,  31A15
@article{CRMATH_2020__358_8_887_0,
author = {Denis Bonheure and Giovanni P. Galdi and Filippo Gazzola},
title = {Equilibrium configuration of a rectangular obstacle immersed in a channel flow},
journal = {Comptes Rendus. Math\'ematique},
pages = {887--896},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {8},
year = {2020},
doi = {10.5802/crmath.95},
language = {en},
}
Denis Bonheure; Giovanni P. Galdi; Filippo Gazzola. Equilibrium configuration of a rectangular obstacle immersed in a channel flow. Comptes Rendus. Mathématique, Tome 358 (2020) no. 8, pp. 887-896. doi : 10.5802/crmath.95. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.95/

[1] Juan Antonio Bello; Enrique Fernández-Cara; Jérôme Lemoine; Jacques Simon The differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier-Stokes flow, SIAM J. Control Optimization, Volume 35 (1997) no. 2, pp. 626-640 | Article | MR 1436642 | Zbl 0873.76019

[2] Denis Bonheure; Filippo Gazzola; Gianmarco Sperone Eight(y) mathematical questions on fluids and structures, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl., Volume 30 (2019) no. 4, pp. 759-815 | Article | MR 4030349 | Zbl 07146063

[3] Giovanni P. Galdi An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems, Springer, 2011 | Zbl 1245.35002

[4] Giovanni P. Galdi; Vincent Heuveline Lift and sedimentation of particles in the flow of a viscoelastic liquid in a channel, Free and moving boundaries (Lecture Notes in Pure and Applied Mathematics) Volume 252, Chapman & Hall/CRC, 2007 | MR 2346983 | Zbl 1403.76187

[5] Filippo Gazzola Mathematical models for suspension bridges. Nonlinear structural instability, MS & A Modeling, Simulation and Applications, Volume 15, Springer, 2015 | Zbl 1325.00032

[6] Filippo Gazzola; Gianmarco Sperone Steady Navier–Stokes equations in planar domains with obstacle and explicit bounds for unique solvability, Arch. Ration. Mech. Anal., Volume 238 (2020) no. 3, pp. 1283-1347 | Article | MR 4160801 | Zbl 07261979

[7] Antoine Henrot; Michel Pierre Shape Variation and Optimization: A Geometrical Analysis, EMS Tracts in Mathematics, Volume 28, European Mathematical Society, 2018 | Zbl 1392.49001

[8] B. P. Ho; L. Gary Leal Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid Mech., Volume 65 (1974), pp. 365-400 | Zbl 0284.76076