Dynamic Kalman filtering to separate low-frequency instabilities from turbulent fluctuations: Application to the Large-Eddy Simulation of unsteady turbulent flows

Abstract

A dynamic method based on Kalman filtering is presented to isolate low-frequency unsteadiness from turbulent fluctuations in the large-eddy simulation (LES) of unsteady turbulent flows. The method can be viewed as an adaptive exponential smoothing, in which the smoothing factor adapts itself dynamically to the local behavior of the flow. Interestingly, the proposed method does not require any empirical tuning. In practice, it is used to estimate a shear-improved Smagorinsky viscosity, in which the low-frequency component of the velocity field is used to estimate a correction term to the Smagorinsky viscosity. The LES of the flow past a circular cylinder at Reynolds number ReD = 4.7 × 104 is examined as a challenging test case. Good comparisons are obtained with the experimental results, indicating the relevance of the shear-improved Smagorinsky model and the efficiency of the Kalman filtering. Finally, the adaptive cut-off of the Kalman filter is investigated, and shown to adapt locally and instantaneously to the complex flow around the cylinder.