Quantifying uncertainties in Direct Numerical Simulations of a turbulent channel flow

Direct numerical simulation (DNS) provides unrivalled levels of detail and accuracy for simulating turbulent flows. However, like all numerical methods, DNS is subject to uncertainties arising from the numerical scheme and input parameters (e.g. mesh resolution). While uncertainty quantification (UQ) techniques are being employed more and more to provide a systematic analysis of uncertainty for lower-fidelity models, their application to DNS is still relatively rare. In light of this, the aim of this work is to apply UQ and sensitivity analysis to the DNS of a canonical wall-bounded turbulent channel flow at low Reynolds number (Reτ=180). To compute the DNS, Incompact3d – a highly scalable open-source framework based on high-order compact finite differences and a spectral Poisson solver – is used as a black-box solver. Stochastic collocation is used to propagate the input uncertainties through Incompact3d to the output quantities of interest (QOIs). To facilitate the non-intrusive forward UQ analysis, the open-source EasyVVUQ package is used to provide integrated capability for sampling, pre-processing, execution, post-processing, and analysis of the computational campaign. Three separate UQ campaigns are conducted. The first two examine the effect of domain size and the numerical parameters (e.g. mesh resolution, time step, sample time), respectively, and adopt Gaussian quadrature rules combined via tensor products to sample the multi-dimensional input space. Finally, the third campaign investigates the performance of a dimension-adaptive sampling strategy that significantly reduces the computational cost compared to the full tensor product approach. The analysis focuses on the cross-channel statistical moments of the QOIs, as well as local and global sensitivity analyses to assess the sensitivity of each QOI with respect to each individual input. This enables an assessment of the robustness and sensitivity of DNS to the user-defined numerical parameters for wall-bounded turbulent flows, and provides an indication of suitable ranges for defining the values of these parameters.

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