DNS-aided explicitly filtered LES

Abstract

The equations for LES are formally derived by low-pass filtering the NS equations with the effect of the small scales on the larger ones captured by a SGS model. However, it is known that the LES equations usually employed in practical applications are inconsistent with the filter operator when no explicit filter is used. Moreover, even for explicitly filtered LES, some inconsistencies remain in the wall-normal direction due to the constraining effect of the wall. A typically undesirable effect stemming from the inconsistency between LES and the filtered NS (fNS) equations is that DNS data can not be used to aid SGS modeling. Using the proposed form of the incompressible fNS equations for flows over flat walls in which the continuity equation, the filter operator, and the boundary condition at the wall are consistently formulated, we compute a set of plane turbulent channel flow explicitly filtered LES at different grid resolutions with the SGS term computed from a parallel DNS computation starting with an equivalent initial condition. The results show that the SGS term computed from DNS provide a truthful SGS model for short times until the numerical errors compound and the two parallel computations diverge. The effective time where the statistics remain similar is longer for lower-order statistics such as mean velocity profile, as expected. This demonstrates that with the consistent fNS equations, the abundant DNS data can be used to inform SGS model development for explicitly filtered LES. Moreover, the diverging of statitics at longer times shows that the SGS contribution is not necessarily homogeous as most SGS models assume, and a more precise correlation between the instantaneous LES velocity field and SGS model is required to capture the dynamics of turbulence.