A robust formulation of the v2-f model

D. R. Laurence, J. C. Uribe, S. V. Utyuzhnikov

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84 Citations (Scopus)


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 ν̄2 - 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 ν̄2 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.

Original languageEnglish
Pages (from-to)169-185
Number of pages17
JournalFlow, Turbulence and Combustion
Issue number3-4
Publication statusPublished - Jan 2005
Externally publishedYes


  • ν̄ - f model
  • Near-wall flow
  • Robust modification
  • Turbulence


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