This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier-Galerkin approximation of the perturbed Navier-Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak solution which is dissipative in the sense defined by Duchon and Robert (2000).
@article{M2AN_2003__37_6_893_0,
author = {Guermond, Jean-Luc and Prudhomme, Serge},
title = {Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {37},
year = {2003},
pages = {893-908},
doi = {10.1051/m2an:2003060},
mrnumber = {2026401},
zbl = {1070.76035},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2003__37_6_893_0}
}
Guermond, Jean-Luc; Prudhomme, Serge. Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) pp. 893-908. doi : 10.1051/m2an:2003060. http://gdmltest.u-ga.fr/item/M2AN_2003__37_6_893_0/
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