High-Order Discontinuous Galerkin Schemes for Large-Eddy Simulations of Moderate Reynolds Number Flows

In this article, we describe the capabilities of high order discontinuous Galerkin methods at the Institute for Aerodynamics and Gasdynamics for the Large-Eddy Simulation of wall-bounded flows at moderate Reynolds numbers. In these scenarios, the prediction of laminar regions, flow transition and developed turbulence poses a great challenge to the numerical scheme, as overprediction of numerical dissipation can significantly influence the accuracy of the integral quantities. While this increases the burden on the numerical scheme and the LES subgrid model, the moderate Reynolds numbers prevent the occurrence of thin wall boundary layers and allows the resolution of the boundary layer without the need for wall modelling strategies. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high order spectral approximations by using high order ansatz functions up to 12th order, which allows us to resolve the significant features of these flows at a very low number of degrees of freedom. Without the need for any additional filtering, explicit or implicit modelling or artificial dissipation, the high order scheme capture the turbulent flow at the considered Reynolds number range very well.

We apply our approach to standard benchmark test cases for transitional and turbulent flows in internal and external aerodynamics: A well investigated square duct channel at

Re

τ

 = 395, a closed channel configuration with streamwise periodic hills at

Re

h

 = 10,595, a circular cylinder flow at

Re

D

 = 3900 and a transitional airfoil test case at

Re

 = 60,000. We focus on a comparison with established schemes of lower order with explicitly or implicitly added subgrid scale models, while using fewer or approximately the same number of degrees of freedom. We demonstrate that for all computations, we achieve an equal or better match to Direct Numerical Simulation and experimental results, while retaining perfect parallel scaling and achieving very low computing times.