Rough boundaries and wall laws
نویسنده
چکیده
We consider Laplace and Stokes operators in domains with rough boundaries and search for an effective boundary condition. The method of homogenization, coupled with the boundary layers, is used to obtain it. In the case of the homogeneous Dirichlet condition at the rough boundary, the effective law is Navier’s slip condition, used in the computations of viscous flows in complex geometries. The corresponding effective coefficient is determined by upscaling. It is given by solving an appropriate boundary layer problem. Finally we address application to the drag reduction. In this review article we will explain how those results are obtained, give precise references for technical details and present open problems.
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