Analytical and numerical study of resolution criteria in large-eddy simulation

Abstract

The present work investigates the influence of the primary filter resolution on various turbulence statistics and the representation of vortical structures in Large-Eddy Simulation (LES) of homogeneous isotropic turbulent flow. The resolution effects are investigated both analytically and numerically for an ideal LES solution with negligible modeling and numerical errors, and as such equivalent to filtered direct numerical simulation data. The Taylor-Green vortex is considered for the numerical investigation. Several resolution criteria, found in the literature, which prescribe the filter width requirements for LES, are investigated and their effect on various turbulent statistics is evaluated analytically. Further, the resolution effect on vortical structures is evaluated numerically using the Taylor-Green vortex. Finally, an optimal resolution for LES is derived via a multi-objective optimization, maximizing the resolved fractions of specifically chosen turbulent quantities while minimizing the computational overhead in comparison with a reference simulation. The optimum resolution criterion was found to be \documentclass[12pt]{minimal}\begin{document}$\kappa _e\lambda \approx 0.27\mathrm{Re}_\lambda ^{0.36}$\end{document}κeλ≈0.27 Re λ0.36. However, a more practical quasi-optimal criterion κeλ ≈ π is proposed resulting in an acceptable trade-off between accuracy and computational overhead.