Near-wall resolution requirement for direct numerical simulation of turbulent flow using multidomain Chebyshev grid

Direct numerical simulation (DNS) of turbulent flow in a periodic channel is performed to study the effect of the wall-normal spatial resolution near the wall on the calculations of turbulence statistics using multidomain Chebyshev grids. A discontinuous spectral element method (DSEM) is employed to calculate the first- and second-order statistics of the flow near the wall. The effect of the spectral approximation order on the resolution requirement is also studied by considering three approximation orders of P=2,5, and 7. The Reynolds number based on the bulk density, bulk velocity, and channel half-height is Re=3266, which corresponds to a friction Reynolds number of Reτ≈204 based on the wall friction velocity and the channel half-height. It is observed that the near-wall resolution requirement strongly depends on the spectral approximation order. For the same total number of grid points, a higher approximation order provides more accurate results. For approximation orders of P=5 and 7, grids with respectively 11 and 8 points inside y+=10 are sufficient to resolve the turbulent statistics near the wall, while a grid with P=2 requires more than 11 points in the same region to achieve the same level of accuracy.