The continuous eddy simulation capability of velocity and scalar probability density function equations for turbulent flows

There is a well developed spectrum of computational methods for turbulent flows: modeling methods such as Reynolds-averaged Navier-Stokes (RANS) and probability density function (PDF) methods, and resolving methods such as large eddy simulation (LES) and filtered density function (FDF) methods. However, the applicability of RANS/PDF methods is limited to flows that do not essentially require the inclusion of resolved motion, and LES/FDF methods are well applicable if resolution criteria can be satisfied [which is often infeasible for very high Reynolds number (Re) wall-bounded turbulent flows]. A highly attractive approach to overcome these problems is the design of hybrid RANS-LES methods, which can be used with varying amounts of resolved and modeled motions. However, this approach faces the problem to ensure communication and balancing of resolved and modeled motions. A well working solution to this problem was presented recently for non-homogeneous flows with respect to velocity two-equation eddy viscosity turbulence models. Exact analytical results regarding the extension of these methods to velocity and passive scalar PDF/FDF methods and their implied RANS/LES equations are presented here. The latter matters with respect to the justification of the theoretical basis of new hybrid methods (realizability) and the availability of a hierarchy of simple and advanced simulation methods (including passive scalar transport). Based on the continuous mode redistribution mechanism, the new simulation methods are capable of providing reliable predictions of very high Re turbulent flows, which cannot be accomplished by using existing techniques.