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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 11, Pages 1763–1803
DOI: https://doi.org/10.31857/S0044466922100027 (Mi zvmmf11466) 		 
This article is cited in 5 scientific papers (total in 5 papers)

General numerical methods

Combined numerical schemes

M. D. Braginab, O. A. Kovyrkinac, M. E. Ladonkinaa, V. V. Ostapenkoc, V. F. Tishkina, N. A. Khandeevac

a Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), 141700, Dolgoprudnyi, Moscow oblast, Russia
c Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
Citations (5)
DOI: https://doi.org/10.31857/S0044466922100027
Abstract: A survey of works concerning high-order accurate numerical methods designed for shock-capturing computations of discontinuous solutions to hyperbolic systems of conservation laws is presented. The basic problems arising in the theory of such methods are formulated, and approaches to their solution are proposed. Primary attention is given to fundamentally new shock-capturing methods (known as combined schemes) that monotonically localize shock fronts, while preserving high accuracy in shock influence areas. Test computations are presented that demonstrate the significant advantages of combined schemes over standard NFC ones when applied to computing discontinuous solutions with shock waves.
Key words: hyperbolic systems of conservation laws, shock waves, high-order accurate shock-capturing methods, combined schemes.
Funding agency Grant number
Russian Foundation for Basic Research 21-51-53012
Russian Science Foundation 21-11-00198
The reported study was funded in part by the Russian Foundation for Basic Research and the National Natural Science Foundation of China (project no. 21-51-53012) (Sections 4–7, 9) and by the Russian Science Foundation (project no. 21-11-00198) (Sections 8, 10).
Received: 05.02.2022
Revised: 05.02.2022
Accepted: 08.06.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 11, Pages 1743–1781
DOI: https://doi.org/10.1134/S0965542522100025
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: M. D. Bragin, O. A. Kovyrkina, M. E. Ladonkina, V. V. Ostapenko, V. F. Tishkin, N. A. Khandeeva, “Combined numerical schemes”, Zh. Vychisl. Mat. Mat. Fiz., 62:11 (2022), 1763–1803; Comput. Math. Math. Phys., 62:11 (2022), 1743–1781
Citation in format AMSBIB
\Bibitem{BraKovLad22}
\by M.~D.~Bragin, O.~A.~Kovyrkina, M.~E.~Ladonkina, V.~V.~Ostapenko, V.~F.~Tishkin, N.~A.~Khandeeva
\paper Combined numerical schemes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 11
\pages 1763--1803
\mathnet{http://mi.mathnet.ru/zvmmf11466}
\crossref{https://doi.org/10.31857/S0044466922100027}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4517571}
\elib{https://elibrary.ru/item.asp?id=49455074}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 11
\pages 1743--1781
\crossref{https://doi.org/10.1134/S0965542522100025}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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