Recent advances in modeling turbulent flows using a finite element method

The benefit of using unstructured meshes for industrial applications of Computational Fluid Dynamics is now well established. The main advantages of unstructured meshes are to enable an easy and fast (with the use of automatic mesh generator) treatment of complex boundaries and to allow local and automatic mesh refinement. Finite Element methods provide a rigorous mathematics formulation. Nevertheless, implementing complex modelization is more tricky than when using finite volume or finite difference methods on structured meshes, especially when dealing with complex sets of non linear equations such as those encountered in turbulence modelling. This paper presents recent works done at the Research and Development Division of Electricité de France on the implementation of various kinds of turbulence models in the finite element code N3S. First will be detailed the numerical procedure used for solving efficiently the Reynolds Averaged Navier-Stokes Equations (RANSE) coupled with a standard k-ε turbulence model. Then, improvement of the k-ε model will be presented. The extension of this algorithm to more complex turbulence models such as Reynolds Stress Transport Models (RSTM) will be discussed. The last part of the paper will be devoted to the discussion of Large Eddy Simulation (LES) on unstructured meshes.