Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows

Guermond, Jean-Luc; Prudhomme, Serge

ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 6, pp. 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).

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