Higher Order Boundary Layer Correctors and Wall Laws Derivation: a Unified Approach
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چکیده
In this work we present a unifying approach of boundary layer approximations for newtonian flows in domains with periodic rugous boundaries. We simplify the problem considering the laplace operator. We construct high order approximations and justify rigorously rates of convergence w.r.t. ǫ, the thickness of the ruogosity. We show a negative result for averaged second-order like wall-laws. To circumvent the underlying difficulty, we propose new boundary conditions including microscopic oscillations. We establish theoretical orders of convergence. In a last step we derive a fully oscillating implicit first order wall-law and show that its rate of convergence is actually of three halves. We provide then a numerical assessment of our claims as well as a counter-example that evidences the impossibility of an averaged second order wall law.
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تاریخ انتشار 2006