On the performance of relaxation filtering for large-eddy simulation

Abstract

In this work, the performance of large-eddy simulation (LES) based on the relaxation-filtering (RF) technique has been investigated quantitatively. In RF-based LES, the velocity field is filtered each nth time step, using a standard finite-difference filter, characterized by a specific order of accuracy m, and a fixed filtering strength σ. Hence, the procedure dissipates the amount of energy related to the residual stresses, and thus models the dissipative effect of the unresolved scales on the resolved scales. Since the order m and strength σ are related to the spectral distribution and the magnitude of the dissipation, respectively, these predefined parameters are crucial for the success of the method. Here, their influence is systematically investigated for the Taylor–Green vortex flow at a Reynolds number of 3000. First, the effects of m and σ are studied a priori in Fourier space. Further, 36 LESs are performed, each with a different combination of order m=4, 6, 8, 10, 12, 14 and strength σ=0.15, 0.2, 0.4, 0.6, 0.8, 1, and the turbulent statistics are compared with those of a direct numerical simulation, filtered at identical resolutions. The a priori, as well as the a posteriori results indicate that, for low filter orders m⩽4, the LES accuracy is rather poor and depends strongly on the filtering strength σ. However, for higher order filters, i.e. m⩾8, the accuracy is quite good and the results, including the resolved and subgrid dissipation rates, are nearly independent of the strength σ for σ⩾0.4. In this case, the spectral dissipation-distribution, determined by m, turns out to be the dominant parameter, whereas the dissipation strength, determined by σ, is of minor importance.