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Article Dans Une Revue Annales de l'Institut Henri Poincaré C, Analyse non linéaire Année : 2007

A RANS 3D model with unbounded eddy viscosities

Julien Lederer
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Résumé

We consider the Reynolds Averaged Navier-Stokes (RANS) model of order one (u, p, k) set in R-3 which couples the Stokes Problem to the equation for the turbulent kinetic energy by k-dependent eddy viscosities in both equations and a quadratic term in the k-equation. We study the case where the velocity and the pressure satisfy periodic boundary conditions while the turbulent kinetic energy is defined on a cell with Dirichlet boundary conditions. The corresponding eddy viscosity in the fluid equation is extended to R3 by periodicity. Our contribution is to prove that this system has a solution when the eddy viscosities are nondecreasing, smooth, unbounded functions of k, and the eddy viscosity in the fluid equation is a concave function.

Dates et versions

hal-00363812 , version 1 (24-02-2009)

Identifiants

Citer

Julien Lederer, Roger Lewandowski. A RANS 3D model with unbounded eddy viscosities. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2007, 24 (3), pp.413-441. ⟨10.1016/j.anihpc.2006.03.011⟩. ⟨hal-00363812⟩
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