On the ability of discontinuous Galerkin methods to simulate under-resolved turbulent flows

Abstract: We investigate the ability of discontinuous Galerkin (DG) methods to simulate under-resolved turbulent flows in large-eddy simulation. The role of the Riemann solver and the subgrid-scale model in the prediction of a variety of flow regimes, including transition to turbulence, wall-free turbulence and wall-bounded turbulence, are examined. Numerical and theoretical results show the Riemann solver in the DG scheme plays the role of an implicit subgrid-scale model and introduces numerical dissipation in under-resolved turbulent regions of the flow. This implicit model behaves like a dynamic model and vanishes for flows that do not contain subgrid scales, such as laminar flows, which is a critical feature to accurately predict transition to turbulence. In addition, for the moderate-Reynolds-number turbulence problems considered, the implicit model provides a more accurate representation of the actual subgrid scales in the flow than state-of-the-art explicit eddy viscosity models, including dynamic Smagorinsky, WALE and Vreman. The results in this paper indicate new best practices for subgrid-scale modeling are needed with high-order DG methods.