Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation

We revisit the grid-point requirement estimates in Choi and Moin ["Grid-point requirements for large eddy simulation: Chapman's estimates revisited," Phys. Fluids 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary layer. We show that by allowing the local grid spacing to scale with the local Kolmogorov length scale, the grid-point requirement for DNS of a spatially developing turbulent boundary layer is N similar to ReLx2.05</mml:msubsup> rather than N similar to ReLx2.64</mml:msubsup>, as suggested by Choi and Moin, where N is the number of grid points and L-x is the length of the plate. In addition to the grid-point requirement, we estimate the time-step requirement for DNS and LES. We show that for a code that treats the convective term explicitly, the time steps required to get converged statistics are Nt similar to ReLx/Rex06/7</mml:msubsup> for wall-modeled LES and Nt similar to ReLx/Rex01/7</mml:msubsup> for wall-resolved LES and DNS (with different prefactors), where Re<mml:msub>x0 is the inlet Reynolds number. The grid-point and time-step requirement estimates allow us to estimate the overall cost of DNS and LES. According to the present estimates, the costs of DNS, wall-resolved LES, and wall-modeled LES scale as Re<mml:msub>Lx2.91, Re<mml:msub>Lx2.72, and Re<mml:msub>Lx1.14, respectively.