An unstructured finite elements method for solving the compressible RANS equations and the Spalart-Allmaras turbulence model

This paper deals with a stabilized finite element method for solving the compressible Navier-Stokes equations combined with the Spalart-Allmaras turbulence model. The aim is to assess the ability of this formulation to solve high Reynolds number turbulent flows over anisotropic meshes. This formulation lies in the framework of the Stream-Line-Upwind-Petrove-galerkin method. We propose a simple and efficient formulation for the stabilization τ matrix and develop a shock-capturing operator. Numerical tests on the 3D boundary layer over a flat plate and on the ONERA-M6 wing show the stability and robustness of the proposed method.