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Applying Richardson’s Extrapolation to Improve the Accuracy of Shock Capturing Combined Schemes Научная публикация

Журнал Mathematical Models and Computer Simulations
ISSN: 2070-0482
Вых. Данные Год: 2026, Том: 18, Номер: 4, Страницы: 538-546 Страниц : 9 DOI: 10.1134/s2070048226700249
Ключевые слова high accurate schemes, shallow water equations, Richardson’s extrapolation, combined schemes
Авторы Kovyrkina O.A. 1 , Kolotilov V.A. 1 , Ostapenko V.V. 1 , Khandeeva N.A. 1
Организации
1 Lavrentiev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Реферат: A numerical algorithm that employs Richardson’s extrapolation to improve the accuracy of combined schemes including the solution of Cauchy problems with discontinuous initial data for systems of hyperbolic differential equations is proposed. Richardson’s extrapolation is applied for a numerical solution obtained by the basic scheme included in the combined scheme in the regions where there are no noticeable nonphysical oscillations. Constraints on the absolute value of the numerical solution errors obtained by Richardson’s formula is used as a criterion for identifying the areas where the internal NFC (Nonlinear Flux Correction) scheme should be applied for smoothing out the oscillations arising in calculations by the basic QL (Quasi-Linear) scheme. The new numerical algorithm was tested on two Cauchy problems with discontinuous initial data for one-dimensional shallow water equations.
Библиографическая ссылка: Kovyrkina O.A. , Kolotilov V.A. , Ostapenko V.V. , Khandeeva N.A.
Applying Richardson’s Extrapolation to Improve the Accuracy of Shock Capturing Combined Schemes
Mathematical Models and Computer Simulations. 2026. V.18. N4. P.538-546. DOI: 10.1134/s2070048226700249 Scopus OpenAlex
Даты:
Поступила в редакцию: 7 окт. 2025 г.
Принята к публикации: 15 дек. 2025 г.
Опубликована в печати: 21 авг. 2026 г.
Идентификаторы БД:
≡ Scopus: 2-s2.0-105047862346
≡ OpenAlex: W7203862134
Альметрики: