Structure preserving model order reduction of shallow water equations
Yazarlar (3)
Bülent Karasözen
Middle East Technical University (Metu), Türkiye
Middle East Technical University (Metu), Türkiye
Doç. Dr. Süleyman Yıldız Middle East Technical University (Metu), Türkiye
Prof. Dr. Murat UZUNCA Sinop Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Mathematical Methods in the Applied Sciences (Q1) | ||
| Dergi ISSN | 0170-4214 Dergi Bilgileri (2021) | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2021 |
| Cilt / Sayı / Sayfa | 44 / 1 / 476–492 | DOI | 10.1002/mma.6751 |
| Makale Linki | https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.6751 | ||
| UAK Araştırma Alanları |
Uygulamalı Matematik
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| Özet |
| In this paper, we present two different approaches for constructing reduced‐order models (ROMs) for the two‐dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After integration in time by the fully implicit average vector field method, ROMs are constructed with proper orthogonal decomposition(POD)/discrete empirical interpolation method that preserves the Hamiltonian structure. In the second approach, the SWE as a partial differential equation with quadratic nonlinearity is integrated in time by the linearly implicit Kahan's method, and ROMs are constructed with the tensorial POD that preserves the linear‐quadratic structure of the SWE. We show that in both approaches, the invariants of the SWE such as the energy, enstrophy, mass and circulation are preserved over a long period of time, leading to stable solutions. We conclude by … |
| Anahtar Kelimeler |
| discrete empirical interpolation | finite-difference methods | linearly implicit methods | preservation of invariants | proper orthogonal decomposition | tensorial proper orthogonal decomposition |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Web of Science | 13 |
| Scopus | 14 |
| Google Scholar | 28 |