Filter shape dependence and effective scale separation in large-eddy simulations based on relaxation filtering

The influence of the filter shape on the effective scale separation and the numerical accuracy of large-eddy simulations based on relaxation filtering (LES-RF) is investigated. The simulation of the turbulent flow development of a high-Reynolds number low-subsonic compressible mixing layer is performed using the LES-RF procedure, for discrete filters of order 2–10. A reference solution is first obtained using high-order numerical algorithms and shows a good agreement with experimental data found in the literature. Discrete filters of order 2, 4, 6, 8 and 10 are then considered to study the influence of the filter shape on numerical results. The 2nd-order scheme turns out to be too dissipative and prevents the emergence of unsteady motions within the mixing layer. For higher order schemes, from 4th- to 10th-order, the flow solutions are turbulent but exhibit mean flows and turbulent intensities depending on the filter. The investigation of the one-dimensional kinetic energy spectra then shows that the 4th-order filter may still be too dissipative whereas large scales remain unaffected using the 6th-, 8th- and 10th-order filters. A further study of the kinetic energy spectra nonetheless demonstrates that the effective spatial bandwidth of the LES increases with the order of the filtering scheme. Simulations using the 6th-, 8th- and 10th-order filters, with mesh sizes chosen to provide the same effective LES cut-off wavenumber, are performed and yield similar results. It is hence found that the value of the effective LES cut-off wavenumber, rather than to the filter shape itself, is mainly responsible for the discrepancies between the flow statistics obtained using different filters. One may conclude that filter shape independence is consequently achieved in the present LES of a mixing layer.