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Abstract. The elliptic relaxation approach of Durbin (Durbin, P.A., J. Theor. Comput. Fluid. Dyn. 3 (1991) 1-13), which accounts for wall blocking effects on the Reynolds stresses, is analysed herein from the numerical stability point of view, in the form of thev 2 − f . This model has been shown to perform very well on many challenging test cases such as separated, impinging and bluff-body flows, and including heat transfer. However, numerical convergence of the original model suggested by Durbin is quite difficult due to the boundary conditions requiring a coupling of variables at walls. A 'code-friendly' version of the model was suggested by Lien and Durbin (Lien, F.S. and Durbin, P.A., Non linear k − ε − v 2 modelling with application to high-lift. In: Proceedings of the Summer Program 1996, Stanford University (1996), pp. 5-22) which removes the need of this coupling to allow a segregated numerical procedure, but with somewhat less accurate predictions. A robust modification of the model is developed to obtain homogeneous boundary conditions at a wall for bothv 2 and f . The modification is based on both a change of variables and alteration of the governing equations. The new version is tested on a channel, a diffuser flow and flow over periodic hills and shown to reproduce the better results of the original model, while retaining the easier convergence properties of the 'code-friendly' version.

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The flow around a trailing edge is computed with a new hybrid method designed to more clearly separate the effects of total and sub-grid turbulent stressmodelling on the time-averaged and instantaneous velocity fields, and in turn, mean momentum and kinetic energy balances. These two velocity fields independently define Reynolds averaged and sub-grid-scale viscosities, and distinct stresses, at the same location. In particular, resolved eddies can emerge, or sweep in and out of the Reynolds averaged near wall layer, without being dampened by higher levels of the viscosity in this RANS dominated layer. The two-field hybrid model, first tested on channel flows, gives accurate predictions of mean velocities and stresses for different Reynolds numbers and coarse meshes. For the trailing edge flow the results of the hybrid model are close to the reference fine LES for mean velocity and turbulent content, whereas the DES-SST on the same coarse mesh gives too early separation.

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