Spatially Variable Thresholding for Stochastic Coherent Adaptive LES

The properties of wavelet transform, viz. the ability to identify and efficiently represent temporal/spatial coherent flow structures, self-adaptiveness, and de-noising, have made them attractive candidates for constructing multi-resolution variable fidelity schemes for simulations of turbulence [10]. Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) [6] is the most recent wavelet-based methodology for numerical simulations of turbulent flows that resolves energy containing turbulent motions using wavelet multi-resolution decomposition and self-adaptivity. In this technique, the extraction of the most energetic structures is achieved using wavelet thresholding filter with a priori prescribed threshold level. SCALES is a methodology, which inherits the advantages of both Coherent Vortex Simulations (CVS) [5] and Large Eddy Simulation (LES) while overcoming the shortcomings of both. Unlike coherent/incoherent and large/small structures decomposition in CVS and LES respectively, in SCALES the separation is between more and less energetic structures. Therefore, unlike CVS, the effect of background flow can not be ignored and needs to be modeled similarly to LES. As a result of using SGS models, the number of degrees-of-freedom is smaller than CVS and consequently a higher grid-compression can be achieved. Ever since the emergence of the wavelet-based multi-resolution schemes for simulations of turbulence, there has been a major limitation for all wavelet-based techniques: the use of a priori defined global (both in space and time) thresholding-