Critical assessment of wall model numerical implementation in LBM

Abstract

In this article, a thorough investigation of wall model numerical implementation at high Reynolds numbers is conducted. In the framework of combined Lattice Boltzmann Method (LBM) and Immersed Boundary Method (IBM), this work focuses on two main axes: First, the influence of the wall model data input interpolation is investigated. After a brief review of the common interpolation methods used in the literature, the accuracy of various interpolation strategies ranging from Inverse Distance Weighing (IDW) to Trilinear methods are assessed. Secondly, the sensitivity of the wall model to its numerical implementation is evaluated by comparing a tried-and-tested wall model with a linearization procedure that aims at dealing with challenging configurations. The comparisons are made on two bidimensional benchmark test-cases, namely the turbulent flat plate and the bump-in-channel. It is shown that first order interpolation methods can lead to spurious oscillations in surface coefficients for challenging test-cases. Moreover, it has been found that the numerical implementation of the wall model has a profound influence on its behavior leading to unphysical friction coefficients if the wall model numerical implementation is not designed to handle properly immersed boundary conditions in the case of complex configurations.