Probabilistic Machine Learning to Improve Generalisation of Data-Driven Turbulence Modelling

TL;DR

This paper introduces a probabilistic machine learning approach using Gaussian Process Emulators to enhance turbulence models, improving generalisation to unseen flows and handling heterogeneous data for better predictions in complex separated flows.

Contribution

The work presents a novel ensemble Gaussian Process Emulator framework that improves turbulence model accuracy and generalisation across diverse flow conditions and datasets.

Findings

Enhanced turbulence predictions in separated flows with adverse pressure gradients

Model reverts to uncorrected form outside training data regions

Demonstrated improved generalisation on benchmark cases

Abstract

A probabilistic machine learning model is introduced to augment the $k-\omega\ SST$ turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods have been used to leverage experimental and high-fidelity data, improving the accuracy of the Reynolds Averaged Navier Stokes (RANS) turbulence models widely used in industry. A significant challenge for such methods is their ability to generalise to unseen geometries and flow conditions. Furthermore, heterogeneous datasets containing a mix of experimental and simulation data must be efficiently handled. In this work, field inversion and an ensemble of Gaussian Process Emulators (GPEs) is employed to address both of these challenges. The ensemble model is applied to a range of benchmark test cases, demonstrating improved turbulence modelling for cases with separated flows with adverse pressure gradients, where RANS simulations are understood to be unreliable. Perhaps more significantly, the simulation reverted to the uncorrected model in regions of the flow exhibiting physics outside of the training data.