On the use of the notion of suitable weak solutions in CFD

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.