Space-dependent turbulence model aggregation using machine learning

Abstract

Computational models of fluid flows based on the Reynolds-Averaged Navier–Stokes (RANS) equations supplemented with a turbulence model are the gold standard in engineering applications. A plethora of turbulence models and related variants exist, none of which are fully reliable outside the range of flow configurations for which they were calibrated. Thus, the choice of a suitable turbulence closure largely relies on subjective expert judgement and engineering know-how. In this article, we propose a data-driven methodology for combining the solutions of a set of competing turbulence models. The individual model predictions are linearly combined for providing an ensemble solution accompanied by estimates of predictive uncertainty due to the turbulence model choice. First, for a set of training flow configurations we assign high weights to component models in the regions where they perform best, and vice versa, based on a measure of distance between high-fidelity data and individual model predictions. The model weights are then mapped into a space of features, representative of the local flow physics, and regressed using a Random Forests (RF) algorithm. Finally, the RF regressor is used to infer spatial distributions of the model weights for unseen configurations. Predictions of new cases are constructed as a convex linear combination of the underlying models solutions, while the between-model variance provides information about regions of high model uncertainty. The method is demonstrated for a class of flows through the compressor cascade NACA65 V103 at Re≃3×105. The results show that the aggregated solution outperforms the accuracy of individual models for the quantity used to inform the RF regressor, and performs well for other quantities well-correlated with the previous one. The estimated uncertainty intervals are generally consistent with the target high-fidelity data. The present approach then represents a viable methodology for a more objective selection and combination of alternative turbulence models in configurations of interest for engineering practice.