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XLES Part II: From Extended Large Eddy Simulation to ODTLES

In turbulence research and flow applications, turbulence models like RaNS (Reynolds averaged Navier-Stokes) models and LES (Large Eddy Simulation) are used. Both models filter the governing flow equations. Thus a scale separation approach is introduced for modeling purposes with the large scales simulated using a numerical scheme while smaller scales are assumed to be less important and might be modeled more or less easily. Unfortunately small scales are frequently of big importance, e.g. in reactive flows, wall bounded flows, or flows with significant Prandtl or Schmidt number effects. Recent alternatives to these standard models are the class of models based on the one-dimensional turbulence (ODT) idea, like ODTLES. The ability of ODT to capture highly turbulent flows (recently up to $Re_τ= 6\times 10^5$) allows ODTLES to realize 3D resolutions basically independent of the turbulent intensity. In two papers we provide a formal theory and application of an innovative modeling strategy for highly turbulent flows in domains of moderate complexity: In part I (see Glawe et al. (2015)) a new general filtering approach, called XLES (extended LES), is introduced. Contrary to LES, XLES is based on 2D filtering of the governing equations, whereby additional small scale terms are interpreted numerically. In this work a new ansatz for the ODTLES model is introduced as one special approach in the XLES family of models by incorporating the ODT model into XLES. The ODT model introduces microstructures not captured by the XLES filtered equations. To illustrate the ODTLES model capabilities, turbulent channel and duct flows up to friction Reynolds number $Re_τ= 10000$ are studied.