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Recent progress in augmenting turbulence models with physics-informed machine learning

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Abstract

In view of the long stagnation in traditional turbulence modeling, researchers have attempted using machine learning to augment turbulence models. This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning. We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models. Future and on-going research efforts are introduced.

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References

  1. Kroll N., Rossow C., Schwamborn D. et al. MEGAFLOW: A numerical flow simulation tool for transport aircraft design [C]. ICAS Congress, Braunschweig, Germany, 2002, 1–105.

  2. Mahaffy J., Chung B., Song C. et al. Best practice guidelines for the use of CFD in nuclear reactor safety applications [R]. Technical Report, Organisation for Economic Cooperation and Development, 2007.

  3. IAEA. Use of computational fluid dynamics codes for safety analysis of nuclear reac- tor systems [R]. Technical Report IAEA-TECDOC-1379, Pisa, Italy: International Atomic Energy Agency, 2002.

  4. Moin P., Kim J. Tackling turbulence with supercomputers [J]. Scientific American, 1997, 276(1): 46–52.

    Article  Google Scholar 

  5. Johnson F. T., Tinoco E. N., Yu N. J. Thirty years of development and application of CFD at Boeing Commercial Airplanes, Seattle [J]. Computers and Fluids, 2005, 34(10): 1115–1151.

    Article  Google Scholar 

  6. Oliver T., Moser R. Uncertainty quantification for RANS turbulence model predictions [C]. APS Division of Fluid Dynamics Meeting, Minneapolis, MN, USA, 2009.

  7. Emory M., Pecnik R., Iaccarino G. Modeling structural uncertainties in Reynolds-averaged computations of shock/boundary layer interactions [C]. 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, FL, USA, 2011, AIAA paper 2011-479.

  8. Emory M., Larsson J., Iaccarino G. Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures [J]. Physics of Fluids, 2013, 25(11): 110822.

    Article  Google Scholar 

  9. Oliver T. A., Moser R. D. Bayesian uncertainty quantification applied to RANS turbulence models [J]. Journal of Physics: Conference Series, 2011, 318: 042032.

    Google Scholar 

  10. Duraisamy K., Iaccarino G., Xiao H. Turbulence modeling in the age of data [J]. Annual Review of Fluid Mechanics, 2019, 51: 357–377.

    Article  MathSciNet  Google Scholar 

  11. Xiao H., Cinnella P. Quantification of model uncertainty in RANS simulations: A review [J]. Progress in Aerospace Sciences, 2019, 108: 1–31.

    Article  Google Scholar 

  12. Launder B., Sharma B. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc [J]. Letters in Heat and Mass Transfer, 1974, 1(2): 131–137.

    Article  Google Scholar 

  13. Menter F. R. Two-equation eddy-viscosity turbulence models for engineering applications [J]. AIAA Journal, 1994, 32(8): 1598–1605.

    Article  Google Scholar 

  14. Spalart P. R., Allmaras S. R. A one equation turbulence model for aerodynamic flows [J]. Recherche Aerospatiale, 1994, 1(1): 5–21.

    Google Scholar 

  15. Spalart P. R. Philosophies and fallacies in turbulence modeling [J]. Progress in Aerospace Sciences, 2015, 74: 1–15.

    Article  Google Scholar 

  16. Singh A. P., Medida S., Duraisamy K. Machine learning-augmented predictive modeling of turbulent separated flows over airfoils [J]. AIAA Journal, 2017, 55(7): 2215–2227.

    Article  Google Scholar 

  17. Tracey B., Duraisamy K., Alonso J. J. A machine learning strategy to assist turbulence model development [C]. 53rd AIAA Aerospace Sciences Meeting, Kissimmee, USA, 2015, AIAA paper 2015-1287.

  18. Parish E. J., Duraisamy K. A paradigm for data-driven predictive modeling using field inversion and machine learning [J]. Journal of Computational Physics, 2016, 305: 758–774.

    Article  MathSciNet  Google Scholar 

  19. Zhu L., Zhang W., Kou J. et al. Machine learning methods for turbulence modeling in subsonic flows around airfoils [J]. Physics of Fluids, 2019, 31(1): 015105.

    Article  Google Scholar 

  20. Ling J., Kurzawski A., Templeton J. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance [J]. Journal of Fluid Mechanics, 2016, 807: 155–166.

    Article  MathSciNet  Google Scholar 

  21. Zhang Z., Song X. D., Ye S. R. et al. Application of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data [J]. Journal of Hydrodynamics, 2019, 31(1): 58–65.

    Article  Google Scholar 

  22. Weatheritt J., Sandberg R. A novel evolutionary algorithm applied to algebraic modifications of the RANS stressstrain relationship [J]. Journal of Computational Physics, 2016, 325: 22–37.

