- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Machine-learning-augmented domain decomposition method for near-wall turbulence modeling

Shiyu Lyu1,*, Jiaqing Kou2,†, and Nikolaus A. Adams1,3

  • 1Chair of Aerodynamics and Fluid Mechanics, School of Engineering and Design, Technical University of Munich, Boltzmannstrasse 15, 85748 Garching, Germany
  • 2Institute of Aerodynamics, RWTH Aachen University, Wüllnerstrasse 5a, 52062 Aachen, Germany
  • 3Munich Institute of Integrated Materials, Energy and Process Engineering, Technical University of Munich, Lichtenbergstrasse 4a, 85748 Garching, Germany

  • *shiyu.lyu@tum.de
  • †Corresponding author: j.kou@aia.rwth-aachen.de
PDF

Phys. Rev. Fluids 9, 044603 – Published 5 April, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.044603

Abstract

To tackle the challenging near-wall turbulence modeling while preserving low computational cost, the near-wall nonoverlapping domain decomposition (NDD) method is proposed, incorporating the machine-learning technique. Using recently proposed implicit NDD (INDD), the solution can be calculated with a Robin-type (slip) wall boundary condition on a relatively coarse mesh and then corrected in the near-wall region at every iteration through an estimated turbulent viscosity profile obtained from a neural network. To maintain a reasonable complexity with acceptable accuracy, only the near-wall field properties, i.e., wall-normal distance, near-wall velocities, streamwise pressure gradients, and one near-wall scale parameter, are employed as the input features for the neural network. The benefit of incorporating machine learning is twofold. First, the near-wall turbulent viscosity is predicted more accurately than by the traditional algebraic functions used in the approximate approach. Second, similarly to the conventional NDD, the present simulations save one order of computational cost over the fully resolved one-block simulations. The accuracy and efficiency of the method are demonstrated on test cases with the k−ɛ model, including turbulent flows in a channel and an asymmetric diffuser at different Reynolds numbers. Results compare favorably with the one-block benchmark solutions and show a better agreement when compared with approximate NDD predictions. In the latter case, a variation of diffuser geometry is also considered to test the model performance on engineering design tasks with another turbulent model (i.e., Spalart-Allmaras), showing good generalization capability on different turbulence closures.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. A. J. Smits, B. J. McKeon, and I. Marusic, High–reynolds number wall turbulence, Annu. Rev. Fluid Mech. 43, 353 (2011).
  2. U. Piomelli, Wall-layer models for large-eddy simulations, Prog. Aerosp. Sci. 44, 437 (2008).
  3. J. S. Baggett, J. Jimenez, and A. G. Kravchenko, Resolution requirements in large-eddy simulations of shear flows, Annu. Res. Briefs 51 (1997).
  4. B. E. Launder and B. I. Sharma, Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc, Lett. Heat Mass Transf. 1, 131 (1974).
  5. K.-Y. Chien, Predictions of channel and boundary-layer flows with a low-reynolds-number turbulence model, AIAA J. 20, 33 (1982).
  6. D. C. Wilcox et al., Turbulence Modeling for CFD (DCW Industries La Canada, CA, 1998), Vol. 2.
  7. B. Launder and D. Spalding, The numerical computation of turbulent flows, Comput. Methods Appl. Mech. Eng. 3, 269 (1974).
  8. H. Grotjans and F. Menter, Wall functions for general application CFD codes, Comput. Fluid Dyn. Eur. Conf. 1, 1112 (1998).
  9. T. Craft, A. Gerasimov, H. Iacovides, and B. Launder, Progress in the generalization of wall-function treatments, Int. J. Heat Fluid Flow 23, 148 (2002).
  10. T. Craft, S. Gant, H. Iacovides, and B. Launder, A new wall function strategy for complex turbulent flows, Numer. Heat Transf., Pt. B 45, 301 (2004).
  11. S. Gant, Development and application of a new wall function for complex turbulent flows, Ph.D. thesis, University of Manchester, 2003.
  12. M. Popovac and K. Hanjalic, Compound wall treatment for rans computation of complex turbulent flows and heat transfer, Flow Turbul. Combust. 78, 177 (2007).
