We first outline the procedure of averaging the incompressible Navier-Stokes equations when the flow is turbulent for various type of filters. We introduce the turbulence model called Bardina’s model, for which we are able to prove existence and uniqueness of a distributional solution. In order to reconstruct some of the flow frequencies that are underestimated by Bardina’s model, we next introduce the approximate deconvolution model (ADM). We prove existence and uniqueness of a “regular weak solution” to the ADM for each deconvolution order , and then that the corresponding sequence of solutions converges to the mean Navier-Stokes Equations when goes to infinity.
@article{SLSEDP_2011-2012____A36_0,
author = {Lewandowski, Roger},
title = {On {Bardina} and {Approximate} {Deconvolution} {Models}},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:36},
pages = {1--12},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2011-2012},
doi = {10.5802/slsedp.27},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.27/}
}
TY - JOUR AU - Lewandowski, Roger TI - On Bardina and Approximate Deconvolution Models JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:36 PY - 2011-2012 SP - 1 EP - 12 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.27/ DO - 10.5802/slsedp.27 LA - en ID - SLSEDP_2011-2012____A36_0 ER -
%0 Journal Article %A Lewandowski, Roger %T On Bardina and Approximate Deconvolution Models %J Séminaire Laurent Schwartz — EDP et applications %Z talk:36 %D 2011-2012 %P 1-12 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.27/ %R 10.5802/slsedp.27 %G en %F SLSEDP_2011-2012____A36_0
Lewandowski, Roger. On Bardina and Approximate Deconvolution Models. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 36, 12 p. doi : 10.5802/slsedp.27. http://www.numdam.org/articles/10.5802/slsedp.27/
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