Geodesic
Convergence of approximate deconvolution models to the mean Navier–Stokes equations
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 2, pp. 171-198

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We consider a 3D Approximate Deconvolution Model ADM which belongs to the class of Large Eddy Simulation (LES) models. We aim at proving that the solution of the ADM converges towards a dissipative solution of the mean Navier–Stokes equations. The study holds for periodic boundary conditions. The convolution filter we first consider is the Helmholtz filter. We next consider generalized convolution filters for which the convergence property still holds.

DOI : 10.1016/j.anihpc.2011.10.001
Classification : 76D05, 35Q30, 76F65, 76D03
Keywords: Navier–Stokes equations, Large eddy simulation, Deconvolution models 
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     author = {Berselli, Luigi C. and Lewandowski, Roger},
     title = {Convergence of approximate deconvolution models to the mean {Navier{\textendash}Stokes} equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {171--198},
     publisher = {Elsevier},
     volume = {29},
     number = {2},
     year = {2012},
     doi = {10.1016/j.anihpc.2011.10.001},
     mrnumber = {2901193},
     zbl = {1302.76083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.10.001/}
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Berselli, Luigi C.; Lewandowski, Roger. Convergence of approximate deconvolution models to the mean Navier–Stokes equations. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 2, pp. 171-198. doi: 10.1016/j.anihpc.2011.10.001

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