Data-driven modelling of the Reynolds stress tensor using random forests with invariance

• Published in: Computers & fluids Vol. 202; p. 104497
• Main Authors: Kaandorp, Mikael L.A., Dwight, Richard P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 30.04.2020; Elsevier BV
• Subjects: Algorithms; Anisotropy; Closures; Computational fluid dynamics; Computer simulation; Invariance; Machine learning; Mathematical analysis; Modelling; Neural networks; Non-linear eddy-viscosity closures; Random forests; Reynolds anisotropy tensor; Reynolds averaged Navier-Stokes method; Reynolds stress; Tensors; Turbulence modelling; Turbulence models; Non-linear eddy-viscosity closures; Machine-learning; Reynolds anisotropy tensor; Random forests; Turbulence modelling
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2020.104497

•A random forest predicting the Reynolds stress in turbulent flows is presented.•Invariance of predictions is achieved by making use of a tensor basis.•The algorithm is trained and tested on 5 different flow configurations.•Predicted Reynolds stresses are propagated, producing improved mean flow fields. A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while guaranteeing Galilean invariance by making use of a tensor basis. By modifying a random forest algorithm to accept such a tensor basis, a robust, easy to implement, and easy to train algorithm is created. The algorithm is trained on several flow cases using DNS/LES data, and used to predict the Reynolds stress anisotropy tensor for new, unseen flows. The resulting predictions of turbulence anisotropy are used as a turbulence model within a custom RANS solver. Stabilization of this solver is necessary, and is achieved by a continuation method and a modified k-equation. Results are compared to the neural network approach of Ling et al. [29]. Results show that the TBRF algorithm is able to accurately predict the anisotropy tensor for various flow cases, with realizable predictions close to the DNS/LES reference data. Corresponding mean flows for a square duct flow case and a backward facing step flow case show good agreement with DNS and experimental data-sets. Overall, these results are seen as a next step towards improved data-driven modelling of turbulence. This creates an opportunity to generate custom turbulence closures for specific classes of flows, limited only by the availability of LES/DNS data.