Effects of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation

T Mukha

doi:10.15514/ispras-2019-31(6)-11

Abstract

The effect of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation is investigated via systematic simulations of fully-developed turbulent channel flow. A total of 16 simulations are conducted using the open-source computational fluid dynamics software OpenFOAM®. Four densities of the computational mesh are considered, with four simulations performed on each, in turn varying in the amount of numerical dissipation introduced by the numerical scheme used for interpolating the convective fluxes. The results are compared to publicly-available data from direct numerical simulation of the same flow. Computed error profiles of all the considered flow quantities are shown to vary monotonically with the amount of dissipation introduced by the numerical schemes. As expected, increased dissipation leads to damping of high-frequency motions, which is clearly observed in the computed energy spectra. But it also results in increased energy of the large-scale motions, and a significant over-prediction of the turbulent kinetic energy in the inner region of the boundary layer. On the other hand, dissipation benefits the accuracy of the mean velocity profile, which in turn improves the prediction of the wall shear stress given by the wall model. Thus, in the current framework, the optimal choice for the dissipation of the numerical schemes may depend on the primary quantity of interest for the conducted simulation. With respect to the resolution of the grid, the change in the accuracy is much less predictable, and the optimal resolution depends on the considered quantity and the amount of dissipation introduced by the numerical schemes.

Highlights

In turbulent boundary layers (TBLs), two fundamental length-scales can be distinguished
One is the thickness of the boundary layer, which governs the size of the largest eddies in the TBL
The magnitude and behavior of this error are very similar to that exhibited by. This confirms the observation made in a previous study [16] that in the case of attached boundary layers the accuracy of the wall model is determined by the accuracy of the velocity signal that it bases its predictions on

Summary

Introduction

In turbulent boundary layers (TBLs), two fundamental length-scales can be distinguished. One is the thickness of the boundary layer, , which governs the size of the largest eddies in the TBL. Wall-resolving, large-eddy simulation (LES) both scales are resolved, leading to an accurate solution, but forcing the size of the computational mesh to scale as . In wall-modelled LES (WMLES) a model for the scales ~δ is employed, allowing to use a mesh that only resolves the large scales ~δ. This reduces the mesh size scaling with to linear, making higher number simulations affordable [1]–[3]. -called wall-stress modelling is used, in which the task of the wall-model is to predict the wall shear stress τ , given the current solution to the LES equations, typically sampled from a single point located at some distance h from the considered location on the wall

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