For increasingly large Reynolds number flows, the computational cost of resolving all of the statistically significant physical scales becomes prohibitively large, such that it is necessary in many cases 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 onto the space spanned by the solution approximation can introduce aliasing errors which can result in numerical instabilities, leading to nonphysical solutions or the failure of the scheme altogether. In Dzanic and Witherden (J. Comput. Phys., 468, 2022), an entropy-based adaptive filtering approach was introduced for the purpose of mitigating numerical instabilities stemming from high-order approximations of discontinuous flow features. It was observed by the authors that this parameter-free shock-capturing approach, referred to as entropy filtering, also allowed for the robust simulation of high Reynolds number flows on under-resolved meshes that would typically be unstable due to aliasing errors. This technical note explores this effect and presents a comparison to standard anti-aliasing approaches through implicit large eddy simulations of a NACA0021 in deep stall from the DESider project as presented by Park et al. (AIAAJ, 55:7, 2017), a case notorious for aliasing driven instabilities in high-order methods that requires a substantial amount of numerical stabilization for the given setup.

翻译：随着雷诺数逐渐增大，解析所有统计显著物理尺度的计算成本变得过高，因此许多情况下必须进行相对于底层流动物理而言亚解析的模拟。对于这些亚解析流的节点间断谱元近似，非线性通量在解近似空间上的配置投影可能引入混叠误差，从而导致数值不稳定性，产生非物理解或使格式完全失效。在 Dzanic 和 Witherden (J. Comput. Phys., 468, 2022) 的工作中，提出了一种基于熵的自适应滤波方法，用于缓解因间断流动特征的高阶近似引起的数值不稳定性。作者观察到，这种无参数激波捕捉方法——被称为熵滤波——还能在亚解析网格上稳健模拟通常因混叠误差而失稳的高雷诺数流动。本技术笔记探讨了这一效应，并通过隐式大涡模拟，与 Park 等人 (AIAAJ, 55:7, 2017) 在 DESider 项目中提出的 NACA0021 深失速案例的标准抗混叠方法进行了比较。该案例因高阶方法中由混叠驱动的失稳而闻名，在给定设置下需要大量数值稳定化处理。