hydrophysicsФундаментальная и прикладная гидрофизикаFundamental and Applied Hydrophysics2073-66732782-5221St. Petersburg Research Center of the Russian Academy of Sciences10.59887/2073-6673.2025.18(4)-3DULUYAhydrophysics-1477Research ArticleФУНДАМЕНТАЛЬНЫЕ ВОПРОСЫ ГИДРОФИЗИКИFUNDAMENTAL ISSUES OF HYDROPHYSICSИспользование псевдоспектрального метода высокого порядка HOSM для моделирования нелинейных волн на поверхности воды конечной глубиныThe use of pseudo-spectral high order method HOSM for simulations of nonlinear waves on the surface of finite depth waterhttps://orcid.org/0000-0001-7782-2991СлюняевА. В.SlunyaevA. V.

Слюняев Алексей Викторович, доктор физико-математических наук, член-корреспондент РАН, заведующий сектором

WoS ResearcherID: A-3272-2014, Scopus Author ID: 55957049100 

603950, Нижний Новгород, ул. Ульянова, д. 46 

603155, Нижний Новгород, ул. Большая Печерская, д. 25/12 

WoS ResearcherID: A-3272-2014, Scopus Author ID: 55957049100

46 Ulyanova Str., Nizhny Novgorod 603950 

25/12 Str. Bolshaya Pecherskaya, Nizhny Novgorod, 603155 

slunyaev@ipfran.ruИнститут прикладной физики им. А.В. Гапонова-Грехова РАН ; Национальный исследовательский университет «Высшая школа экономики»РоссияA.V. Gaponov-Grekhov Institute of Applied Physics RAS ; HSE UniversityRussian Federation2025221220251842849Copyright © Слюняев А.В., 20252025Слюняев А.В.Slunyaev A.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://hydrophysics.spbrc.ru/jour/article/view/1477

Исследованы режимы и ограничения метода численного решения уравнений гидродинамики, использующего аппроксимацию приповерхностного потенциала скорости разложением Тейлора высокого порядка (High Order Spectral Method, HOSM). Этот подход рассматривается в контексте моделирования больших ансамблей полей смещения морской поверхности в условиях конечной глубины. Основное внимание уделено описанию сильно нелинейных волн и волн с широким частотным спектром. Исследование выполнено в планарной геометрии.

Regimes and limitations of the numerical solution method for hydrodynamic equations using the approximation of the near-surface velocity potential by the high-order Taylor expansion (High Order Spectral Method, HOSM) are investigated. This approach is considered in the context of simulation of large ensembles of sea surface displacement fields under finite-depth conditions. The main attention is paid to the description of strongly nonlinear waves and waves with a wide frequency spectrum. The study is performed in planar geometry.

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The authors declare that there are no conflicts of interest present.