March 17, 2010 5:4 Journal of Turbulence paper˙TD09˙jot˙031110 Journal of Turbulence Vol. 00, No. 00, 200x, 1–23 RESEARCH ARTICLE Large Eddy Simulations Using Truncated Navier-Stokes Equations with the Automatic Filtering Criterion T. Tantikul a, ∗ and J.A. Domaradzki a, ∗∗ a Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA. 90089-1191 (Received 00 Month 200x; final version received 00 Month 200x) We propose a Large Eddy Simulation (LES) technique based on previously developed Trancated Navier Stokes (TNS) method. In TNS the Navier Stokes equations are solved through a sequence of direct numerical simulation runs and a periodic processing of small scales to provide the necessary dissipation. In the simplest case the processing is accomplished by filtering the turbulent fields with a properly chosen filter. In the previous work the period for processing was selected in advance for each case using heuristic arguments validated by trial and error. In this work we develop a criterion that automates the selection of a time instant in simulations when the processing occurs. The criterion is based on the relationship between the energy of the flow field and the energy of the same field filtered with the chosen filter. The procedure is tested in LES of the turbulent channel flow performed at various Reynolds numbers and in domains of different sizes for which DNS and experimental data are available for comparison. Keywords: Large Eddy Simulations; Truncated Navier-Stokes Equations; Explicit Filtering; Automatic Filtering Criterion 1. Introduction Several classifications of subgrid-scale (SGS) models for LES have been proposed in the literature on the subject. In a review paper of Domaradzki and Adams [1] the SGS models are divided into two general categories: the traditional models that use the explicit expressions for the SGS terms, the SGS stress tensor in particular, and the models that construct the unknown primitive variables such as velocity in order to use these variables to compute the SGS terms directly from the definitions. The traditional SGS modeling approaches can be subdivided into three groups: the eddy viscosity models, the similarity models, and the mixed models. The examples of the models in the other group are the velocity estimation model proposed by Domaradzki et al. [2, 3] and the approximate deconvolution model (ADM) of Stolz et al. [4]. Kosovic et al. [5] divided SGS models into three groups, characterized by the use of explicit filtering. First are the models that use an explicit SGS expression but do not employ explicit filtering, for instance the classical Smagorinsky eddy viscosity model. Second are the models that use an explicit SGS expression and employ explicit filtering, e.g., the dynamic Smagorinsky model. The third category are the so-called implicit models because equations of motion are solved without * Email : tantikul@usc.edu ** Email : jad@usc.edu ISSN: 1468-5248 (online only) c  200x Taylor & Francis DOI: 10.1080/14685240YYxxxxxxx http://www.informaworld.com