# A large eddy simulation method for DGSEM using non-linearly optimized relaxation filters

## TL;DR

This paper introduces a novel dissipative spatial filter for large eddy simulation within DGSEM, optimized via data-driven methods, enhancing turbulence modeling especially for high Reynolds number flows without complex derivative computations.

## Contribution

It presents a data-optimized dissipative filter for DGSEM-based LES, improving turbulence modeling and computational efficiency for high Reynolds number flows.

## Key findings

- Optimal filters effectively model turbulence in HIT and Taylor Green Vortex flows.
- The method performs well in high Reynolds number regimes.
- It simplifies wall-modeled LES by avoiding second derivatives.

## Abstract

In this paper, we apply a specifically designed dissipative spatial filter as sub-grid scale model within the increasingly popular discontinuous Galerkin methods and the closely related flux reconstruction high order methods for large eddy simulation. The parameters of the filter kernel are optimized with data obtained from direct numerical simulation, that is filtered and used as a ground truth to fit the overall kinetic energy and dissipation rate over time. The optimization is carried out for polynomial degree 3 to 10. The optimal kernels are rigorously tested in the limit of infinite Reynolds number flows (HIT and Taylor Green Vortex flow). Additionally, a brief extension to plane turbulent channel flow is given. Besides the overall good performance, the method is especially attractive in combination with wall modeled LES, because it avoids the computation of second order derivatives for very high Reynolds number flows.