  13. S. Utyuzhnikov, Some new approaches to building and implementation of wall-functions for modeling of near-wall turbulent flows, Comput. Fluids 34, 771 (2005).
  14. S. Utyuzhnikov, Robin-type wall functions and their numerical implementation, Appl. Numer. Math. 58, 1521 (2008).
  15. A. Jones and S. Utyuzhnikov, Application of a near-wall domain decomposition method to turbulent flows with heat transfer, Comput. Fluids 119, 87 (2015).
  16. S. Utyuzhnikov, Domain decomposition for near-wall turbulent flows, Comput. Fluids 38, 1710 (2009).
  17. S. Utyuzhnikov, Towards development of unsteady near-wall interface boundary conditions for turbulence modeling, Comput. Phys. Commun. 185, 2879 (2014).
  18. M. Petrov, S. Utyuzhnikov, A. Chikitkin, and V. Titarev, On extension of near-wall domain decomposition to turbulent compressible flows, Comput. Fluids 210, 104629 (2020).
  19. A. Jones and S. Utyuzhnikov, Efficient computation of turbulent flow in ribbed passages using a non-overlapping near-wall domain decomposition method, Comput. Phys. Commun. 217, 1 (2017).
  20. S. Lyu and S. Utyuzhnikov, A computational slip boundary condition for near-wall turbulence modeling, Comput. Fluids 246, 105628 (2022).
  21. S. T. Bose and P. Moin, A dynamic slip boundary condition for wall-modeled large-eddy simulation, Phys. Fluids 26, 015104 (2014).
  22. H. J. Bae, A. Lozano-Durán, S. T. Bose, and P. Moin, Dynamic slip wall model for large-eddy simulation, J. Fluid Mech. 859, 400 (2019).
  23. S. Utyuzhnikov, Generalized wall functions and their application for simulation of turbulent flows, Int. J. Numer. Methods Fluids 47, 1323 (2005).
  24. E. Balaras, C. Benocci, and U. Piomelli, Two-layer approximate boundary conditions for large-eddy simulations, AIAA J. 34, 1111 (1996).
  25. W. Cabot and P. Moin, Approximate wall boundary conditions in the large-eddy simulation of high reynolds number flow, Flow Turbul. Combust. 63, 269 (2000).
  26. S. Kawai and J. Larsson, Wall-modeling in large eddy simulation: Length scales, grid resolution, and accuracy, Phys. Fluids 24, 015105 (2012).
  27. M. Wang and P. Moin, Dynamic wall modeling for large-eddy simulation of complex turbulent flows, Phys. Fluids 14, 2043 (2002).
  28. S. Kawai and J. Larsson, Dynamic non-equilibrium wall-modeling for large eddy simulation at high reynolds numbers, Phys. Fluids 25, 015105 (2013).
  29. C. Duprat, G. Balarac, O. Métais, P. M. Congedo, and O. Brugière, A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient, Phys. Fluids 23, 015101 (2011).
  30. A. Jones and S. Utyuzhnikov, A near-wall domain decomposition approach in application to turbulent flow in a diffuser, Appl. Math. Modell. 40, 329 (2016).
  31. A. Chikitkin, S. Utyuzhnikov, M. Petrov, and V. Titarev, Non-overlapping domain decomposition for modeling essentially unsteady near-wall turbulent flows, Comput. Fluids 202, 104506 (2020).
  32. S. L. Brunton, B. R. Noack, and P. Koumoutsakos, Machine learning for fluid mechanics, Annu. Rev. Fluid Mech. 52, 477 (2020).
  33. J. Kou and W. Zhang, Data-driven modeling for unsteady aerodynamics and aeroelasticity, Prog. Aerosp. Sci. 125, 100725 (2021).
  34. B. D. Tracey, K. Duraisamy, and J. J. Alonso, A machine learning strategy to assist turbulence model development, in 53rd AIAA Aerospace Sciences Meeting (AIAA, Kissimmee, Florida, 2015), p. 1287.
  35. D. A. Bezgin, S. J. Schmidt, and N. A. Adams, A data-driven physics-informed finite-volume scheme for nonclassical undercompressive shocks, J. Comput. Phys. 437, 110324 (2021).
  36. A. D. Jagtap, Z. Mao, N. Adams, and G. E. Karniadakis, Physics-informed neural networks for inverse problems in supersonic flows, J. Comput. Phys. 466, 111402 (2022).
  37. M. Milano and P. Koumoutsakos, Neural network modeling for near wall turbulent flow, J. Comput. Phys. 182, 1 (2002).
  38. K. Fukami, K. Fukagata, and K. Taira, Super-resolution reconstruction of turbulent flows with machine learning, J. Fluid Mech. 870, 106 (2019).
