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

Jean-Luc Guermond; Serge Prudhomme

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 6, page 893-908
  • ISSN: 0764-583X

Abstract

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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).

How to cite

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Guermond, Jean-Luc, and Prudhomme, Serge. "Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows." ESAIM: Mathematical Modelling and Numerical Analysis 37.6 (2010): 893-908. <http://eudml.org/doc/194197>.

@article{Guermond2010,
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 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). },
author = {Guermond, Jean-Luc, Prudhomme, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Navier–Stokes equations; turbulence; large Eddy simulation.; convergence; Fourier-Galerkin approximation; weak solution},
language = {eng},
month = {3},
number = {6},
pages = {893-908},
publisher = {EDP Sciences},
title = {Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows},
url = {http://eudml.org/doc/194197},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Guermond, Jean-Luc
AU - Prudhomme, Serge
TI - Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 6
SP - 893
EP - 908
AB - 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).
LA - eng
KW - Navier–Stokes equations; turbulence; large Eddy simulation.; convergence; Fourier-Galerkin approximation; weak solution
UR - http://eudml.org/doc/194197
ER -

References

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