A Solution Verification Study for URANS Simulations of Flow Over a 5:1 Rectangular Cylinder Using Grid Convergence Index and Least Squares Procedures

A verification study was conducted for URANS (Unsteady Reynolds-Averaged Navier–Stokes) simulations of flow around a 5:1 rectangular cylinder at a Reynolds number of 56,700 (based on the cylinder depth) using the k–ω SST (shear stress transport) turbulence model and the γ−Reθ transition model for three types of grids (a fully structured grid and two hybrid grids generated using Delaunay and advancing front techniques). The grid convergence index (GCI) and least squares (LS) procedures were employed to estimate discretization error and associated uncertainties. The result indicates that the LS procedure provides the most reliable estimates of discretization error uncertainties for solution variables in the structured grid from the k–ω SST model. From the six solution variables of interest, the highest relative uncertainty was typically observed in the root-mean-square (rms) of lift coefficient, followed by time-averaged reattachment length and peak rms of pressure coefficient on the top and bottom surfaces of the cylinder. The solution variable with the lowest uncertainty was Strouhal number, followed by time-averaged drag coefficient. It is also noted that the GCI and LS procedures produce noticeably different uncertainty estimates, primarily due to inconsistences in their estimated observed orders of accuracy and safety factors. To successfully apply the procedures to practical problems, further research is required to reliably estimate uncertainties in solutions with “noisy” grid convergence behaviors and observed orders of accuracy.