Data-driven Reynolds stress modeling with physics-informed machine learning

Jinlong Wu, Carlos Michelén-Ströfer, Jianxun Wang, Heng Xiao

A complex physical system characterized by a wide range of temporal and spatial scales, turbulence is among the last unsolved problems in classical physics that affects natural and engineered systems from sub-meter to planetary scales. Current simulations of turbulent flows rely on Reynolds Averaged Navier Stokes equations with closure models. In light of the decades-long stagnation in traditional turbulence modeling, we proposed data-driven, physics-informed machine learning method for turbulence modeling.

This repository contains tutorial Python scripts used to generated results published in the [Wang2017Physics] and [Wu2018Physicsa]. Also see: [Wu2018Representation]. Review relevant review articles: [Duraisamy2019Turbulence] and [Xiao2019RANS]

You can download the Jupyter Notebook to run and play with the code, or simply download the HTML version of the tutorial](regressionSolver.html) generated by the Jupyter Notebook.

Please send bug reports and comments to: Heng Xiao (hengxiao@vt.edu)

References

• [Wang2017Physics] J.-X. Wang, J.-L. Wu, and H. Xiao. Physics informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data. Physical Review Fluids, 2(3), 034603, 1-22, 2017. DOI:10.1103/PhysRevFluids.2.034603

• [Wu2018Physics] J.-L. Wu, H. Xiao and E. G. Paterson. Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework. Physical Review Fluids, 3, 074602, 1-28, 2018. DOI: 10.1103/PhysRevFluids.3.074602

• [Wu2018Representation] J.-L. Wu, R. Sun, S. Laizet and H. Xiao. Representation of Reynolds stress perturbations with application in machine-learning-assisted turbulence modeling. Computer Methods in Applied Mechanics and Engineering，346, 707-726, 2019. DOI: 10.1016/j.cma.2018.09.010

• [Duraisamy2019Turbulence] K. Duraisamy, G. Iaccarino, and H. Xiao. Turbulence modeling in the age of data. Annual Review of Fluid Mechanics, 51, 357-377, 2019. DOI: 10.1146/annurev-fluid-010518-040547

• [Xiao2019RANS] H. Xiao and P. Cinnella. Quantification of model uncertainty in RANS simulations: A review. Progress in Aerospace Sciences. In Press, 2018. Invited review article. Also available at: arXiv:1806.10434