Turbulent injection assisted by diffusion models for scale-resolving simulations

Diffusion model; Direct-numerical-simulation; Energy spectrum; Flow problems; Homogeneous isotropic turbulence; Large-eddy simulations; Length scale; Memory efficient; Turbulent inflow conditions; Turbulent kinetic energy; Computational Mechanics; Condensed Matter Physics; Mechanics of Materials; Mechanical Engineering; Fluid Flow and Transfer Processes; Physics - Fluid Dynamics

Abstract :

[en] The present research proposes a new memory-efficient method using diffusion models to inject turbulent inflow conditions into large eddy simulation and direct numerical simulation for various flow problems. A guided diffusion model was trained on decaying homogeneous isotropic turbulence samples, characterized by different turbulent kinetic energy levels and integral length scales. Samples generated by the diffusion model accurately reproduce turbulence statistics, such as the energy spectrum and the two-point autocorrelation functions, while preserving the ability to generate instantaneous three-dimensional velocity fields with detailed fluctuations. Physical representativeness is also evaluated by injecting the synthetic samples into a free domain (i.e., without any wall boundary) through an inlet boundary condition. The method demonstrates promising results regarding energy spectrum, spatial correlation, turbulent kinetic energy level, and integral length scales without increasing the development distance as compared to a library-based method.

Disciplines :

Physics

Author, co-author :

Boxho, Margaux ; Département HiFi CFD & CAA, Cenaero, Charleroi, Belgium

Dominique, Joachim ; Département HiFi CFD & CAA, Cenaero, Charleroi, Belgium

Benamara, T. ; Département HiFi CFD & CAA, Cenaero, Charleroi, Belgium

Rasquin, Michel ; Département HiFi CFD & CAA, Cenaero, Charleroi, Belgium

Salesses, Lionel ; Département HiFi CFD & CAA, Cenaero, Charleroi, Belgium

Sainvitu, Caroline ; Département HiFi CFD & CAA, Cenaero, Charleroi, Belgium

Louppe, Gilles ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Big Data

Toulorge, Thomas ; Département HiFi CFD & CAA, Cenaero, Charleroi, Belgium

Language :

English

Title :

Turbulent injection assisted by diffusion models for scale-resolving simulations

Publication date :

August 2025

Journal title :

Physics of Fluids

ISSN :

1070-6631

eISSN :

1089-7666

Publisher :

American Institute of Physics

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/5.0278541/20643021/085169_1_5.0278541.pdf

Funders :

SPW - Service Public de Wallonie

Funding text :

The ARIAC Project (No. 2010235) funded by the Service Public de Wallonie (SPW Recherche) is gratefully acknowledged for funding this research. The present research benefited from computational resources made available on Lucia, the Tier-1 supercomputer of the Walloon Region, infrastructure funded by the Walloon Region under the Grant Agreement No. 910247.

Commentary :

The following article has been submitted to/accepted by Physics of Fluid (AIP Publishing LLC). After publication, it will be available https://doi.org/10.1063/5.0278541

Available on ORBi :

since 29 January 2026

Statistics

Number of views

6 (0 by ULiège)

