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, Volume 37 (2003) no. 6, p. 893-908

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).

DOI : https://doi.org/10.1051/m2an:2003060
Classification:  35Q30,  65N35,  76M05
Keywords: Navier-Stokes equations, turbulence, large Eddy simulation
@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},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {6},
     year = {2003},
     pages = {893-908},
     doi = {10.1051/m2an:2003060},
     zbl = {1070.76035},
     mrnumber = {2026401},
     language = {en},
     url = {http://www.numdam.org/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, Volume 37 (2003) no. 6, pp. 893-908. doi : 10.1051/m2an:2003060. http://www.numdam.org/item/M2AN_2003__37_6_893_0/

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