On the accuracy of high-order discretizations for underresolved turbulence simulations

TLDR: It is shown that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing, so proper stabilization is necessary for a successful computation of underresolved turbulence.

Abstract: In this paper, we investigate the accuracy of a high-order discontinuous Galerkin discretization for the coarse resolution simulation of turbulent flow. We show that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing. Thus, for high-order simulations of underresolved turbulence, proper stabilization is necessary for a successful computation. Two different mechanisms are chosen, and their impact on the accuracy of underresolved high-order computations of turbulent flows is investigated. Results of these approximations for the Taylor–Green Vortex problem are compared to direct numerical simulation results from literature. Our findings show that the superior discretization properties of high-order approximations are retained even for these coarsely resolved computations.