Nudging-based data assimilation of the turbulent flow around a square cylinder

Abstract: We investigate the prediction of the turbulent flow around a canonical square cylinder at Re= 22000 solving the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The limitations of URANS modelling are overcome through the application of a data assimilation technique involving a feedback control term, allowing to drive the URANS predictions towards reference data. Using regularly-spaced temporally-resolved reference data that are extracted from DNS, we assess the abilities of the data assimilation methodology in improving the unsteady URANS predictions. While improving the low-frequency oscillations of the wake flow, we also demonstrate the ability to recover the high-frequency dynamics of Kelvin-Helmholtz instabilities. The influence of spatial resolution of reference data is systematically investigated. The data resolution which is required to improve the prediction of flow structures of interest is related to their wavelength. Using a spacing of the order of one cylinder length between data points, we already observe synchronisation of the low-frequency vortex shedding that leads to a significant decrease in temporal and spectral errors as computed by spectral proper orthogonal decomposition. Furthermore,improved accuracy in terms of mean flow prediction of URANS is achieved. Using spacing of the order of the wavelength of the Kelvin-Helmholtz vortices, we even recover those shear layer structures which are absent in the baseline simulation.