On numerical uncertainties in scale-resolving simulations of canonical wall turbulence

The present study focuses on applying different metrics to assess accuracy, robustness and sensitivity of scale-resolving simulations of turbulent channel flow, when the numerical parameters are systematically varied. Derived by combining well-established uncertainty quantification techniques and computer experiments, the metrics act as powerful tools for understanding the behavior of flow solvers and exploring the impact of their numerical parameters as well as systematically comparing different solvers. A few examples for uncertain behavior of the solvers, i.e. the behaviors that are unexpected or not fully explainable with our a-priori knowledge, is provided. Two open-source software, Nek5000 and OpenFOAM, are considered with the focus on grid resolution and filtering in Nek5000, and grid resolution and numerical dissipation in OpenFOAM. Considering all metrics as well as the computational efficiency, Nek5000 is shown to outperform OpenFOAM. The propagated uncertainty (a measure of robustness) in the profiles of channel flow quantities of interest (QoIs), together with corresponding Sobol sensitivity indices quantitatively measure the impact and relative contribution of different numerical parameters at different wall-distances. The locations with larger confidence intervals indicate where a QoI is more sensitive to the variation of the numerical parameters. In OpenFOAM, increasing the numerical dissipation at all considered grid resolutions leads to decreasing the uncertainties at the price of losing accuracy. In contrast, the influence of filtering in Nek5000 is found to be more complicated and relying on the grid resolution. In particular, the filter cutoff is found to be more influential than the filter weight, and at high number of Gauss–Lobatto–Legendre (GLL) points per element, it is shown that there exist optimal values for the filter cutoff which result in more accurate QoIs. From the same analysis, it is also concluded that considering the number of GLL points as an indicator of resolution and accuracy in the context of Nek5000 may require additional consideration. The analyses and metrics presented in this study are general and can be applied to any type of flow simulation. They facilitate not only the validation-and-verification process, but also the selection of adequate numerical parameters to achieve accurate and reliable results.