Verification testing in computational fluid dynamics: an example using Reynolds-averaged Navier-Stokes methods for two-dimensional flow in the near wake of a circular cylinder

Verification testing was performed for various Reynolds-averaged Navier-Stokes methods for uniform flow past a circular cylinder at Re= 5232. The standard and renormalized group (RNG) versions of the k-(epsilon) method were examined, along with the Boussinesq, Speziale and Launder constitutive relationships. Wind tunnel experiments for flow past a circular cylinder were also performed to obtain a comparative data set. Preliminary studies demonstrate poor convergence for the Speziale relationship. Verification testing with the standard and RNG k-(epsilon) models suggests that the simulations exhibit global monotonic convergence for the Boussinesq models. However, the global order of accuracy of the methods was much lower than the expected order of accuracy of 2. For this reason, pointwise convergence ratios and orders of accuracy were computed to show that not all sampling locations had converged (standard k-(epsilon) model: 19% failed to converge; RNG k-(epsilon) model: 14% failed to converge). When the non-convergent points were removed from consideration, the average orders of accuracy are closer to the expected value (standard k-(epsilon) model: 1.41; RNG k-(epsilon) model: 1.27). Poor iterative and global grid convergence was found for the RNG k-(epsilon)/Launder model. The standard and RNG k-(epsilon) models with the Boussinesq relationship were compared with experimental data and yielded results significantly different from the experiments.