  39. J. Ling, A. Kurzawski, and J. Templeton, Reynolds averaged turbulence modelling using deep neural networks with embedded invariance, J. Fluid Mech. 807, 155 (2016).
  40. J.-X. Wang, J.-L. Wu, and H. Xiao, Physics-informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on DNS data, Phys. Rev. Fluids 2, 034603 (2017).
  41. E. J. Parish and K. Duraisamy, A paradigm for data-driven predictive modeling using field inversion and machine learning, J. Comput. Phys. 305, 758 (2016).
  42. J. Weatheritt and R. Sandberg, A novel evolutionary algorithm applied to algebraic modifications of the rans stress–strain relationship, J. Comput. Phys. 325, 22 (2016).
  43. Y. Zhao, H. D. Akolekar, J. Weatheritt, V. Michelassi, and R. D. Sandberg, Rans turbulence model development using CFD-driven machine learning, J. Comput. Phys. 411, 109413 (2020).
  44. A. Beck, D. Flad, and C.-D. Munz, Deep neural networks for data-driven les closure models, J. Comput. Phys. 398, 108910 (2019).
  45. R. Maulik, O. San, J. D. Jacob, and C. Crick, Sub-grid scale model classification and blending through deep learning, J. Fluid Mech. 870, 784 (2019).
  46. X. I. A. Yang, S. Zafar, J.-X. Wang, and H. Xiao, Predictive large-eddy-simulation wall modeling via physics-informed neural networks, Phys. Rev. Fluids 4, 034602 (2019).
  47. Z. Zhou, G. He, and X. Yang, Wall model based on neural networks for les of turbulent flows over periodic hills, Phys. Rev. Fluids 6, 054610 (2021).
  48. H. J. Bae and P. Koumoutsakos, Scientific multi-agent reinforcement learning for wall-models of turbulent flows, Nat. Commun. 13, 1443 (2022).
  49. A. Lozano-Durán and H. J. Bae, Machine learning building-block-flow wall model for large-eddy simulation, J. Fluid Mech. 963, A35 (2023).
  50. L. Zhu, W. Zhang, J. Kou, and Y. Liu, Machine learning methods for turbulence modeling in subsonic flows around airfoils, Phys. Fluids 31, 015105 (2019).
  51. P. S. Volpiani, R. F. Bernardini, and L. Franceschini, Neural network-based eddy-viscosity correction for RANS simulations of flows over bi-dimensional bumps, Int. J. Heat Fluid Flow 97, 109034 (2022).
  52. A. P. Singh, S. Medida, and K. Duraisamy, Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils, AIAA J. 55, 2215 (2017).
  53. P. Spalart and S. Allmaras, A one-equation turbulence model for aerodynamic flows, in 30th Aerospace Sciences Meeting and Exhibit (Reno, NV, USA, 1992), p. 439.
  54. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
  55. M. Manhart, N. Peller, and C. Brun, Near-wall scaling for turbulent boundary layers with adverse pressure gradient: A priori tests on dns of channel flow with periodic hill constrictions and dns of separating boundary layer, Theor. Comput. Fluid Dyn. 22, 243 (2008).
  56. H. G. Weller, G. Tabor, H. Jasak, and C. Fureby, A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys. 12, 620 (1998).
  57. S. V. Patankar and D. B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, in Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion (Elsevier, Amsterdam, 1983), pp. 54–73.
  58. J. P. Van Doormaal and G. D. Raithby, Enhancements of the simple method for predicting incompressible fluid flows, Numer. Heat Transf. 7, 147 (1984).
  59. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga et al., Pytorch: An imperative style, high-performance deep learning library, Adv. Neural Inf. Proc. Syst. 32 (2019).
  60. C. U. Buice and J. K. Eaton, Experimental investigation of flow through an asymmetric plane diffuser, Centre Turbul. Res. Annu. Res. Brief. 1995, 117 (1995).
  61. A. Hellsten, P. Rautaheimo, and M. Orpana, 8th Ercoftac/Iahr/Cost Workshop on Refined Turbulence Modelling, ERCOFTAC, Helsinki University of Technology, Espoo, Finland, 1999.
  62. J. Gullman-Strand, O. Törnblom, B. Lindgren, G. Amberg, and A. V. Johansson, Numerical and experimental study of separated flow in a plane asymmetric diffuser, Int. J. Heat Fluid Flow 25, 451 (2004).

Outline

Information

Phys. Rev. Fluids 9, 044603– Published 5 April, 2024
  • Received 31 October 2023
  • Accepted 7 March 2024
Crossmark - Check for updates button

©2024 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation