Numerical approximation of laminar flows over rough walls with sharp asperities

We consider a viscous incompressible fluid filling an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rough wall. The latter is assumed to consist of a plane wall covered with periodically distributed asperities which size depends on a small parameter ε > 0. The assumption of sharp asperities is made, that is the height of the asperities does not vanish as ε → 0. The rough wall is at rest and the plane wall is moving at a constant horizontal velocity. We assume that the flow is governed by the stationary Stokes equations. We give an asymptotic approximation of the Stokes flow, under the rugose region, by a Couette flow, depending on the size ε of asperities. We then build a numerical approximation of the Couette flow based on a partial domain decomposition method. Classification MSC : 35B40, 35C20, 35Q30, 65N99 ∗email : [email protected] †email : [email protected]