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On convergence of numerical schemes when calculating Riemann problems for shallow water equations Научная публикация

Журнал Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304
Вых. Данные Год: 2024, Страницы: B171-B202 Страниц : 32 DOI: 10.33048/semi.2024.21.B10
Ключевые слова high-accuracy numerical schemes, Riemann problems for shallow water equations, local convergence of numerical solutions
Авторы Kovyrkina O.A. 1 , Ostapenko V.V. 1 , Polunina E.I 1
Организации
1 Lavrentyev Institute of Hydrodynamics of SB RAS, Lavrentyev Prospect, 15, 630090, Novosibirsk, Russia

Информация о финансировании (2)

1 Российский научный фонд 22-11-00060
2 Министерство науки и высшего образования Российской Федерации FWGG-2021-0001

Реферат: We investigate the convergence of four high order numerical schemes when calculating Riemann problems for shallow water equations. We compare a couple of the NFC (Nonlinear Flux Correction) schemes: the second order TVD (Total Variation Diminishing) and the fth-order in space, the third-order in time A-WENO (Alternative Weighted Essentially Non-Oscillatory) with a couple of the third-order QL (Quasi-Linear) schemes: RBM (Rusanov-Burstein-Mirin) and CWA (Compact high order Weak Approximation), where nonlinear flux correction is not applied. It is shown that inside the shock influence areas for the NFC schemes, unlike the QL schemes, there is no uniform local convergence of the numerical solution to the exact constant one. At the same time, inside the centered rarefaction waves, solutions of these schemes with different orders converge to the different invariants of the exact solution: with the first order to the invariant that transferred along the characteristics outgoing from the center of the rarefaction wave; and with the order not lower than the second to the invariant that is constant inside the rarefaction wave. For numerical solutions of the studied schemes we perform the classi cation of various types of convergence to the corresponding exact solutions of the calculated Riemann problems.
Библиографическая ссылка: Kovyrkina O.A. , Ostapenko V.V. , Polunina E.I.
On convergence of numerical schemes when calculating Riemann problems for shallow water equations
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2024. P.B171-B202. DOI: 10.33048/semi.2024.21.B10 WOS Scopus
Идентификаторы БД:
Web of science: WOS:001473642800010
Scopus: 2-s2.0-85216969577
Цитирование в БД: Пока нет цитирований
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