Development of a subgrid-scale model for Burgers turbulence using statistical mechanics-based methods

Turbulent flows can be simulated using direct numerical simulations (DNS), but DNS is computationally expensive. Reduced-order models implemented into Reynolds-averaged Navier-Stokes and large eddy simulations (LES) can reduce the computational cost, but need to account for subgrid-scale (SGS) turbulence through closure relations. Turbulence modeling has presented a significant challenge due to the non-linearities in the flow and multi-scale behavior. Well-established features of the turbulent energy cascade can be leveraged through statistical mechanics to provide a characterization of turbulence. This paper presents a physics-based data-driven SGS model for LES using the concepts of statistical mechanics. The SGS model is implemented and tested using the stochastic Burgers equation. DNS data are used to calculate Kramers-Moyal (KM) coefficients, which are then implemented as an SGS closure model. The presented data-driven KM method outperforms traditional methods in capturing the multi-scale behavior of Burgers turbulence.