Mathematical perspectives on Large Eddy Simulation models for turbulent flows

J. L. Guermond*, J. T. Oden, Serge Prudhomme

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Scopus citations

Abstract

The main objective of this paper is to review and report on key mathematical issues related to the theory of Large Eddy Simulation of turbulent flows. We review several LES models for which we attempt to provide mathematical justifications. For instance, some filtering techniques and nonlinear viscosity models are found to be regularization techniques that transform the possibly ill-posed Navier-Stokes equation into a well-posed set of PDE's. Spectral eddy-viscosity methods are also considered. We show that these methods are not spectrally accurate, and, being quasi-linear, that they fail to be regularizations of the Navier-Stokes equations. We then propose a new spectral hyper-viscosity model that regularizes the Navier-Stokes equations while being spectrally accurate. We finally review scale-similarity models and two-scale subgrid viscosity models. A new energetically coherent scale-similarity model is proposed for which the filter does not require any commutation property nor solenoidality of the advection field. We also show that two-scale methods are mathematically justified in the sense that, when applied to linear non-coercive PDE's, they actually yield convergence in the graph norm.

Original languageEnglish (US)
Pages (from-to)194-248
Number of pages55
JournalJournal of Mathematical Fluid Mechanics
Volume6
Issue number2
DOIs
StatePublished - Jun 1 2004

Keywords

  • Large eddy simulation
  • Navier-Stokes equations
  • Turbulence

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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