On the Riemann flux performance in DG-based implicit LES at very high Reynolds numbers

Abstract eng:
We discuss the effect of the Riemann flux in implicit large eddy simulations carried out with the discontinuous Galerkin (DG) method at very high Reynolds numbers. The study is based on a set of computations of the inviscid TGV (Taylor-Green vortex) test problem spanning different grid sizes and polynomial orders. Inviscid cases have been chosen so that the isolated effects of the Riemann solver could be assessed in a scenario that mimics that of under-resolved computations at very high Reynolds numbers. Comparisons are made mainly between the Lax-Friedrichs and Roe solvers and significant differences are found, especially for higher-order solutions. An explanation based on dispersion-diffusion (eigensolution) analysis [1] is proposed as to why Riemann solvers that take into account the complete set of physical eigenvalues consistently via upwinding are expected to display a more accurate and robust behaviour for DG-based implicit LES over a wider range of Mach numbers.

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