Grid-point requirements for direct numerical simulation of compressible turbulent boundary layers

The grid-point requirements (N) for direct numerical simulation (DNS) of compressible turbulent boundary layers are estimated. By assuming the grids are nested and allowing grid spacing to scale with the Kolmogorov length scale, we find that N∼Reτ2.23(Tw/Tr)1.93 for Ma∞≤1, N∼Reτ2.23Ma∞1.35(Tw/Tr)1.93 for 1<Ma∞<5, and N∼Reτ2.23Ma∞3.15(Tw/Tr)1.93 for Ma∞≥5, where Reτ is the friction Reynolds number, Ma∞ is the free-stream Mach number, Tw and Tr are the wall temperature and recovery temperature, respectively. This paper demonstrates the necessity of reevaluating the grid-point requirements for DNS when compressibility effects are significant.