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

Abstract

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.