High Order Multi-Scale Wall-Laws, Part I : The Periodic Case

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dc.creatorBresch, Didier
dc.creatorMilisic, Vuk
dc.date2006-11-03
dc.date2007-12-17
dc.date.accessioned2026-07-07T08:49:23Z
dc.date.available2026-07-07T08:49:23Z
dc.descriptionIn this work we present new wall-laws boundary conditions including microscopic oscillations. We consider a newtonian flow in domains with periodic rough boundaries that we simplify considering a Laplace operator with periodic inflow and outflow boundary conditions. Following the previous approaches, see [A. Mikelic, W. Jäger, J. Diff. Eqs, 170, 96-122, (2001) ] and [Y. Achdou, O. Pironneau, F. Valentin, J. Comput. Phys, 147, 1, 187-218, (1998)], we construct high order boundary layer approximations and rigorously justify their rates of convergence with respect to epsilon (the roughness' thickness). We establish mathematically a poor convergence rate for averaged second-order wall-laws as it was illustrated numerically for instance in [Y. Achdou, O. Pironneau, F. Valentin, J. Comput. Phys, 147, 1, 187-218, (1998)]. In comparison, we establish exponential error estimates in the case of explicit multi-scale ansatz. This motivates our study to derive implicit first order multi-scale wall-laws and to show that its rate of convergence is at least of order epsilon to the three halves. We provide a numerical assessment of the claims as well as a counter-example that evidences the impossibility of an averaged second order wall-law. Our paper may be seen as the first stone to derive efficient high order wall-laws boundary conditions.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0611083
dc.identifierhttp://arxiv.org/abs/math/0611083
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144280
dc.subjectAnalysis of PDEs
dc.subjectClassical Physics
dc.subject76D05, 35B27, 76Mxx, 65Nxx
dc.titleHigh Order Multi-Scale Wall-Laws, Part I : The Periodic Case
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