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

Abstract

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.

Keywords

Navier-Stokes equations / Turbulence modeling / Finite elements

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