Assessment of the Gradient Jump Penalisation in Large-Eddy Simulations of Turbulence

Abstract: This research investigates the efficacy of the gradient jump penalisation (GJP) in large eddy simulations (LES) when coupled with active subgrid-scale (SGS) models. GJP is a stabilisation method tailored for the continuous Galerkin spectral element method, aiming at mitigating non-physical oscillations induced by discontinuous velocity gradients across element interfaces. We demonstrate that GJP effectively smoothens fields from LES without a salient impact on flow dynamics for the Taylor--Green vortex (TGV) at $Re=1600$, periodic hill flows at bulk Reynolds numbers $Re_b=10595$ and $37000$, as well as turbulent channel flow at $Re_{\tau} \approx 550$. In the TGV case, the application of GJP results in decreased fluctuations at only high wavenumbers compared to simulations without GJP. The periodic hill flow simulations indicate the applicability of GJP in wall-resolved LES (WRLES) involving curved geometries, though it tends to dissipate some of the finer details in the solution. Finally, in the analysis of the canonical turbulent channel flow cases, GJP leads a higher resolved turbulent kinetic energy than simulations without GJP and direct numerical simulations. GJP's mechanism is identified as providing enhanced dissipation at high wavenumbers but accompanied with insufficient dissipation at low wavenumbers, leading to a pronounced spectral cut-off. Non-physical oscillations on element interfaces are reflected as spikes in the power spectral density. By evaluating the sharpness of the strongest spike, GJP is shown to smoothen the spectra, however without completely removing the gradient jumps at low computational resolution.