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We consider the case of a homogeneous, isotropic, fully developed, turbulent flow. We show analytically by using the − 5/3 Kolmogorov's law that the time averaged consistency error of the N th approximate deconvolution LES model converges to zero following a law as the cube root of the averaging radius, independently of the Reynolds number. The consistancy… (More)

In averaging the Navier-Stokes equations the problem of closure arises. Scale similarity models address closure by (roughly speaking) extrapolation from the (known) resolved scales to the (unknown) unresolved scales. In a posteriori tests scale similarity models are often the most accurate but can prove to be unstable when used in a numerical simulation. In… (More)

- W Layton, R Lewandowski
- 2005

The purpose of this report is to give a self-contained and detailed mathematical introduction to the analysis in the report [LL04c] of the accuracy of some predictive model's of turbulence. The models are based on approximate de-convolution methods and were introduced into LES by Stolz and Adams. We recall the development of the models, review the known… (More)

In 1934 J. Leray proposed a regularization of the Navier-Stokes equations whose limits were weak solutions of the NSE. Recently, a modification of the Leray model, called the Leray-alpha model, has atracted study for turbulent flow simulation. One common drawback of Leray type regularizations is their low accuracy. Increasing the accuracy of a simulation… (More)

- W Layton, R Lewandowski
- 2004

We prove that that the time averaged consistency error of the Nth approximate deconvolution LES model converges to zero uniformly in the kinematic viscosity and in the Reynolds number as the cube root of the averaging radius. We also give a higher order but non-uniform consistency error bound for the zeroth order model directly from the Navier-Stokes… (More)

We consider four turbulent models to simulate the boundary mixing layer of the ocean. We show the existence of solutions to these models in the steady-state case then we study the mathematical stability of these solutions.

- Anne-Claire Bennis, Roger Lewandowski, Edriss S Titi
- 2008

On introduit uné equation de déconvolution qui généralise l'algorithme de Van-Cittert pour des conditions aux limites de type océananique avec vent fixé. On en déduit un modèle de SGE pour lequel on a existence et unicité d'une solutionrégulì ere. Nous détaillons un ensemble de simulations numériques qui montrent l'intérêt pratique du modèle. Abstract We… (More)

We consider a Large Eddy Simulation (LES) model for the equations of Magnetohydrodynamics (MHD). We study an α-model that is obtained by adapting to the MHD the approach by Stolz and Adams with van Cittert approximate deconvolution operators. We work with periodic boundary conditions and use the Helmholtz filter. We prove existence and uniqueness of a… (More)

We consider a deconvolution model for 3D periodic flows. We show the existence of a global attractor for the model.