Number of downloads

10 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

J. S. Carullo, S. Nasir, R. D. Cress, W. F. Ng, K. A. Thole, L. J. Zhang, and H. K. Moon, “ The effects of freestream turbulence, turbulence length scale, and exit Reynolds number on turbine blade heat transfer in a transonic cascade,” J. Turbomach. 133, 011030 ( 2011). 10.1115/1.4001366
A. Sengupta, N. Gupta, and B. N. Ubald, “ Separation-induced transition on a T106A blade under low and elevated free stream turbulence,” Phys. Fluids 36, 026119 ( 2024). 10.1063/5.0189358
N. S. Dhamankar, G. A. Blaisde, and A. S. Lyrintzis, “ A overview of turbulent inflow boundary conditions for large eddy simulations,” in 22nd AIAA Computational Fluid Dynamics Conference, AIAA Paper No. AIAA 2015-3213, 2015.
P. Schlatter and R. Örlü, “ Turbulent boundary layers at moderate Reynolds numbers: Inflow length and tripping effects,” J. Fluid Mech. 710, 5- 34 ( 2012). 10.1017/jfm.2012.324
F. Picella, M. A. Bucci, S. Cherubini, and J.-C. Robinet, “ A synthetic forcing to trigger laminar-turbulent transition in parallel wall bounded flows via receptivity,” J. Comput. Phys. 393, 92- 116 ( 2019). 10.1016/j.jcp.2019.04.011
A. Ceci, A. Palumbo, J. Larsson, and S. Pirozzoli, “ Numerical tripping of high-speed turbulent boundary layers,” Theor. Comput. Fluid Dyn. 36, 865 ( 2022). 10.1007/s00162-022-00623-0.
C. Martha, “ Toward high-fidelity subsonic jet noise prediction using petascale supercomputers,” Ph.D. thesis ( Purdue University, West Lafayette, IN, 2012).
T. S. Lund, X. Wu, and K. D. Squires, “ Generation of inflow data for spatially-developing boundary layer simulations,” J. Comput. Phys. 140, 233- 258 ( 1998). 10.1006/jcph.1998.5882
X. Wu, “ Inflow turbulence generation methods,” Annu. Rev. Fluid Mech. 49, 23- 49 ( 2017). 10.1146/annurev-fluid-010816-060322
S. Xu and M. P. Martin, “ Assessment of inflow boundary conditions for compressible turbulent boundary layers,” Phys. Fluids 16, 2623- 2639 ( 2004). 10.1063/1.1758218
S. Lee, S. K. Lele, and P. Moin, “ Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow,” Phys. Fluids 4, 1521- 1530 ( 1992). 10.1063/1.858425
A. Smirnov, S. Shi, and I. Celik, “ Random flow generation technique for large eddy simulation and particle-dynamics modeling,” J. Fluids Eng. 123, 359- 371 ( 2001). 10.1115/1.1369598
P. Batten, U. Goldberg, and S. Chakravarthy, “ Interfacing statistical turbulence closures with large-eddy simulation,” AIAA J. 42, 485- 492 ( 2004). 10.2514/1.3496
L. Davidson and M. Billson, “ Hybrid LES-RANS using synthesized turbulent fluctuations for forcing in the interface region,” Int. J. Heat Fluid Flow 27, 1028- 1042 ( 2006). 10.1016/j.ijheatfluidflow.2006.02.025
L. Davidson, “ Hybrid LES-RANS: Inlet boundary conditions for flows with recirculation,” in Advances in Hybrid RANS-LES Modelling ( Springer, Berlin, Heidelberg, 2008), pp. 55- 66.
P. Druault, E. Lamballais, J. Delville, and J.-P. Bonnet, “ Development of experiment/simulation interfaces for hybrid turbulent results analysis via the use of DNS,” in First Symposium on Turbulence and Shear Flow Phenomena ( Begell House, 1999), pp. 779- 784.
G. Berkooz, P. Holmes, and J. Lumley, “ The proper orthogonal decomposition in the analysis of turbulent flows,” Annu. Rev. Fluid Mech. 25, 539- 575 ( 1993). 10.1146/annurev.fl.25.010193.002543
M. Klein, A. Sadiki, and J. Janicka, “ A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations,” J. Comput. Phys. 186, 652- 665 ( 2003). 10.1016/S0021-9991(03)00090-1
