The governing equations for compressible turbulent shear flows are the spatially filtered, Favre-averaged compressible Navier–Stokes equations. The spatial filtering removes the small-scale (subgrid-scale) components, while the three-dimensional, time-dependent large-scale (resolved-scale) motion is retained. For a function f, its filtered form and its Favre-filtered form are respectively, where G is the filter function and ρ is the density. Favre filtering and spatial filtering of the Navier–Stokes equations yield where uiis the velocity in the ith coordinate direction, p is the static pressure, T is the static temperature, and the Einstein summation notation is used (i.e., the appearance of a repeated index in a term implies summation over all values of the index). Additionally, The particular form of this energy equation, proposed by Knight et al. (1998), was found by Martin, Piomelli, and Candler (1999) to provide an accurate model of the subgrid-scale turbulent diffusion in decaying compressible isotropic turbulence. Closure of the aforementioned system of equations requires specification of a model for the subgrid-scale stress, τij, and heat flux, Qj. Two basic categories of closure have been proposed, namely, (1) explicit subgrid-scale models and (2) the monotone integrated large eddy simulation (LES) method, known as MILES, the subclass of implicit LES models using mononicity-preserving high-resolution algorithms. We present examples of each category in the following sections. Historically, the earliest subgrid-scale models were based on explicit mathematical models for τijand Qj. In this chapter, we present results for several explicit subgrid-scale models.
|Original language||English (US)|
|Title of host publication||Implicit Large Eddy Simulation|
|Subtitle of host publication||Computing Turbulent Fluid Dynamics|
|Publisher||Cambridge University Press|
|Number of pages||41|
|State||Published - Jan 1 2007|
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