Representation of sub-grid scale turbulence with Periodic Box Homogeneous Direct Numerical Simulation*

Large Eddy Simulations (LESs) use Sub-Grid Scale (SGS) models to account for the effects of the unresolved scales of turbulence. The complex processes that occur in the small scales make the development of SGS models challenging. In this study, we propose the use of a Periodic Box (PB) Direct Numerical Simulation (DNS), simulating Homogeneous Isotropic Turbulence (HIT), to represent the unresolved scales of a LES. As a proof of concept, the local characteristic strain rate in the LES is used as a representation of the local turbulence. This is matched with the characteristic strain rate at the large scales of the PB DNS, thereby coupling them.

This model was tested by simulating HIT in a LES. The turbulence spectra from the LES and the PB DNS were compared with the exact solution from a full DNS simulation. The results show a seamless coupling between the large and small scales. Further, an a priori test is conducted by coupling the PB DNS with a filtered full DNS. This evaluates the capability of a PB DNS to function as the SGS model. The results show that this model is more accurate than the common Smagorinsky model while working within the same assumptions. The findings showcase the capability of a PB DNS to provide a near-exact representation of SGS turbulence to a LES.