Implementation and Validation of an Algebraic Wall Model for LES in Nek5000

Abstract

Turbulent flows are most often wall-bounded, rendering the treatment of the wall essential. In this work, the near-wall layer is modelled in large eddy simulations which enables simulating high Reynolds number flows. An algebraic wall model has been implemented in the spectral element code Nek5000. It consists of an approximate boundary condition that relates the wall shear stress to the velocity measured close to the wall, on the upper edge of the first spectral element. The wall shear stress model approximates the law of the wall for hydraulically smooth cases. The model is applied to channel flow cases at \(Re_{\tau }=1000\) and at \(Re_{\tau }=5200\). The wmLES results obtained with the present implementation are seen to compare very well with those of reference direct numerical simulations in the resolved region. They also remain remarkably close to the reference results for a large part of the under-resolved region; which is not necessarily the case when using low order implementations and even other types of high order discretizations, as found in the literature. Various parameters are studied such as the time averaging, the height of the near wall under-resolved element, and the mesh requirements. The obtained results indicate that accurate results can be obtained with Nek5000 at a reduced cost thanks to this newly implemented wmLES model. This work provides the necessary guidelines for simple flows, and it will serve as a first basis for simulating more complex flows at high Reynolds numbers.