Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France. email@example.com.
2 ICES, formerly TICAM, The University of Texas at Austin, TX 78712, USA
3 On leave at Universidad de los Andes, Bogotá, Colombia. firstname.lastname@example.org.
Revised: 1 July 2003
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).
Mathematics Subject Classification: 35Q30 / 65N35 / 76M05
Key words: Navier–Stokes equations / turbulence / large Eddy simulation.
© EDP Sciences, SMAI, 2003