Discontinuous Galerkin solution of RANS equations on curved mesh

Discontinuous Galerkin (DG) finite element method was adopted for the numerical approximation of the Reynolds-averaged Navier-Stokes(RANS) equations with the Spalart-Allmaras turbulence model. In order to make the solver robust, the original turbulence model equation were modified accordingly. Furthermore, high order approximation of the real solid boundary was used and several layers of curved meshes were constructed to avoid inconsistent mesh cross-overs. For the computation of the distance of each quadrature point to the nearest curved wall boundaries, a fast straightforward numerical method was proposed. The DG discretization of the RANS equations were demonstrated for turbulent flows past a NACA0012 airfoil and RAE airfoil based on hybrid mesh. Numerical results indicate that highly accurate solutions can be obtained with the modified turbulent equation on coarse curved hybrid mesh.