L. di Mare, M. Klein, W. P. Jones, and J. Janicka, “ Synthetic turbulence inflow conditions for large-eddy simulation,” Phys. Fluids 18, 025107 ( 2006). 10.1063/1.2130744
J. Hoepffner, Y. Naka, and K. Fukagata, “ Realizing turbulent statistics,” J. Fluid Mech. 676, 54- 80 ( 2011). 10.1017/jfm.2011.32
N. S. Dhamankar, G. A. Blaisdell, and A. S. Lyrintzis, “ Overview of turbulent inflow boundary conditions for large-eddy simulations,” AIAA J. 56, 1317- 1334 ( 2018). 10.2514/1.J055528
N. C. W. Treleaven, M. Staufer, A. Spencer, A. Garmory, and G. J. Page, “ Application of the PODFS method to inlet turbulence generated using the digital filter technique,” J. Comput. Phys. 415, 109541 ( 2020). 10.1016/j.jcp.2020.109541
M. Hao, J. Hope-Collins, and L. di Mare, “ Generation of turbulent inflow data from realistic approximations of the covariance tensor,” Phys. Fluids 34, 115140 ( 2022). 10.1063/5.0106664
Y. Dreze, M. Hao, and L. di Mare, “ Divergence-free turbulent inflow data from realistic covariance tensor,” Phys. Fluids 35, 025120 ( 2023). 10.1063/5.0136568
S. Schmidt and M. Breuer, “ Source term based synthetic turbulence inflow generator for eddy-resolving predictions of an airfoil flow including a laminar separation bubble,” Comput. Fluids 146, 1- 22 ( 2017). 10.1016/j.compfluid.2016.12.023
E. Sergent, “ Vers une méthodologie de couplage entre la simulation des Grandes Échelles et les modèles statistiques,” Ph.D. thesis (Ecole Centrale de Lyon, 2002).
N. Jarrin, S. Benhamadouche, D. Laurence, and R. Prosser, “ A synthetic-eddy-method for generating inflow conditions for large-eddy simulations,” Int. J. Heat Fluid Flow 27, 585- 593 ( 2006). 10.1016/j.ijheatfluidflow.2006.02.006
M. Pamiès, P.-E. Weiss, E. Garnier, S. Deck, and P. Sagaut, “ Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows,” Phys. Fluids 21, 045103 ( 2009). 10.1063/1.3103881
B. Xie, F. Gao, J. Boudet, L. Shao, and L. Lu, “ Improved vortex method for large-eddy simulation inflow generation,” Comput. Fluids 168, 87- 100 ( 2018). 10.1016/j.compfluid.2018.03.069
D. Muñoz-Esparza, B. Kosović, J. van Beeck, and J. Mirocha, “ Erratum: ‘A stochastic perturbation method to generate inflow turbulence in large-eddy simulation models: Application to neutrally stratified atmospheric boundary layers,’ ” Phys. Fluids 27, 039901 ( 2015). 10.1063/1.4913572
R. DeLeon, C. Umphrey, and I. Senocak, “ Turbulent inflow generation through buoyancy perturbations with colored noise,” AIAA J. 57, 532 ( 2019). 10.2514/1.J057245.
A. Keating and U. Piomelli, “ A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation,” J. Turbul. 7, N12 ( 2006). 10.1080/14685240612331392460
M. Rasquin, T. Toulorge, M. Bechlars, and K. Hillewaert, “ Direct numerical simulations of airfoil cascades for the improvement of turbulence models through database generation,” in 15th European Conference on Turbomachinery Fluid Dynamics & Thermodynamics, 2023.
A. Keating, U. Piomelli, E. Balaras, and H.-J. Kaltenbach, “ A priori and a posteriori tests of inflow conditions for large-eddy simulation,” Phys. Fluids 16, 4696- 4712 ( 2004). 10.1063/1.1811672
J. Ho, A. Jain, and P. Abbeel, “ Denoising diffusion probabilistic models,” in Proceedings of the 34th International Conference on Neural Information Processing Systems (NIPS'20) ( Curran Associates Inc., Red Hook, NY, 2020).
Z. Xiao, K. Kreis, and A. Vahdat, “ Tackling the generative learning trilemma with denoising diffusion GANs,” arXiv:2112.07804 ( 2021).
