A positivity preserving finite element–finite volume solver for the Spalart–Allmaras turbulence model

We propose a stable numerical method preserving the positivity of the turbulent viscosity in the Spalart–Allmaras model focusing in particular on the stiffness of the source term. The goal is to apply this model for turbulent flows using an effective numerical method based on a mixed FE–FV method. A mathematical analysis of stability and positivity of the continuous and numerical models is provided. Numerical tests on the 3D boundary layer over a flat plate show the convergence and robustness of the proposed method confirming the theoretical analysis.