Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 57, Issue 9, Pages 1153-1170Publisher
JOHN WILEY & SONS LTD
DOI: 10.1002/fld.1853
Keywords
Navier-Stokes; weak solutions; suitable solutions; existence/uniqueness; turbulence; LES
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The notion of suitable weak solutions for the three-dimensional incompressible Navier Stokes equations together with some standard regularization techniques for constructing these solutions is reviewed. The novel result presented in this paper is that Faedo-Galerkin weak solutions to the Navier-Stokes equations are suitable provided they are constructed using finite-dimensional spaces having a discrete commutator property and satisfying a proper inf-sup condition. Low-order mixed finite element spaces appear to be acceptable for this purpose. Connections between the notion Of Suitable Solutions and LES modeling are investigated. A proposal for a large eddy scale model based on the notion of suitable solutions is made and numerically illustrated. Copyright (C) 2008 John Wiley & Sons, Ltd.
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