Smoothing algorithms for mean-flow extraction in large-eddy simulation of complex turbulent flows

Abstract

Based on physical arguments, the importance of separating the mean-flow from turbulence in the modeling of the subgrid-scale eddy-viscosity is emphasized. Therefore, two distinct time-domain smoothing algorithms are proposed to estimate the mean-flow as the simulation progresses, namely, an exponentially weighted moving average (or exponential smoothing) and an adaptive low-pass Kalman filter. These algorithms highlight the longer-term evolution or cycles of the flow but erase short-term fluctuations. Indeed, it is our assumption that the mean-flow (in the statistical sense) may be approximated as the low-frequency component of the velocity field and that the turbulent part of the flow adds itself to this “unsteady mean.” The cutoff frequency separating these two components is fixed according to some characteristic time-scale of the flow in the exponential smoothing, but inferred dynamically from the recent history of the flow in the Kalman filter. In practice, these two algorithms are implemented in large-eddy simulations that rely on a shear-improved Smagorinsky’s model. In this model, the magnitude of mean-flow rate of strain is subtracted from the magnitude of the instantaneous rate of strain in the subgrid-scale eddy-viscosity. Two test-cases have been investigated: a turbulent plane-channel flow (Rew=395) and the flow past a circular cylinder in the subcritical turbulent regime (ReD=4.7×104). Comparisons with direct numerical simulation and experimental data demonstrate the good efficiency of the whole modeling. This allows us to address nonhomogeneous unsteady configurations without adding significant complication and computational cost to the standard Smagorinsky’s model. From a computational viewpoint, this modeling deserves interest since it is entirely local in space. It is therefore adapted for parallelization and convenient for boundary conditions.