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arXiv · 2410.02948

Elastoinertial turbulence: Data-driven reduced-order model based on manifold dynamics

Manish Kumar·C. Ricardo Constante-Amores·Michael D. Graham
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Abstract

Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensive due to the need to resolve the multi-scale nature of the system. While DNS of 2D EIT typically requires $O(10^6)$ degrees of freedom, we demonstrate here that a data-driven modeling framework allows for the construction of an accurate model with 50 degrees of freedom. We achieve a low-dimensional representation of the full state by first applying a viscoelastic variant of proper orthogonal decomposition to DNS results, and then using an autoencoder. The dynamics of this low-dimensional representation are learned using the neural ODE method, which approximates the vector field for the reduced dynamics as a neural network. The resulting low-dimensional data-driven model effectively captures short-time dynamics over the span of one correlation time, as well as long-time dynamics, particularly the self-similar, nested traveling wave structure of 2D EIT in the parameter range considered.

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Manish Kumar, C. Ricardo Constante-Amores, Michael D. Graham. 2024-10-03. Elastoinertial turbulence: Data-driven reduced-order model based on manifold dynamics. https://doi.org/10.1017/jfm.2025.130

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