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.
Keywords: Navier–Stokes equations, Large eddy simulation, Deconvolution models
@article{AIHPC_2012__29_2_171_0, 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://www.numdam.org/articles/10.1016/j.anihpc.2011.10.001/} }
TY - JOUR AU - Berselli, Luigi C. AU - Lewandowski, Roger TI - Convergence of approximate deconvolution models to the mean Navier–Stokes equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2012 SP - 171 EP - 198 VL - 29 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.001/ DO - 10.1016/j.anihpc.2011.10.001 LA - en ID - AIHPC_2012__29_2_171_0 ER -
%0 Journal Article %A Berselli, Luigi C. %A Lewandowski, Roger %T Convergence of approximate deconvolution models to the mean Navier–Stokes equations %J Annales de l'I.H.P. Analyse non linéaire %D 2012 %P 171-198 %V 29 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.001/ %R 10.1016/j.anihpc.2011.10.001 %G en %F AIHPC_2012__29_2_171_0
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, Volume 29 (2012) no. 2, pp. 171-198. doi : 10.1016/j.anihpc.2011.10.001. http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.001/
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