P. Dhariwal and A. Nichol, “ Diffusion models beat GANs on image synthesis,” in Proceedings of the 35th International Conference on Neural Information Processing Systems (NIPS'21) ( Curran Associates Inc., Red Hook, NY, 2024).
Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, “ Score-based generative modeling through stochastic differential equations,” in International Conference on Learning Representations, 2021.
Q. Zhang and Y. Chen, “ Fast sampling of diffusion models with exponential integrator,” in The Eleventh International Conference on Learning Representations, 2023.
K. Fukami, Y. Nabae, K. Kawai, and K. Fukagata, “ Synthetic turbulent inflow generator using machine learning,” Phys. Rev. Fluids 4, 064603 ( 2019). 10.1103/PhysRevFluids.4.064603
J. Kim and C. Lee, “ Deep unsupervised learning of turbulence for inflow generation at various Reynolds numbers,” J. Comput. Phys. 406, 109216 ( 2020). 10.1016/j.jcp.2019.109216
T. N. Kanishk, P. Tyagi, and R. K. Singh, “ Generation and parameterization of forced isotropic turbulent flow using autoencoders and generative adversarial networks,” in ASME International Mechanical Engineering Congress and Exposition ( American Society of Mechanical Engineers, 2021).
M. Z. G. Yousif, M.-T. Zhang, L. Yu, R. Vinuesa, and H. Lim, “ A transformer-based synthetic-inflow generator for spatially developing turbulent boundary layers,” arXiv:2206.01618 ( 2022).
X.-Y. Liu, M. H. Parikh, X. Fan, P. Du, Q. Wang, Y.-F. Chen, and J.-X. Wang, “ CoNFiLD-inlet: Synthetic turbulence inflow using generative latent diffusion models with neural fields,” arXiv:2411.14378 ( 2024).
T. Asaka, K. Yoshimatsu, and K. Schneider, “ Machine learning-based vorticity evolution and super-resolution of homogeneous isotropic turbulence using wavelet projection,” Phys. Fluids 36, 025120 ( 2024). 10.1063/5.0185165
M. Lienen, D. Lüdke, J. Hansen-Palmus, and S. Günnemann, “ From zero to turbulence: Generative modeling for 3D flow simulation,” in The Twelfth International Conference on Learning Representations, 2024.
A. Saydemir, M. Lienen, and S. Günnemann, “ Unfolding time: Generative modeling for turbulent flows in 4D,” arXiv:2406.11390v2 ( 2024).
K. Hillewaert, “ Development of the discontinuous Galerkin method for high-resolution, large scale CFD and acoustics in industrial geometries,” Ph.D. thesis ( Ecole Polytechnique de Louvain/iMMC, 2013).
C. Carton de Wiart, K. Hillewaert, L. Bricteux, and G. Winckelmans, “ Implicit LES of free and wall bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method,” Int. J. Numer. Methods Fluids 78, 335- 354 ( 2015). 10.1002/fld.4021
R. I. Loehrke and H. M. Nagib, “ Control of free-stream turbulence by means of honeycombs: A balance between suppression and generation,” J. Fluids Eng. 98, 342 ( 1976). 10.1115/1.3448313
É. Salze, A. Pereira, P. Souchotte, J. Regnard, F. Gea-Aguilera, and M. Gruber, “ New modular fan rig for advanced aeroacoustic tests: Acoustic characterization of the facility,” in 25th AIAA/CEAS Aeroacoustics Conference, AIAA Paper No. AIAA 2019-2603, 2019.
J. Grondin, M. Leborgne, L. Baert, I. Lepot, A. Gouttière, D. Dieu, D. Wunsch, E. Boufidi, M. Madasseri Payyappalli, F. Fontaneto et al., “ Coupled design of multi-component distortion-generating devices for aircraft engine ground tests—Part I: Design methodology and numerical validation,” in ASME Turbo Expo: Turbomachinery Technical Conference and Exposition ( American Society of Mechanical Engineers, 2024).
F. Czwielong and S. Becker, “ Active turbulence grid-controlled inflow turbulence and replication of heat exchanger flow fields in fan applications,” Int. J. Turbomach. Propul. Power 8, 1 ( 2023). 10.3390/ijtpp8010001
