Grid-Convergence of Reynolds-Averaged Navier-Stokes Solutions for Benchmark Flows in Two Dimensions

A detailed grid-convergence study has been conducted to establish reference solutions corresponding to the one-equation linear eddy-viscosity Spalart-Allmaras turbulence model for two-dimensional turbulent flows around the NACA0012 airfoil and a flat plate. The study involved the three widely used codes CFL3D (NASA), FUN3D (NASA), and TAU (DLR, The German Aerospace Center), as well as families of uniformly refined structured grids that differed in the grid density patterns. Solutions computed by different codes on different grid families appeared to converge to the same continuous limit but exhibited strikingly different convergence characteristics. The grid resolution in the vicinity of geometric singularities, such as a sharp trailing edge, was found to be the major factor affecting accuracy and convergence of discrete solutions; the effects of this local grid resolution were more prominent than differences in discretization schemes and/or grid elements. The results reported for these relatively simple turbulent flows demonstrated that CFL3D, FUN3D, and TAU solutions were very similar on the finest grids used in the study, but even those grids were not sufficient to conclusively establish an asymptotic convergence order.