## Abstract

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∼ReLx2.05 rather than N∼ReLx2.64, as suggested by Choi and Moin, where N is the number of grid points and Lx 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∼ReLx/Rex06/7 for wall-modeled LES and Nt∼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.

Original language | English (US) |
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Article number | 015108 |

Journal | Physics of Fluids |

Volume | 33 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2021 |

## All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes