INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2005; 49:975–997 Published online 3 August 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/d.1034 An eddy viscosity model with near-wall modications M. M. Rahman ∗; † and T. Siikonen ‡ Laboratory of Applied Thermodynamics; Department of Mechanical Engineering; Helsinki University of Technology; S ahk omiehentie 4; FIN-02015 HUT; Finland SUMMARY An extended version of the isotropic k – model is proposed that accounts for the distinct eects of low-Reynolds number (LRN) and wall proximity. It incorporates a near-wall correction term to amplify the level of dissipation in nonequilibrium ow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient ows, involving ow separation and reattachment. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and the Schwarz’ inequality for turbulent shear stresses. The model coecients= functions preserve the anisotropic characteristics of turbulence. The model is validated against a few ow cases, yielding pre- dictions in good agreement with the direct numerical simulation (DNS) and experimental data. Com- parisons indicate that the present model is a signicant improvement over the standard eddy viscosity formulation. Copyright ? 2005 John Wiley & Sons, Ltd. KEY WORDS: near-wall correction; turbulence anisotropy; realizability; ow separation and reattach- ment 1. INTRODUCTION A large number of scientic and engineering calculations adhering to turbulent ows are established on the k – model. The standard k – model is devised for high Reynolds number turbulent ows and is traditionally used in wall-bounded ows in conjunction with a wall function approach to patch the core region of the ow to the wall region. In this way, the problem of modelling the direct inuence of viscosity is avoided. Unfortunately, universal wall functions do not exist in complex ows. Turbulent ows involving boundary layer separation or complex alterations of the surface transport properties represent such examples. It requires the direct integration of the modelled turbulence equations to a solid boundary that plays a crucial role. In particular, predictions of a high Reynolds number turbulence model can be ∗ Correspondence to: M. M. Rahman, Laboratory of Applied Thermodynamics, Department of Mechanical Engineering, Helsinki University of Technology, S ahk omiehentie 4, FIN-02015 HUT, Finland. † E-mail: mizanur.rahman@hut. ‡ E-mail: timo.siikonen@hut. Received 3 March 2005 Revised 10 May 2005 Copyright ? 2005 John Wiley & Sons, Ltd. Accepted 12 May 2005