On the anti-aliasing properties of entropy filtering for discontinuous spectral element approximations of under-resolved turbulent flows

TL;DR

This paper investigates how entropy filtering can reduce aliasing errors and improve stability in high-order spectral element simulations of under-resolved turbulent flows, such as airfoil stall conditions.

Contribution

It demonstrates that entropy filtering effectively mitigates aliasing-driven instabilities in turbulent flow simulations without compromising accuracy, offering a robust alternative to traditional anti-aliasing methods.

Findings

Entropy filtering reduces aliasing errors in turbulent flow simulations.

It maintains accuracy comparable to over-integration methods.

Performance slightly decreases at higher approximation orders.

Abstract

For large Reynolds number flows, it is typically necessary to perform simulations that are under-resolved with respect to the underlying flow physics. For nodal discontinuous spectral element approximations of these under-resolved flows, the collocation projection of the nonlinear flux can introduce aliasing errors which can result in numerical instabilities. In Dzanic and Witherden (J. Comput. Phys., 468, 2022), an entropy-based adaptive filtering approach was introduced as a robust, parameter-free shock-capturing method for discontinuous spectral element methods. This work explores the ability of entropy filtering for mitigating aliasing-driven instabilities in the simulation of under-resolved turbulent flows through high-order implicit large eddy simulations of a NACA0021 airfoil in deep stall at a Reynolds number of 270,000. It was observed that entropy filtering can adequately mitigate aliasing-driven instabilities without degrading the accuracy of the underlying high-order scheme on par with standard anti-aliasing methods such as over-integration, albeit with marginally worse performance at higher approximation orders.