A variational finite element model for large-eddy simulations of turbulent flows

The authors introduce a new Large Eddy Simulation model in a channel, based on the projection on finite element spaces as filtering operation in its variational form, for a given triangulation {T (h) } (h > 0). The eddy viscosity is expressed in terms of the friction velocity in the boundary layer due to the wall, and is of a standard sub grid-model form outside the boundary layer. The mixing length scale is locally equal to the grid size. The computational domain is the channel without the linear sub-layer of the boundary layer. The no-slip boundary condition (or BC for short) is replaced by a Navier (BC) at the computational wall. Considering the steady state case, the authors show that the variational finite element model they have introduced, has a solution (v (h) , p (h) ) (h > 0) that converges to a solution of the steady state Navier-Stokes equation with Navier BC.