A robust formulation of the v2−f model

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 the $$\bar v^2 - f$$ . 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 κ − ε − υ 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 both $$\bar v^2 $$ 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.