The Stokes equations with Fourier boundary conditions on a wall with asperities
Youcef Amirat, Blanca Climent-Ezquerra, Enrique Fernández‐Cara, Jacques Simon · Mathematical Methods in the Applied Sciences · 2001
Abstract We study the effect of the rugosity of a wall on the solution of the Stokes system complemented with Fourier boundary conditions. We consider the case of small periodic asperities of size ε . We prove that the velocity field, pressure and drag, respectively, converge to the velocity field, pressure and drag of a homogenized Stokes problem, where a different friction coefficient appears. This shows that, contrarily to the case of Dirichlet boundary conditions, rugosity is dominant here. Copyright © 2001 John Wiley & Sons, Ltd.