ON THE HIGH ACCURACY NS-ALPHA-DECONVOLUTION TURBULENCE MODEL

Abstract

We analyze the mathematical and physical properties of, and present numerical experiments for, the recently proposed NS-α-deconvolution model of fluid turbulence. This family of models has the well-known NS-α model as its zeroth-order model, and applies the Nth van Cittert deconvolution operator to the filtered terms in NS-α to create the Nth-order NS-α-deconvolution model. This model is proposed in Ref. 29, where it is shown to have consistency error O(α2N + 2). Herein we prove that the model admits unique regular solutions, is frame invariant, and improves the consistency error of NS-α from O(α2) to O(α2N + 2) while requiring (N + 1)1/2 times more (typically 1 ≤ N ≤ 5) degrees of freedom for complete resolution. Numerical experiments show that adding approximate deconvolution to NS-α significantly improves accuracy in computations.