A Verification Exercise for Two 2-D Steady Incompressible Turbulent Flows

This paper presents the main results of a detailed Verification study performed for two 2-D, steady, incompressible, turbulent flows taken from the Ercoftac Classic Database, cases 18 and 30. The procedure used for uncertainty estimation is based on a least squares variant of the well-known Grid Convergence Index method. The procedure is tested in different sets of single-block structured grids for each of the two test cases. We have selected several significant integral and local flow quantities to check the reliability of the uncertainty estimates. In the absence of an analytical solution as a reference, we have checked on overlap of the uncertainty ranges found for these flow variables in different grid sets. This has been done for various well-known eddy-viscosity turbulence models. The results of this study show that the uncertainty estimation based on grid refinement studies is not straightforward in complex turbulent flows. For the level of grid refinement adopted, the convergence properties are dependent on the flow quantity selected, the turbulence model, the physical location and the grid lay-out. Furthermore, it is impossible to establish the asymptotic order of convergence for almost all the flow quantities selected. The least squares version of the GCI improves the reliability of the uncertainty estimates when compared with the use of grid triplets. However, the desired 95% target of overlapping error bars is not always satisfied.