On the use of split forms and wall modeling to enable accurate high-Reynolds number discontinuous Galerkin simulations on body-fitted unstructured grids

The discontinuous Galerkin (DG) method is a promising numerical method to enable high- order simulations of turbulent flows associated with complex geometries. The method allows implicit large eddy simulations, however affordable simulations of very high Reynolds’ number flows require wall models. In addition, high Reynolds’ number typically implies the simulations are under-resolved. This becomes problematic as a high polynomial order may lead to aliasing instabilities on coarse grids, often leading to blow-up. Split formulations, first introduced in the finite-difference community, are a promising approach to address this problem. The present study shows that split forms and wall models can be used to enable the discontinuous Galerkin method to do very high Reynolds’ number simulations on unstructured grids.