Elastoinertial turbulence: Data-driven reduced-order model based on manifold dynamics
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| Format: | Preprint |
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2024
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| _version_ | 1866908273385406464 |
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| author | Kumar, Manish Constante-Amores, C. Ricardo Graham, Michael D. |
| author_facet | Kumar, Manish Constante-Amores, C. Ricardo Graham, Michael D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02948 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elastoinertial turbulence: Data-driven reduced-order model based on manifold dynamics Kumar, Manish Constante-Amores, C. Ricardo Graham, Michael D. Fluid Dynamics 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. |
| title | Elastoinertial turbulence: Data-driven reduced-order model based on manifold dynamics |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2410.02948 |