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 ([email protected]) +

[bibliography] References

[bibliography]

• [[[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. https://doi.org/10.1103/PhysRevFluids.2.034603[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. https://doi.org/10.1103/PhysRevFluids.3.074602[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. https://doi.org/10.1016/j.cma.2018.09.010[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. https://doi.org/10.1146/annurev-fluid-010518-040547[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: https://arxiv.org/abs/1806.10434[arXiv:1806.10434]