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E ective boundary conditions for laminar ows over periodic rough boundaries
 

Summary: Eective boundary conditions for laminar ows over
periodic rough boundaries
Yves Achdou  ,
O.Pironneau y ,
F.Valentin z
October 5, 1998
Abstract
Eective boundary conditions or wall laws are proposed for a laminar
ow over a rough wall with periodic roughness elements. These eective
conditions are posed on a regularized boundary which allows the details
of the wall to be avoided and dramatically reduces the computational
cost. The eective conditions stem from an asymptotic expansion of the
solution, which is presented here. Both rst and second order conditions
are discussed and tested numerically on bidimensional cases.
1 Introduction
Rough boundaries are a challenge to numerical simulations because they are
dicult to discretize and they require many mesh nodes near them even with
unstructured meshes.
Yet there are many practical problems which have rough boundaries: elec-
tromagnetic scattering by an obstacle coated with an absorbing inhomogeneous

  

Source: Achdou, Yves - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6

 

Collections: Mathematics