Toward accelerated data-driven Rayleigh–Bénard convection simulations

K. Nakai, Y. Saiki, Machine-learning inference of fluid variables from data using reservoir computing. Phys. Rev. E (2018). https://doi.org/10.1103/physreve.98.023111

H. Schaeffer, Learning partial differential equations via data discovery and sparse optimization. Proc. R. Soc. A Math. Phys. Eng. Sci. 473(2197), 20160446 (2017). https://doi.org/10.1098/rspa.2016.0446

N.B. Erichson, M. Muehlebach, M. Mahoney, Physics-informed autoencoders for lyapunov-stable fluid flow prediction, in Machine Learning and the Physical Sciences Workshop, Conference on Neural Information Processing Systems (2019). arXiv:1905.10866

K. Champion, B. Lusch, J.N. Kutz, S.L. Brunton, Data-driven discovery of coordinates and governing equations. Proc. Natl. Acad. Sci. 116(45), 22445–22451 (2019). https://doi.org/10.1073/pnas.1906995116

T. Nakamura, K. Fukami, K. Hasegawa, Y. Nabae, K. Fukagata, Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow. Phys. Fluids 33(2), 025116 (2021). https://doi.org/10.1063/5.0039845

M. Raissi, P. Perdikaris, G.E. Karniadakis, Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019). https://doi.org/10.1016/j.jcp.2018.10.045

Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, A. Anandkumar, Fourier Neural Operator for Parametric Partial Differential Equations. arXiv (2020). arxiv:2010.08895

M. Gamahara, Y. Hattori, Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2, 054604 (2017). https://doi.org/10.1103/PhysRevFluids.2.054604

A. Vollant, G. Balarac, C. Corre, Subgrid-scale scalar flux modelling based on optimal estimation theory and machine-learning procedures. J. Turbul. 18(9), 854–878 (2017). https://doi.org/10.1080/14685248.2017.1334907

R. Maulik, O. San, A. Rasheed, P. Vedula, Subgrid modelling for two-dimensional turbulence using neural networks. J. Fluid Mech. 858, 122–144 (2018). https://doi.org/10.1017/jfm.2018.770

F. Sarghini, G. de Felice, S. Santini, Neural networks based subgrid scale modeling in large eddy simulations. Comput. Fluids 32(1), 97–108 (2003). https://doi.org/10.1016/S0045-7930(01)00098-6

J.B. Freund, J.F. MacArt, J.A. Sirignano, DPM: a deep learning PDE augmentation method (with application to large-eddy simulation). CoRR abs/1911.09145 (2019) arxiv:1911.09145

H.J. Bae, P. Koumoutsakos, Scientific multi-agent reinforcement learning for wall-models of turbulent flows. Nat. Commun. 13(1), 1443 (2022). https://doi.org/10.1038/s41467-022-28957-7

Y. Zhao, H.D. Akolekar, J. Weatheritt, V. Michelassi, R.D. Sandberg, Rans turbulence model development using CFD-driven machine learning. J. Comput. Phys. 411, 109413 (2020). https://doi.org/10.1016/j.jcp.2020.109413

O. Obiols-Sales, A. Vishnu, N. Malaya, A. Chandramowliswharan, CFDNet, in Proceedings of the 34th ACM International Conference on Supercomputing. ACM (2020). https://doi.org/10.1145/3392717.3392772

J. Ling, A. Kurzawski, J. Templeton, Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. (2016). https://doi.org/10.1017/jfm.2016.615

A.-m. Farahmand, S. Nabi, D.N. Nikovski, Deep reinforcement learning for partial differential equation control, in 2017 American Control Conference (ACC) (2017), p. 3120–3127. https://doi.org/10.23919/ACC.2017.7963427

J. Tompson, K. Schlachter, P. Sprechmann, K. Perlin, Accelerating Eulerian fluid simulation with convolutional networks. CoRR (2016) arxiv:1607.03597

R. Maulik, O. San, A neural network approach for the blind deconvolution of turbulent flows. J. Fluid Mech. 831, 151–181 (2017). https://doi.org/10.1017/jfm.2017.637

M. Milano, P. Koumoutsakos, Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182(1), 1–26 (2002). https://doi.org/10.1006/jcph.2002.7146

A. Sanchez-Gonzalez, J. Godwin, T. Pfaff, R. Ying, J. Leskovec, P. Battaglia, Learning to simulate complex physics with graph networks, in Proceedings of the 37th International Conference on Machine Learning, Proceedings of Machine Learning Research. ed. by A. Singh vol. 119, pp. 8459–8468. PMLR (2020). https://proceedings.mlr.press/v119/sanchez-gonzalez20a.html

D. Kochkov, J.A. Smith, A. Alieva, Q. Wang, M.P. Brenner, S. Hoyer, Machine learning-accelerated computational fluid dynamic. Proc. Natl. Acad. Sci. (2021). https://doi.org/10.1073/pnas.2101784118

R. Fang, D. Sondak, P. Protopapas, S. Succi, Deep learning for turbulent channel flow. arXiv (2018). arxiv:1812.02241

S. Pandey, P. Teutsch, P. Mäder, J. Schumacher, Direct data-driven forecast of local turbulent heat flux in Rayleigh–Bénard convection. Phys. Fluids 34(4), 045106 (2022). https://doi.org/10.1063/5.0087977

