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

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.

Quantitative Comparison of Numerical Errors for High-Speed Flux Schemes

“…waves or structures of size approaching the grid spacing [3,4]. Recent work by Mukha suggests numerical dissipation can even lead to overprediction of kinetic energy at the largest scales [5]. In the end, the crux of the issue lies with the limits of computational resources: with infinite compute time, one could simply use grids refined enough such that the smallest length-scales in the flow are highly resolved even by a diffusive method, but this is unreasonable for most problems, particularly in high-velocity regimes.…”