Structure preserving model order reduction of shallow water equations

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dc.authoridKarasozen, Bulent/0000-0003-1037-5431
dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.contributor.authorKarasozen, Bulent
dc.contributor.authorYildiz, Suleyman
dc.contributor.authorUzunca, Murat
dc.date.accessioned2025-03-23T19:47:07Z
dc.date.available2025-03-23T19:47:07Z
dc.date.issued2021
dc.departmentSinop Üniversitesi
dc.description.abstractIn 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 demonstrating the accuracy and the computational efficiency of the reduced solutions by a numerical test problem.
dc.description.sponsorship100/2000 Ph.D. Scholarship Program
dc.description.sponsorship100/2000 Ph.D. Scholarship Program
dc.identifier.doi10.1002/mma.6751
dc.identifier.endpage492
dc.identifier.issn0170-4214
dc.identifier.issn1099-1476
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85088286076
dc.identifier.scopusqualityQ1
dc.identifier.startpage476
dc.identifier.urihttps://doi.org/10.1002/mma.6751
dc.identifier.urihttps://hdl.handle.net/11486/7289
dc.identifier.volume44
dc.identifier.wosWOS:000550679200001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherWiley
dc.relation.ispartofMathematical Methods in the Applied Sciences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectdiscrete empirical interpolation
dc.subjectfinite-difference methods
dc.subjectlinearly implicit methods
dc.subjectpreservation of invariants
dc.subjectproper orthogonal decomposition
dc.subjecttensorial proper orthogonal decomposition
dc.titleStructure preserving model order reduction of shallow water equations
dc.typeArticle

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