Suppressing Non-physical Oscillations at Element Interfaces in the Spectral-Element Method via Entropy Spectral Vanishing Viscosity

  • Du, Shiyu (KTH Royal Institute of Technology)
  • Münsch, Manuel (FAU Erlangen-Nürnberg)
  • Jansson, Niclas (KTH Royal Institute of Technology)
  • Schlatter, Philipp (FAU Erlangen-Nürnberg)

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Aiming at facilitating large-eddy simulation (LES) in a continuous Galerkin spectral-element method (CG-SEM) context, this contribution provides a promising alternative to suppress the non-physical oscillations in under-resolved simulations of turbulence based on CG-SEM via the combination of a modal filter, the entropy viscosity and spectral vanishing viscosity (SVV). The entropy indicator associated with local kinetic energy is restricted to the element interfaces by a modal filter, while the intensity and the high-frequency biasing of the dissipation are controlled by two parameters. This method shows its capability in mitigating the wiggles at the element interfaces while preserving the physics of the LES. To demonstrate the performance, the turbulent flow over a circular cylinder at Re_D = 3900 is simulated with a marginal resolution. For the baseline case without any regularisation, non-physical oscillations are observed at element interfaces in the wake zone and propagate into the interior of elements, polluting the entire field. By applying the entropy-SVV to the simulation, the wiggles are suppressed while the turbulent flow physics is kept to great details, hence improving the smoothness of the solution and even the turbulence statistics. In the final contribution, we will also include a quantitative description of the influence on the details of the separation including the separation angle and recirculation length, parameter optimisation of the entropy-SVV term and in-depth investigations in an LES coupled with active sub-grid scale models.