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 rather than N similar to ReLx2.64, 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 for wall-modeled LES and Nt similar to ReLx/Rex01/7 for wall-resolved LES and DNS (with different prefactors), where Rex0 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 ReLx2.91, ReLx2.72, and ReLx1.14, respectively.

Automated summary

This paper revisits the grid-point and time-step requirements for DNS and LES of turbulent boundary layers and establishes more general requirements. By considering the relationship between local grid spacing and the Kolmogorov length scale, accurate requirements for different simulation methods are proposed. According to the estimated costs, the computational costs of different simulation methods also vary.