One critical aspect of Leray models for the Large Eddy Simulation (LES) of incompressible flows at moderately large Reynolds number (in the range of few thousands) is the selection of the filter radius. This drives the effective regularization of the filtering procedure, and its selection is a trade-off between stability (the larger, the better) and accuracy (the smaller, the better). In this paper, we consider the classical Leray-\(\alpha \) and a recently introduced (by one of the authors) Leray model with a deconvolution-based indicator function, called Leray-\(\alpha \)-NL. We investigate the sensitivity of the solutions to the filter radius by introducing the sensitivity systems, analyzing them at the continuous and discrete levels, and numerically testing them on two benchmark problems.
The research presented in this work was carried out during LR’s visit at the Department of Mathematics and Computer Science at Emory University in the fall semester 2014. This support is gratefully acknowledged. This research has been supported in part by the NSF under grants DMS-1620384/DMS-1620406 (Quaini and Veneziani), DMS-1262385 (Quaini), Emory URC Grant 2015 Numerical Methods for Flows at Moderate Reynolds Numbers in LVAD (Veneziani), and DMS-1522191 (Rebholz).