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

Mikael L.A. Kaandorp*, Richard P. Dwight

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

14 Citations (Scopus)
87 Downloads (Pure)


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.

Original languageEnglish
Article number104497
Number of pages16
JournalComputers and Fluids
Publication statusPublished - 30 Apr 2020


  • Machine-learning
  • Non-linear eddy-viscosity closures
  • Random forests
  • Reynolds anisotropy tensor
  • Turbulence modelling


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