R. Ranjan, S. M. Deshpande, and R. Narasimha, “ A high-resolution compressible DNS study of flow past a low pressure gas turbine blade,” in Advances in Computation, Modeling and Control of Transitional and Turbulent Flows ( World Scientific, 2015), pp. 291- 301.
S. B. Pope, Turbulent Flows ( Cambridge University Press, 2000).
T. Passot and A. Pouquet, “ Numerical simulation of compressible homogeneous flows in the turbulent regime,” J. Fluid Mech. 181, 441- 466 ( 1987). 10.1017/S0022112087002167
R. S. Rogallo, “ Numerical experiments in homogeneous turbulence,” Technical Memorandum Report No. NASA-TM-81315 ( NASA Ames, 1981).
L. F. Richardson, Weather Prediction by Numerical Process, 2nd ed., Cambridge Mathematical Library ( Cambridge University Press, 2007).
A. N. Kolmogorov, “ The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9- 13 ( 1991). 10.1098/rspa.1991.0075
S. Banerjee, R. Krahl, F. Durst, and C. Zenger, “ Presentation of anisotropy properties of turbulence, invariants versus eigenvalue approaches,” J. Turbul. 8, N32 ( 2007). 10.1080/14685240701506896
J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, and S. Ganguli, “ Deep unsupervised learning using nonequilibrium thermodynamics,” in Proceedings of the 32nd International Conference on Machine Learning, Proceedings of Machine Learning Research, edited by F. Bach and D. Blei ( PMLR, Lille, France, 2015), Vol. 37, pp. 2256- 2265.
T. Karras, M. Aittala, S. Laine, and T. Aila, “ Elucidating the design space of diffusion-based generative models,” in Proceedings of the 36th International Conference on Neural Information Processing Systems (NIPS'22) ( Curran Associates Inc., Red Hook, NY, 2022).
F. Rozet and G. Louppe, “ Score-based data assimilation,” in Thirty-Seventh Conference on Neural Information Processing Systems, 2023.
Y. Song and S. Ermon, “ Generative modeling by estimating gradients of the data distribution,” in Proceedings of the 33rd International Conference on Neural Information Processing Systems ( Curran Associates Inc., Red Hook, NY, 2019).
J. Song, C. Meng, and S. Ermon, “ Denoising diffusion implicit models,” in International Conference on Learning Representations, 2021.
Y. Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le, “ Flow matching for generative modeling,” in The Eleventh International Conference on Learning Representations, 2023.
F. Rozet, G. Andry, F. Lanusse, and G. Louppe, “ Learning diffusion priors from observations by expectation maximization,” in Proceedings of the 38th International Conference on Neural Information Processing Systems, (NIPS'24), 2024.
F. Rozet, see https://github.com/francois-rozet/sda/tree/master/sda for “ Sda” ( 2023).
F. Rozet, see https://github.com/probabilists/azula for “ Azula” ( 2025).
P. K.-M. Huang, S.-A. Chen, and H.-T. Lin, “ Score-based conditional generation with fewer labeled data by self-calibrating classifier guidance,” in The Twelfth International Conference on Learning Representations, (ICLR, 2024).
J. Ho and T. Salimans, “ Classifier-free diffusion guidance,” arXiv:2207.12598 ( 2022).
Z. Xiong, S. Nagarajan, and S. K. Lele, “ Simple method for generating inflow turbulence,” AIAA J. 42, 2164- 2166 ( 2012). 10.2514/1.6157
D. Papadogiannis, S. Mouriaux, J.-S. Cagnone, K. Hillewaert, F. Duchaine, and S. Hiernaux, “ Influence of the numerical strategy on wall-resolved LES of a compressor cascade,” in Proceedings of the 13th European Conference on Turbomachinery, Fluid Dynamics and Thermodynamics (ETC13), 2019.