Numerical investigation of split form nodal discontinuous Galerkin schemes for the implicit LES of a turbulent channel flow

Abstract

Gassner et al. (Split form nodal discontinuous Galerkin schemes with summation - by - parts property for the compressible Euler equations. Journal of Computational Physics, 327:3966, Dec. 2016) proposed a promising alternative stabilization technique for the discontinuous Galerkin scheme, which relies on the reformulation of the non-linear advection terms into split forms. It has been observed, that these split forms can stabilize the inviscid Taylor Green Vortex with high-order approximations, which are unstable with over-integration. In this paper, we apply different split form discontinous Galerkin schemes for the implicit large eddy simulation of a fully developed turbulent channel flow and investigate their robustness and accuracy for wall-bounded flows. Furthermore, we compare these results to implicit large eddy simulation with over-integrated high-order approximations in terms of statistical values and turbulence spectra. Finally, we show that the use of high-order split form discontinuous Galerkin scheme can significantly improve the results in comparison to low-order discretizations.