Large Eddy Simulations of Turbulent Channel Flows Using Split Form DG Schemes

Spatial and temporal eigensolution analysis of the discontinuous Galerkin (DG) method shows the favorable dispersion and diffusion properties of such methods when high order polynomial approximations are used, making them very suitable for application to under-resolved turbulent flows. The recent introduction of split forms of the inviscid fluxes for the discontinuous Galerkin method improves the robustness of the scheme, such that stable simulations are obtained even for very high polynomial orders and severely under-resolved cases. The present work investigates the robustness and accuracy of very high order split form DG schemes applied to turbulent channel flows for severely and moderately under-resolved configurations. In addition to using two distinct approximate Riemann solvers for the interface fluxes, a central formulation is also employed and analyzed. Improved results are obtained when a subgrid scale model is added to the equations in order to increase the dissipation at the smallest resolved scales. The remarkable stability observed for the scheme even for the dissipation-free, central formulation enables the development of tailored subgrid scale turbulence models that improve the results of practical, under-resolved engineering simulations.