S.J. Kimmel, J.A. Domaradzki, Large eddy simulations of Rayleigh–Bénard convection using subgrid scale estimation model. Phys. Fluids 12(1), 169–184 (2000). https://doi.org/10.1063/1.870292

F. Dabbagh, F.X. Trias, A. Gorobets, A. Oliva, New subgrid-scale models for large-eddy simulation of Rayleigh–Bénard convection. J. Phys.: Conf. Ser. 745(3), 032041 (2016). https://doi.org/10.1088/1742-6596/745/3/032041

A. Sergent, P. Joubert, P. Le Quéré, Large eddy simulation of turbulent thermal convection using a mixed scale diffusivity model. Prog. Comput. Fluid Dyn. Int. J. 6, 40–49 (2006). https://doi.org/10.1504/PCFD.2006.009481

R. Ostilla-Monico, Y. Yang, E.P. van der Poel, D. Lohse, R. Verzicco, A multiple-resolution strategy for direct numerical simulation of scalar turbulence. J. Comput. Phys. 301, 308–321 (2015). https://doi.org/10.1016/j.jcp.2015.08.031

G. Grötzbach, Spatial resolution requirements for direct numerical simulation of the Rayleigh–Bénard convection. J. Comput. Phys. 49(2), 241–264 (1983). https://doi.org/10.1016/0021-9991(83)90125-0

R.J.A.M. Stevens, R. Verzicco, D. Lohse, Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495–507 (2010). https://doi.org/10.1017/S0022112009992461

M. Plumley, K. Julien, Scaling laws in Rayleigh–Bénard convection. Earth Space Sci. 6(9), 1580–1592 (2019). https://doi.org/10.1029/2019EA000583

K.P. Iyer, J.D. Scheel, J. Schumacher, K.R. Sreenivasan, Classical 1/3 scaling of convection holds up to ra = 10¹⁵. Proc. Natl. Acad. Sci. 117(14), 7594–7598 (2020). https://doi.org/10.1073/pnas.1922794117

E.P. van der Poel, R. Ostilla-Mónico, R. Verzicco, D. Lohse, Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh–Bénard convection. Phys. Rev. E 90, 013017 (2014). https://doi.org/10.1103/PhysRevE.90.013017

R. Verzicco, R. Camussi, Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19–49 (2003). https://doi.org/10.1017/S0022112002003063

Q. Wang, K.L. Chong, R.J.A.M. Stevens, R. Verzicco, D. Lohse, From zonal flow to convection rolls in Rayleigh–Bénard convection with free-slip plates. J. Fluid Mech. 905, 21 (2020). https://doi.org/10.1017/jfm.2020.793

E.P. van der Poel, R.J.A.M. Stevens, K. Sugiyama, D. Lohse, Flow states in two-dimensional Rayleigh–Bénard convection as a function of aspect-ratio and Rayleigh number. Phys. Fluids 24(8), 085104 (2012). https://doi.org/10.1063/1.4744988

Q. Wang, R. Verzicco, D. Lohse, O. Shishkina, Multiple states in turbulent large-aspect-ratio thermal convection: what determines the number of convection rolls? Phys. Rev. Lett. 125, 074501 (2020). https://doi.org/10.1103/PhysRevLett.125.074501

E.P. van der Poel, R.J.A.M. Stevens, D. Lohse, Comparison between two- and three-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 736, 177–194 (2013). https://doi.org/10.1017/jfm.2013.488

J. Bradbury, R. Frostig, P. Hawkins, M.J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, Q. Zhang, JAX: Composable Transformations of Python+NumPy programs. http://github.com/google/jax

R.E. Lynch, J.R. Rice, D.H. Thomas, Direct solution of partial difference equations by tensor product methods. Numerische Mathematik 6, 185–199 (1964)

H.J. Bae, A. Lozano-Duran, Towards exact subgrid-scale models for explicitly filtered large-eddy simulation of wall-bounded flows 2017.

J.A. Langford, R.D. Moser, Breakdown of continuity in large-eddy simulation. Phys. Fluids 13(5), 1524–1527 (2001). https://doi.org/10.1063/1.1358876

A. Beck, D. Flad, C.-D. Munz, Deep neural networks for data-driven les closure models. J. Comput. Phys. 398, 108910 (2019). https://doi.org/10.1016/j.jcp.2019.108910

E.A. Spiegel, A generalization of the mixing-length theory of turbulent convection. Astrophys J 138, 216 (1963)

M.E. Levine, A.M. Stuart, A Framework for Machine Learning of Model Error in Dynamical Systems. arXiv (2021). arXiv:2107.06658

N. Foroozani, J.J. Niemela, V. Armenio, K.R. Sreenivasan, Reorientations of the large-scale flow in turbulent convection in a cube. Phys. Rev. E 95, 033107 (2017). https://doi.org/10.1103/PhysRevE.95.033107

T.M. Eidson, Numerical simulation of the turbulent Rayleigh–Bénard problem using subgrid modelling. J. Fluid Mech. 158, 245–268 (1985). https://doi.org/10.1017/S0022112085002634

S.J. Kimmel, J.A. Domaradzki, Large eddy simulations of Rayleigh–Bénard convection using subgrid scale estimation model. Phys. Fluids 12(1), 169–184 (2000). https://doi.org/10.1063/1.870292

J. Lee, H. Choi, N. Park, Dynamic global model for large eddy simulation of transient flow. Phys. Fluids 22(7), 075106 (2010). https://doi.org/10.1063/1.3459156