Synchronizing large eddy simulations with direct numerical simulations via data assimilation

Abstract

The synchronization of large eddy simulations to direct numerical simulations via a data assimilation scheme is investigated in Kolmogorov flows, where the large scales of the velocity field in large eddy simulations are replaced by those in the direct numerical simulations. We show that, when the amount of assimilated data exceeds a threshold given by a threshold wavenumber, all large eddy simulations with the same subgrid-scale model converge to an orbit that is synchronized with the direct numerical simulations in phase. The threshold wavenumbers for the standard and dynamic Smagorinsky models are smaller than those for the dynamic mixed model and are reduced when the filter scale increases. The error in the synchronized large eddy simulations is examined in detail. We reveal that for larger filter scales, unexpectedly, the velocity simulated with the standard and the dynamic Smagorinsky models can be more accurate than the one calculated with the dynamic mixed model. The robustness of the results is assessed in simulations where the assimilated data are perturbed by random noise and in homogeneous turbulence which is driven by a linear forcing term. Good synchronization is still obtained in both cases. The Smagorinsky models still display better performance than the dynamic mixed model.