vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университет10.23947/2587-8999-2018-2-1-1-8vmait-63Research ArticleСтатьиВариационная ассимиляция данных о температуре для модели гидротермодинамики Балтийского моря: решение проблемы открытых границVariational assimilation of temperature for the model of hydrodynamics of the Baltic Sea: the solution of the open boundary problemhttps://orcid.org/0000-0001-9055-1655АгошковВалерий ИвановичAgoshkovValery Ivanovich

Агошков Валерий Иванович, главный научный сотрудник Института вычислительной математики им. Г.И. Марчука РАН (119333, г. Москва, ул. Губкина, 8), профессор Московского государственного университета имени М. В. Ломоносова (119991, г. Москва, Ленинские горы, д. 1), профессор, доктор физико-математических наук, заслуженный деятель науки Российской Федерации

Agoshkov Valery Ivanovich, Principal Researcher of the Institute of Numerical Mathematics of the Russian Academy of Sciences (Gubkin St. 8, Moscow, Russian Federation), Professor of the Lomonosov Moscow State University (Leninskie Gory 1, Moscow, Russian Federation), Professor, Doctor of Sciences in Physics and Mathematics, Honored Scientist of the Russian Federation.

agoshkov@inm.ras.ruhttps://orcid.org/0000-0003-1340-8083ШелопутТатьяна ОлеговнаSheloputTatiana Olegovna

Шелопут Татьяна Олеговна, аспирант Института вычислительной математики им. Г.И. Марчука РАН (119333, г. Москва, ул. Губкина, 8)

Sheloput Tatiana Olegovna, graduate student of the Institute of Numerical Mathematics of the Russian Academy of Sciences (Gubkin St. 8, Moscow, Russian Federation)

sheloput@phystech.eduИВМ РАН (119333, г. Москва, ул. Губкина, 8) Московский государственный университет имени М. В. Ломоносова (119991, г. Москва, Ленинские горы, д. 1)РоссияInstitute of Numerical Mathematics of the Russian Academy of Sciences (Gubkin St. 8, Moscow, Russian Federation) Lomonosov Moscow State University (Leninskie Gory 1, Moscow, Russian Federation)Russian FederationИнститут вычислительной математики им. Г.И. Марчука РАН (119333, г. Москва, ул. Губкина, 8)РоссияInstitute of Numerical Mathematics of the Russian Academy of Sciences (Gubkin St. 8, Moscow, Russian Federation)Russian Federation2018280320232163Copyright © Агошков В.И., Шелопут Т.О., 20232023Агошков В.И., Шелопут Т.О.Agoshkov V.I., Sheloput T.O.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/63

В данной работе рассматривается задача моделирования акваторий с «жидкими» (открытыми) границами. Используется математическая модель циркуляции Балтийского моря, разработанная в ИВМ РАН. Модель основана на системе уравнений термогидродинамики в приближении Буссинеска и гидростатики. Для аппроксимации по времени используется метод расщепления. Для восстановления неизвестных функций в граничных условиях на открытых границах исследуется и решается задача ассимиляции температуры (солености). Для ускорения процедуры ассимиляции используется метод разделения областей.

The problem of modeling water areas with «liquid» (open) lateral boundaries is discussed. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermohydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method is used for time approximation in the model. Temperature (salinity) assimilation problem is investigated and solved for reconstructing unknown functions in boundary conditions at open boundaries. The domain decomposition method was used for acceleration of the assimilation procedure.

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