A fully coupled RANS Spalart–Allmaras SUPG formulation for turbulent compressible flows on stretched-unstructured grids

When high Reynolds turbulent flows are combined with complex and large size geometries, computers are no longer enough powerful to deal with Direct Numerical Simulation (DNS) and with the resolution of all the scales of turbulence motion. Therefore, the RANS approaches solve averaged equations and use a model to simulate these scales. This model contains dissipation processes that should not be polluted by the numerical diffusion needed to stabilized approximations for convection-dominated flows. In this paper, we proposed a strongly coupled numerical formulation for the Spalart–Allmaras model, in the framework of stabilized finite element methods. Computations are performed for compressible Newtonian fluids (2D and 3D) on unstructured grids of high aspect ratio. Results are compared with experimental data and also with solutions obtained by different numerical strategies.