# On the use of kinetic energy preserving DG-schemes for large eddy simulation

## TL;DR

This paper evaluates high-order DG methods with Riemann solvers for LES, highlighting their limitations at coarse resolutions and proposing a novel kinetic energy preserving split form DG approach that improves accuracy and stability in under-resolved turbulent flows.

## Contribution

It introduces a new split form DG LES strategy that preserves kinetic energy, enhancing stability and accuracy at coarse resolutions compared to traditional iLES methods.

## Key findings

- iLES DG performs well at ~40% dissipation resolution
- Traditional iLES DG becomes inaccurate at coarser resolutions
- Split form DG offers similar accuracy at high resolution and better fidelity at coarse resolutions

## Abstract

High Order DG methods with Riemann solver based interface numerical flux functions offer an interesting dispersion dissipation behaviour: dispersion errors are very low for a broad range of scales, while dissipation errors are very low for well resolved scales and are very high for scales close to the Nyquist cutoff. This observation motivates the trend that DG methods with Riemann solvers are used without an explicit LES model added. Due to under-resolution of vortical dominated structures typical for LES type setups, element based high order methods suffer from stability issues caused by aliasing errors of the non-linear flux terms. A very common strategy to fight these aliasing issues (and instabilities) is so-called polynomial de-aliasing, where interpolation is exchanged with projection based on an increased number of quadrature points. In this paper, we start with this common no-model or implicit LES (iLES) DG approach with polynomial de-aliasing and Riemann solver dissipation and review its capabilities and limitations. We find that the strategy gives excellent results, but only when the resolution is such, that about 40\% of the dissipation is resolved. For more realistic, coarser resolutions used in classical LES e.g. of industrial applications, the iLES DG strategy becomes quite in-accurate. The core of this work is a novel LES strategy based on split form DG methods that are kinetic energy preserving. Such discretisations offer excellent stability with full control over the amount and shape of the added artificial dissipation. This premise is the main idea of the work and we will assess the LES capabilities of the novel split form DG approach. We will demonstrate that the novel DG LES strategy offers similar accuracy as the iLES methodology for well resolved cases, but strongly increases fidelity in case of more realistic coarse resolutions.