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We introduce a new Large Eddy Simulation model in a channel, based on theprojection on finite element spaces as filtering operation in its variationalform, for a given triangulation $\{{\cal T}_h \}_{h>0}$. The eddy viscosity isexpressed in terms of the friction velocity in the boundary layer due to thewall, and is of a standard sub grid-model form outside the boundary layer. Themixing length scale is locally equal to the grid size. The computational domainis the channel without the linear sub-layer of the boundary layer. The no slipboundary condition (BC) is replaced by a Navier (BC) at the computational wall.Considering the steady state case, we show that the variational finite elementmodel we have introduced, has a solution $(\vv_h, p_h)_{h>0}$ that converges toa solution of the steady state Navier-Stokes Equation with Navier BC.

A Variational Finite Element Model for Large-Eddy Simulations of Turbulent Flows