A robust formulation of the v2-f model

The elliptic relaxation approach of Durbin [1], which accounts for wall blocking e¤ects on the Reynolds stresses, is analysed herein from the numerical stability point of view, in the form of the v2 ¡ f . This model has been shown to perform very well on many challenging test cases such as separated, impinging and blu¤-body ‡ows, and including heat transfer. However, numerical convergence of the original model suggested by Durbin is quite di¢cult 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 [9] which removes the need of this coupling to allow a segregated numerical procedure, but with somewhat less accurate predictions. A robust modi...cation of the model is developed to obtain homogeneous boundary conditions at a wall for both v2 and f . The modi...cation is based on both a change of variables and alteration of the governing equations. The new version is tested on a channel, a di¤user ‡ow and ‡ow 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.