    Article  MathSciNet  Google Scholar 

  23. Weatheritt J., Sandberg R. D. The development of algebraic stress models using a novel evolutionary algorithm [J]. International Journal of Heat and Fluid Flow, 2017, 68: 298–318.

    Article  Google Scholar 

  24. Wu J., Xiao H., Paterson E. G. Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework [J]. Physical Review Fluids, 2018, 3: 074602.

    Article  Google Scholar 

  25. Xiao H., Wu J., Wang J. et al. Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes equations: A data-driven, physics-based, Bayesian approach [J]. Journal of Computational Physics, 2016, 324: 115–136.

    Article  MathSciNet  Google Scholar 

  26. Wang J., Wu J. L., Xiao H. Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data [J]. Physical Review Fluids, 2017, 2(3): 034603.

    Article  Google Scholar 

  27. Wang J., Huang J., Duan L. et al. Prediction of Reynolds stresses in high-Mach-number turbulent boundary layers using physics-informed machine learning [J]. Theoretical and Computational Fluid Dynamics, 2019, 33(1): 1–19.

    Article  MathSciNet  Google Scholar 

  28. Wu J., Xiao H., Sun R. et al. Reynolds-averaged Navier-Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned [J]. Journal of Fluid Mechanics, 2019, 869: 553–586.

    Article  MathSciNet  Google Scholar 

  29. Wu J., Wang J., Xiao H. et al. A priori assessment of prediction confidence for data-driven turbulence modeling [J]. Flow, Turbulence and Combustion, 2017, 99(1): 25–46.

    Article  Google Scholar 

  30. Zhang W., Zhu L., Liu Y. et al. Progresses in the application of machine learning in turbulence modeling [J]. Acta Aerodynamica Sinica, 2019, 37(3): 444–454 (in Chinese).

    Google Scholar 

  31. Wu J., Sun R., Laizet S. et al. Representation of stress tensor perturbations with application in machine-learning-assisted turbulence modeling [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 346: 707–726.

    Article  MathSciNet  Google Scholar 

  32. Xiao H., Wu J., Laizet S. et al. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations [J]. Fluid Dynamics, 2019 (Submitted).

  33. Breuer M., Peller N., Rapp C. et al. Flow over periodic hills: Numerical and experimental study in a wide range of Reynolds numbers [J]. Computers and Fluids, 2009, 38(2): 433–457.

    Article  Google Scholar 

  34. Xiao H., Wu J., Laizet S. et al. Flow over periodic hills of parameterized geometries: Example code and dataset for data-driven turbulence modeling [EB/OL]. https://github.com/xiaoh/para-database-for-PIML, 2019.

  35. Rumsey C. L. NASA Langley turbulence modeling portal [EB/OL]. https://turbmodels.larc.nasa.gov, 2018.

  36. Zhang X., Michelen-Ströfer C., Xiao H. Regularization of ensemble kalman methods for inverse problems [J]. 2019 (Submitted).

  37. Wu J., Michelen-Ströfer C., Xiao H. Physics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows [J]. Computers and Fluids, 2019, 193: 104292.

    Article  MathSciNet  Google Scholar 

  38. Michelén-Ströfer C., Zhang X., Xiao H. et al. Enforcing boundary conditions on physical fields in Bayesian inversion [J]. 2019 (Submitted).

  39. Spalart P., Shur M. On the sensitization of turbulence models to rotation and curvature [J]. Aerospace Science and Technology, 1997, 1(5): 297–302.

    Article  Google Scholar 

  40. Ling J., Templeton J. Evaluation of machine learning algorithms for prediction of regions of high Reynolds-averaged Navier-Stokes uncertainty [J]. Physics of Fluids, 2015, 27(8): 085103.

    Article  Google Scholar 

  41. Xiao H., Wu J. L., Laizet S. et al. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations [J]. Computers and Fluids, 2019, Preprint arxiv: 1910.01264.

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Acknowledgement

We present a brief review of recent progress in our group on data-driven turbulence modeling. The results shown here have been published previously and references to original publications are provided.

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Correspondence to Heng Xiao.

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Biography: Xinlei Zhang (1991-), Male, Ph. D. Candidate

This article is based on an invited lecture delivered at the 30th National Conference on Hydrodynamics, Hefei, China, August 18, 2019.

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Zhang, X., Wu, J., Coutier-Delgosha, O. et al. Recent progress in augmenting turbulence models with physics-informed machine learning. J Hydrodyn 31, 1153–1158 (2019). https://doi.org/10.1007/s42241-019-0089-y

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  • DOI: https://doi.org/10.1007/s42241-019-0089-y

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