A priori and a posteriori evaluations of sub-grid scale models for the Burgers' equation

In large eddy simulations (LES) of turbulent flows, large scale motions are resolved by the numerical simulation while the effect of the small scale motions is represented as sub-grid scale (SGS) stresses computed with SGS models. In the present study, we perform a priori and a posteriori evaluations of five SGS models for the one dimensional Burgers' equation with the high-order flux reconstruction (FR) or correction procedure via reconstruction (CPR) approach. It is shown that all models, except the scale similarity model (SSM) and the mixed model (MM), demonstrate very little correlation with the DNS results. The stability of the SSM is investigated. The effects of numerical dissipation and the models' influence on LES are discussed. Based on the present study, we advocate the use of implicit LES (ILES) in LES in the context of discontinuous high-order methods, or any numerical methods with built-in numerical dissipation.