Realizable Uni ed RANS-LES and Dynamic LES Methods for Turbulent Flow Simulations

Existing LES methods face three basic problems: a huge variety of LES models are currently applied, dynamic LES methods are either very expensive or have to be combined with ow-dependent empirical stabilization techniques, and the cost of LES for wall-bounded ow simulations are way too high for most applications. Solutions for these three problems can be developed by deriving non-dynamic, dynamic, and uni ed LES methods on the basis of a consistent stochastic theory. This approach results in a hierarchy of realizable LES models, corresponding dynamic LES methods that overcome the stability problems of existing dynamic LES methods, and uni ed RANS-LES methods that provide a reduction of LES cost by a factor of 0:07 Re, which is huge for a high Reynolds number Re. The paper explains the theoretical background of the novel dynamic and uni ed LES methods based on stochastic analysis. Applications to several ows reveal the signi cant advantages of these methods in comparison to usually applied LES methods.