MATHEMATICAL ANALYSIS OF A SPECTRAL HYPERVISCOSITY LES MODEL FOR THE SIMULATION OF TURBULENT FLOWS

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 cuto wavenumber goes to innity, the solution of the model converges (up to subsequences) to a weak solution which is dissipative in the sense dened by Duchon and Robert (2000).

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