A variational finite element model for Large-Eddy simulations of turbulent flows

Abstract

We 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 {Th}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 (BC) is replaced by a Navier (BC) at the computational wall. Considering the steady state case, we show that the variational finite element model we have introduced, has a solution (vh, ph)h>0 that converges to a solution of the steady state Navier-Stokes Equation with Navier BC.