Impact of the resolution on DNS results in pipe and channel flows.

Recent results about the overlap region in wall-bounded flows suggest that a combination of log and linear functions is a better representation than the classic log law and covers a wider region of the profile. Utilizing these results requires a very exact representation of the indicator function Ξ ≡ y⁺dU⁺/dy⁺=Y dU/dY. Unfortunately, the convergence and resolution of direct numerical simulations (DNSs) have not received adequate attention for most of the computations of wall-bounded turbulence. For the case of pipe flow, after decades of experience, we recognize that the fully-developed pipe is the ideal flow for comparing computations and experiments, following the experiments of Princeton and Bologna. Regarding channel flows, these have been the most extensively studied in turbulent flows for many years and provide good test cases. Numerically, we have utilized the OpenPipeFlow code for a large pipe of length 10πR. Simulations have been run for friction Reynolds numbers of 500 and 1000 using different meshes. These meshes are comparable to or better than many other DNS and they have been run for up to 100 eddy-turnover times, which exceeds most of the earlier computations. The simulations show a strong dependence on the mesh in the radial direction, needing a grid of around one wall unit.