Multi-Objective CFD-Driven Development of Coupled Turbulence Closure Models

TL;DR

This paper presents a multi-objective, CFD-driven approach for developing coupled turbulence closure models, improving predictions in complex flows by training multiple models simultaneously with a focus on their interactions.

Contribution

It introduces two novel concepts: multi-expression training for coupled models and a multi-objective optimization framework, advancing data-driven turbulence modeling capabilities.

Findings

Improved mean flow predictions in benchmark cases.

Enhanced coupling of momentum and thermal models.

Robust multi-objective training results.

Abstract

This paper introduces two novel concepts in data-driven turbulence modeling that enable the simultaneous development of multiple closure models and the training towards multiple objectives. The concepts extend the evolutionary framework by Weatheritt and Sandberg (2016), which derives interpretable and implementation-ready expressions from high-fidelity simulation data. By assigning a shared fitness value to the evolved closure models and utilizing the CFD-driven training approach by Zhao et al. (2020), the multi-expression training concept introduced here is able to account for the coupling between the trained models, i.e. Reynolds stress anisotropy, turbulent heat flux and turbulence production correction models. As a second concept, a multi-objective optimization algorithm is applied to the framework. The extension yields a diverse set of candidate models and allows a trade-off between the training objectives after analyzing the training results. In this study, the novel concepts are applied to a benchmark periodic hills case and a vertical natural convection flow. The predictions of mean flow quantities are improved compared to decoupled training strategies with distinct and robust improvements for strongly coupled momentum and thermal fields. The coupled training of closure models and the balancing of multiple training objectives are considered important capabilities on the path towards generalized data-driven turbulence models.