On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence

We assess the performance of a high-order discontinuous Galerkin (DG) approach to simulate wall-bounded turbulent flows for a range of Reynolds numbers. First, a plane channel flow configuration with turbulent heat transfer at R e τ = 640 is considered. Second, a detached flow configuration is investigated. This configuration represents the flow over periodically arranged hills. Four bulk Reynolds numbers Re b are considered: 2800, 10 595, 19 000, and 37 000. For R e b = 2800 direct numerical simulation (DNS) is used. Large-eddy simulations (LES) based on the WALE subgrid-scale model are carried out for the higher Re b . The simulation results are compared to reference data from CFD and experiment. hp -convergence analyses are performed which demonstrate the superior performance of increasing the polynomial order as compared to refining the mesh. It appears from this work that the use of a subgrid modelling approach together with local hp-adaptation could greatly improve the accuracy of the solution without penalising the computational cost of the simulation.