On non-linear Stokes problems with viscosity depending on the distance to the wall

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• 作者：Jacques Rappaz ^{jacques.rappaz@epfl.ch" class="auth_mail" title="E-mail the corresponding author} ; Jonathan Rochat ^{jonathan.rochat@epfl.ch" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Comptes Rendus Mathematique
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：354
• 期：5
• 页码：499-502
• 全文大小：226 K

文摘

In fluid mechanics, the RANS modeling (Reynolds Averaged Navier–Stokes equation) assumes that the period of the averaged solutions to the Navier–Stokes equations is several orders of magnitude larger than the turbulent fluctuations. A type of simple model often used by engineers is a mixing-length model called “Smagorinsky modeling”. In this paper, we present some theoretical and numerical results on a mixing-length model in which the eddy viscosity is depending on the strain tensor and on the distance to the wall of the fluid flow domain. In particular, we show that the so-called von Karman model becomes an ill-posed problem when the laminar viscosity tends to zero.