Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 6, pp. 893-908.

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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 : 10.1051/m2an:2003060
Classification : 35Q30, 65N35, 76M05
Mots-clés : Navier-Stokes equations, turbulence, large Eddy simulation 
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     title = {Mathematical analysis of a spectral hyperviscosity {LES} model for the simulation of turbulent flows},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {893--908},
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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 , Tome 37 (2003) no. 6, pp. 893-908. doi : 10.1051/m2an:2003060. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003060/

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