Model Reduction for Transport-Dominated Problems via Cross-Correlation Based Snapshot Registration
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912412410576896 |
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| author | Gowrachari, Harshith Stabile, Giovanni Rozza, Gianluigi |
| author_facet | Gowrachari, Harshith Stabile, Giovanni Rozza, Gianluigi |
| contents | Traditional linear approximation methods, such as proper orthogonal decomposition and the reduced basis method, are ill-suited for transport-dominated problems due to the slow decay of the Kolmogorov $n$-width, leading to inefficient and inaccurate reduced-order models. In this work, we propose a model reduction approach for transport-dominated problems by employing cross-correlation based snapshot registration to accelerate the Kolmogorov $n$-width decay, thereby enabling the construction of efficient and accurate reduced-order models using linear approximation methods. We propose a complete framework comprising offline-online stages for the development of reduced order models using the cross-correlation based snapshots registration. The effectiveness of the proposed approach is demonstrated using two test cases: 1D travelling waves and the higher-order methods benchmark test case, 2D isentropic convective vortex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Model Reduction for Transport-Dominated Problems via Cross-Correlation Based Snapshot Registration Gowrachari, Harshith Stabile, Giovanni Rozza, Gianluigi Numerical Analysis Traditional linear approximation methods, such as proper orthogonal decomposition and the reduced basis method, are ill-suited for transport-dominated problems due to the slow decay of the Kolmogorov $n$-width, leading to inefficient and inaccurate reduced-order models. In this work, we propose a model reduction approach for transport-dominated problems by employing cross-correlation based snapshot registration to accelerate the Kolmogorov $n$-width decay, thereby enabling the construction of efficient and accurate reduced-order models using linear approximation methods. We propose a complete framework comprising offline-online stages for the development of reduced order models using the cross-correlation based snapshots registration. The effectiveness of the proposed approach is demonstrated using two test cases: 1D travelling waves and the higher-order methods benchmark test case, 2D isentropic convective vortex. |
| title | Model Reduction for Transport-Dominated Problems via Cross-Correlation Based Snapshot Registration |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.01299 |