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Mathematical analysis of a spectral hyperviscosityLES model for the simulation of turbulent flows

Published online by Cambridge University Press:  15 November 2003

Jean-Luc Guermond  and
Serge Prudhomme
Jean-Luc Guermond
Affiliation:
LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France. [email protected]. ICES, formerly TICAM, The University of Texas at Austin, TX 78712, USA
Serge Prudhomme
Affiliation:
ICES, formerly TICAM, The University of Texas at Austin, TX 78712, USA On leave at Universidad de los Andes, Bogotá, Colombia. [email protected].
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Abstract

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 perturbedNavier–Stokes equations and we show that, as the cutoff wavenumbergoes to infinity, the solution of the modelconverges (up to subsequences) to a weak solution which is dissipativein the sense defined by Duchon and Robert (2000).

Keywords

Navier–Stokes equationsturbulencelarge Eddy simulation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 6 , November 2003 , pp. 893 - 908
Copyright
© EDP Sciences, SMAI, 2003

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