Data-driven Reynolds-averaged turbulence modeling with generalizable non-linear correction and uncertainty quantification using Bayesian deep learning

Abstract

The past few years have witnessed a renewed blossoming of data-driven turbulence models. Quantification of the concomitant modeling uncertainty, however, has mostly been omitted, and the generalization performance of the data-driven models is still facing great challenges when predicting complex flows with different flow physics not seen during training. A robust data-driven Reynolds-averaged turbulence model with uncertainty quantification and non-linear correction is proposed in this work with the Bayesian deep neural network. In this model, the Reynolds stress tensor is decomposed into linear and non-linear parts. The linear part is taken as the usual linear eddy viscosity model while the non-linear counterpart is learned by a Bayesian deep neural network. Independent tensor bases of invariants and tensors constituted by mean strain rate tensor and rotation rate tensor are embedded into the neural network to effectively consider key turbulence features in different flows. The proposed model is well validated through numerical simulations of four canonical flows that significantly deviate in geometrical configurations and/or Reynolds numbers from those in the training data. With the non-linear corrections of embedded invariants and tensors representing key features of turbulence, the proposed model not only improves the predictive capabilities of Reynolds-averaged turbulence models on the same mesh but also has better generalization performance when simulating complex turbulent flows with large scale separation. In addition, this model allows us to quantitatively demonstrate the confidence interval of the predicted flow quantities that are originated from the model itself.

Testing a Generalized Two-Equation Turbulence Model for Computational Aerodynamics of a Mid-Range Aircraft

“…Furthermore, with the advancement of machine learning (ML) algorithms, which are able to make predictions based on huge amounts of available flow data, data-driven RANS turbulence modeling has been recently developing [13]. The data extracted from either experiments or high-fidelity CFD simulations are infused into the learning procedure, while ML techniques are used to link the turbulence modeling behavior to geometric and mean flow variables [14].…”