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Stefan Hickel
Institute of Aerodynamics and Fluid Mechanics Technische Universitat Munchen Boltzmannstr. 15, 85748 Garching bei Munchen, Germany; Chair of Computational Aerodynamics Faculty of Aerospace Engineering, TU Delft Kluyverweg 1, 2629 HS Delft, Netherlands

Emile Touber
Department of Aeronautics, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.

Julien Bodart
Université de Toulouse, Institut Supérieur de l'Aéronautique et de l'Espace (ISAE) BP 54032 - 31055 TOULOUSE Cedex 4,France; Center for Turbulence Research Stanford University, Stanford, CA 94305, USA

J. Larsson
Department of Mechanical Engineering, University of Maryland, USA


Wall-models are essential for enabling large-eddy simulations (LESs) of realistic problems at high Reynolds numbers. The present study is focused on approaches that directly model the wall shear stress, specifically on filling the gap between models based on wall-normal ordinary differential equations (ODEs) that assume equilibrium and models based on full partial differential equations (PDEs) that do not. We develop ideas for how to incorporate non-equilibrium effects (most importantly, strong pressure-gradient effects) in the wall-model while still solving only wall-normal ODEs. We test these ideas using two reference databases: an adverse pressure-gradient turbulent boundary-layer and a shock/boundary-layer interaction problem, both of which lead to separation and re-attachment of the turbulent boundary layer.