The prediction and investigation of very high Reynolds number turbulent wall flows pose a significant challenge: experimental studies and large eddy simulation (LES) are often inapplicable to these flows, and Reynolds-averaged Navier–Stokes (RANS) methods often fail to characterize the essential flow characteristics, in particular, for separated flows. These facts explain the need for the development of hybrid RANS-LES methods. The predominant approach to deal with this question is the combination of RANS and LES equation elements. This often implies shortcomings in simulations: the lack of control of modeled and resolved motions, which are involved in hybrid simulations, can lead to inconsistencies and imbalances. A novel approach based on a theoretical solution to the latter problem (referred to as continuous eddy simulation method) is investigated here via simulations of periodic hill flows (involving flow separation and reattachment) for a range of very high Reynolds numbers. We study the mechanism and simulation performance of these new hybrid methods. The results presented demonstrate their excellent performance and advantages to differently designed hybrid methods. We also consider the reliability of flow predictions for which data for model validation are unavailable. Criteria for the reliability of such hybrid simulations are suggested. It is shown that the new hybrid method satisfy these criteria for reliable flow predictions. The results indicate the existence of an asymptotic flow regime far above Reynolds numbers that can be realized in experimental studies and resolved LES.

Large eddy simulations involving dynamic subgrid-scale stress models reveal questions regarding the formulation of dynamic stress models. The dynamic Smagorinsky model, for example, yields large fluctuations and can easily become unstable. An analysis explains the reasons for these problems: it is shown that the dynamic Smagorinsky model involves an incorrect scale dependence which may produce significant errors leading to instabilities. These problems are addressed by analyzing the implications of the realizability constraint, this means the constraint that an acceptable turbulence closure model be based on the statistics of a velocity field that is physically achievable or realizable. The realizable dynamic stress models obtained have strong theoretical support: these models are the result of a well based systematic development of stress models. From a practical point of view, the realizable dynamic stress models obtained have the advantage that they do not support the development of instabilities due to possibly huge model errors. It is also shown that the consideration of nonlinear dynamic stress models further improves the accuracy of simulations.

The concept of dynamic large eddy simulation (LES) is highly attractive: such methods can dynamically adjust to changing flow conditions, which is known to be highly beneficial. For example, this avoids the use of empirical, case dependent approximations (like damping functions). Ideally, dynamic LES should be local in physical space (without involving artificial clipping parameters), and it should be stable for a wide range of simulation time steps, Reynolds numbers, and numerical schemes. These properties are not trivial, but dynamic LES suffers from such problems over decades. We address these questions by performing dynamic LES of periodic hill flow including separation at a high Reynolds number Re = 37 000. For the case considered, the main result of our studies is that it is possible to design LES that has the desired properties. It requires physical consistency: a PDF-realizable and stress-realizable LES model, which requires the inclusion of the turbulent kinetic energy in the LES calculation. LES models that do not honor such physical consistency can become unstable. We do not find support for the previous assumption that long-term correlations of negative dynamic model parameters are responsible for instability. Instead, we concluded that instability is caused by the stable spatial organization of significant unphysical states, which are represented by wall-type gradient streaks of the standard deviation of the dynamic model parameter. The applicability of our realizability stabilization to other dynamic models (including the dynamic Smagorinsky model) is discussed.