Technical Report 2017-001

Formulation of a Wall Model for LES in a Collocated Finite-Volume Framework

Mattias Liefvendahl, Timofey Mukha, and Saleh Rezaeiravesh

January 2017

Wall-modelled Large-Eddy Simulation (WMLES) is a turbulence modelling approach that aims to reduce the computational costs of traditional (wall-resolved) LES by introducing special treatment of the near-wall region. In this report, a detailed derivation is given of a widely used wall model which is based on implicitly enforcing the correct local wall shear stress. The model is developed in the framework of a collocated finite volume method, with unstructured meshes and arbitrary polyhedral grid cells. The expression for the law of the wall proposed by Spalding is used to relate the finite volume cell flow velocity to the wall-shear stress. The computational cost and predictive accuracy of the overall method is evaluated by a series of turbulent channel flow simulations covering a range of Re-numbers, from 10 000 to 125 000, based on the bulk velocity and channel half-height. For validation, the WMLES-results are compared to publicly available results from direct numerical simulations. It is demonstrated that the WMLES approach significantly reduces the computational cost, as compared to wall-resolved LES, while maintaining an acceptable accuracy of, at least, first-order statistical moments of the unknowns.

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