Résumés > Tonioni Niccolo'

ABSTRACT 

Turbulent flows, a longstanding challenge in classical physics, are characterized by their nonlinear, multi-scale, and chaotic behavior. While the Navier-Stokes equations, coupled with the thermodynamic equation for the fluid state, provide a comprehensive mathematical foundation, solving them numerically remains computationally expensive. This poses a challenge for iterative applications, such as closed-loop control or design optimization, which require surrogate models for faster simulations. In this paper, reduced-order models (ROMs) are explored as a promising solution. ROMs are techniques designed to capture the essential dynamics of turbulent flows at a significantly reduced computational cost by identifying and exploiting features inherent in the flow field [1]. Two main classes of ROMs can be defined: projection-based methods and operator-based methods. Projection-based models, while effective, are inherently intrusive, as they require the application of basis expansions and projections onto the full-order model's operators. In contrast, operator-based ROMs offer non-intrusive alternatives but depend on prior knowledge of the ROM structure. To address the limitations of both approaches, this work explores the potential of neural compression algorithms, i.e. the application of neural networks for unsupervised feature extraction to compress data into lower-dimensional representations.

Recent studies by Fukami et al. [2], Agostini [3], Eivazi et al. [4] and Solera-Rico et al. [5] have demonstrated the superior performance of convolutional neural network-based standard autoencoders (AE) and variational auto encoders (VAE) over traditional projection-based methods, such as Proper Orthogonal Decomposition (POD). However, further research is needed to evaluate the performance of these methods on experimental datasets characterized by diverse flow regimes and to improve the interpretability of the transformations learned by these methods. As a proof of concept, this study examines the flow developing around a one degree-of-freedom elastically-mounted cylinder experiencing vortex-induced vibrations [6]. The dataset consists of time-resolved, two-component velocity snapshots obtained experimentally by Particle Image Velocimetry for different Reynolds numbers, ranging from 6000 to 16000, based on the cylinder diameter and the free-stream velocity , in the wake of the oscillating cylinder. This work makes several contributions: (i) it assesses the performance of both AE and VAE compared to POD in reconstructing unseen flow regimes; (ii) it develops a single model capable of representing all Reynolds numbers in the dataset with just three variables; and (iii) it proposes novel techniques to analyze and exploit the mapping learned by the neural network.

REFERENCES 

[1] P. J. Schmid, Chapter Six - Data-driven and operator-based tools for the analysis of turbulent flows, Editor(s): Paul Durbin, Advanced Approaches in Turbulence, Elsevier, Pages 243-305, ISBN 9780128207741, 2021.

[2] K. Fukami, T. Nakamura, and K. Fukagata, Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data, Physics of Fluids 32, 2020.

[3] L. Agostini, Exploration and prediction of fluid dynamical systems using auto-encoder technology, Physics of Fluids 32, 2020.

[4] H. Eivazi, S. Le Clainche, S. Hoyas, and R. Vinuesa, Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows, Expert Systems with Applications 202, 117038, 2022.

[5] A. Solera-Rico, C. Sanmiguel Vila, M. Gómez-López, Y. Wang, A. Almashjary, S. T. Dawson, and R. Vinuesa, β-variational autoencoders and transformers for reduced-order modelling of fluid flows, Nature Communications 15, 1361, 2024.

[6] A. Schmider, F. Kerhervé, A. Spohn, & L. Cordier. Improved VIV energy harvesting with a virtual damper–spring system. Ocean Engineering, 293, 116668, 2024. 

[7] L. McInnes, J. Healy, UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction, ArXiv e-prints 1802.03426, 2018.