On the anti-aliasing properties of entropy filtering for under-resolved turbulent flows
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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.
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