Grid Convergence Study for a Two-dimensional Simulation of Flow around a Square Cylinder at a Low Reynolds Number

This paper describes a systematic method of refining a computational grid for the Direct Numerical Simulation (DNS) of flow about a square cylinder. The grid refinement method involves two stages. The first stage constructs computational meshes based on reasonable estimates of cell size and grid stretching ratios and investigates the sensitivity of the computed flow field to these parameters. The findings from this stage are used as a guide for further grid refinement. In the second stage, the grid is divided into four regions to minimise the grid stretching ratio. The smallest cell is sized so the boundary layer on the front face of the cylinder is adequately resolved. Solutions on seven different grids are presented to investigate the effect of numerical scheme, boundary conditions and grid independence. The level of grid independence is evaluated using a form of Richardson extrapolation and the study shows that the finest grid solution has a Grid Convergence Index (GCI) of less than 5%.