# Large Eddy Simulation Requirements for the Flow over Periodic Hills

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## Abstract

Large eddy simulations are carried out for flows in a channel with streamwise-periodic constrictions, a well-documented benchmark case to study turbulent flow separation from a curved surface. Resolution criteria such as wall units are restricted to attached flows and enhanced criteria, such as energy spectra or two-point correlations, are used to evaluate the effective scale separation in the present large eddy simulations. A detailed analysis of the separation above the hill crest and of the early shear layer development shows that the delicate flow details in this region may be hardly resolved on coarse grids already at *R**e* = 10595, possibly leading to a non monotonic convergence with mesh refinement. The intricate coupling between numerical and modeling errors is studied by means of various discretization schemes and subgrid models. It is shown that numerical schemes maximizing the resolution capabilities are a key ingredient for obtaining high-quality solutions while using a reduced number of grid points. On this respect, the introduction of a sharp enough filter is an essential condition for separating accurately the resolved scales from the subfilter scales and for removing ill-resolved structures. The high-resolution approach is seen to provide solutions in very good overall agreement with the available experimental data for a range of Reynolds numbers (up to 37000) without need for significant grid refinement.

## Keywords

Large eddy simulation High-accuracy method Periodic hill flow## Notes

### Acknowledgments

This work was granted access to the HPC resources of IDRIS and CCRT under the allocation 1736 made by GENCI (Grand Equipement National de Calcul Intensif).

### Compliance with Ethical Standards

### **Conflict of interests**

The authors declare that they have no conflict of interest.

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