Stochastic coherent adaptive LES with time-dependent thresholding

With the recent development of wavelet-based techniques for computational fluid dynamics, adaptive numerical simulations of turbulent flows have become feasible [1]. Adaptive wavelet methods are based on wavelet threshold filtering that makes it possible to separate coherent energetic eddies, which are numerically simulated, from residual background flow structures that are filtered out. By varying the filter thresholding level different approaches with different fidelity are obtained: from the highly accurate wavelet-based direct numerical simulation (WDNS) that do not involve any model to the stochastic coherent adaptive large eddy simulation (SCALES) that needs a closure modeling procedure, e.g. [2]. The prescription of a given threshold for SCALES filtering directly links to the desired turbulence resolution. By decreasing the thresholding level more and more eddies with smaller energy are directly simulated so that the effect of unresolved background flow becomes less and less important and, correspondingly, the influence of the modeling procedure as well. To date, the SCALES method has been applied for both decaying and forced turbulence with a specified thresholding level that is based on a-priori studies, e.g. [3]. In this work, a new original strategy is presented for which the wavelet filtering threshold is not prescribed but determined on the fly for a given level of turbulence resolution. A completely adaptive eddy capturing approach that allows to perform variable fidelity numerical simulations of turbulence is proposed. The new method is based on wavelet filtering with time-dependent thresholding that automatically