High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow

Classical fixed-coefficient eddy-viscosity models for large-eddy simulations (LES), e.g., the Smagorinsky [Mon. Weather Rev. 93, 99 (1963)] and the structure-function model [Métais and Lesieur, J. Fluid Mech. 239, 157 (1992)], have deficiencies with accurately describing laminar flow regions and the viscous sublayer of near-wall turbulence. This is mainly due to unphysically large model contributions in such flow regions and is one main reason for the difficulty with correctly predicting laminar-turbulent transition using such models. For transitional flows, subgrid-scale (SGS) models must be able to properly deal with at least the two limits of the laminar and the turbulent fluid state. The dynamic Smagorinsky model [Germano et al., Phys. Fluids A 3, 1760 (1991)] alleviates this problem by dynamically computing a small, but not necessarily vanishing, value for the model coefficient in laminar regions and in the vicinity of the wall. In this contribution we analyze high-pass filtered (HPF) eddy-viscosity models which were proposed recently and independently by Vreman [Phys. Fluids 15, L61 (2003)] and Stolz et al. [Direct and Large-Eddy Simulation V (Kluwer, Dordrecht, 2004), pp. 81–88]. We investigate high-pass filtering suitable for such HPF eddy-viscosity models, e.g., the Smagorinsky or the (filtered) structure-function model. Furthermore, we suggest suitable high-pass filters and examine the influence of different high-pass filters on the results of LES of transitional and turbulent incompressible channel flow. Except for the filter shape, the cutoff wavenumber of the high-pass filter is the only parameter besides the eddy-viscosity model coefficient, and its influence can be minimized by a proposed adaptation of the model coefficient. We find that high-pass filtering employed to the computational quantities prior to the calculation of the eddy-viscosity and strain rate in the SGS model significantly improves the quality of the prediction of transitional and turbulent flows without using any ad-hoc adaptation or dynamic procedure. Of particular importance is that the sensitivity of the results to the model coefficient is considerably reduced by the high-pass filtering. Furthermore, the proposed high-pass filters enable the computation of the structure function in the filtered or HPF structure-function models in all spatial directions also for inhomogeneous flows and on non-equidistant grids, removing the arbitrariness of a special treatment of selected (e.g., wall-normal) directions. Simulation results are presented for incompressible turbulent channel flow at Reynolds numbers Reτ (based on the channel half-width and the friction velocity) of 180 and 590 and for forced laminar-turbulent transition in a plane channel, demonstrating the effectiveness of the proposed approach. The results are compared to data of direct numerical simulations and to data obtained using the dynamic Smagorinsky model with different test filters.