A finite element, filtered eddy-viscosity method for the navier-stokes equations with large Reynolds number

Eunjung Lee, Max D. Gunzburger

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1 Citation (Scopus)

Abstract

The direct numerical simulation of the Navier-Stokes system in turbulent regimes is a formidable task due to the disparate scales that have to be resolved. Turbulence modeling attempts to mitigate this situation by somehow accounting for the effects of small-scale behavior on that at large-scales, without explicitly resolving the small scales. One such approach is to add viscosity to the problem; the Smagorinsky and Ladyzhenskaya models and other eddy-viscosity models are examples of this approach. Unfortunately, this approach usually results in over-dampening at the large scales, i.e., large-scale structures are unphysically smeared out. To overcome this fault of simple eddy-viscosity modeling, filtered eddy-viscosity methods that add artificial viscosity only to the high-frequency modes were developed in the context of spectral methods. We apply the filtered eddy-viscosity idea to finite element methods based on hierarchical basis functions. We prove the existence and uniqueness of the finite element approximation and its convergence to solutions of the Navier-Stokes system; we also derive error estimates for finite element approximations.

Original languageEnglish
Pages (from-to)384-398
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume385
Issue number1
DOIs
Publication statusPublished - 2012 Jan 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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