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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 79–84
DOI: https://doi.org/10.31857/S2686954320020071 (Mi danma77) 		 
This article is cited in 8 scientific papers (total in 8 papers)

INFORMATICS

Combined monotone bicompact scheme of higher order accuracy in domains of influence of nonstationary shock waves

M. D. Braginab, B. V. Rogova

a Institute for Applied Mathematics of the Russian Academy of Sciences, Moscow, Russian Federation
b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
Full-text PDF (485 kB) Citations (8)
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DOI: https://doi.org/10.31857/S2686954320020071
Abstract: A new method is proposed for constructing a combined shock-capturing scheme that monotonically localizes shock wave fronts and, at the same time, has increased accuracy in smoothness regions of calculated generalized solutions. In this method, the solution of the combined scheme is constructed using monotonic solutions of a bicompact scheme of the first order of approximation in time and the fourth order of approximation in space obtained for different time steps in the entire computational domain. This construction method is much simpler than a previously proposed method. Test calculations are presented that demonstrate the advantages of the new scheme compared to the WENO5 scheme of the fifth order of approximation in space and the third order of approximation in time.
Keywords: bicompact scheme, WENO scheme, combined scheme, shock wave, local accuracy.
Funding agency Grant number
Russian Science Foundation 16–11–10033
The research presented in Sections 4 and 5 was supported by the Russian Science Foundation, grant no. 16-11-10033.
Presented: B. N. Chetverushkin
Received: 12.02.2020
Revised: 12.02.2020
Accepted: 26.02.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 239–243
DOI: https://doi.org/10.1134/S1064562420020076
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: M. D. Bragin, B. V. Rogov, “Combined monotone bicompact scheme of higher order accuracy in domains of influence of nonstationary shock waves”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 79–84; Dokl. Math., 101:3 (2020), 239–243
Citation in format AMSBIB
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\by M.~D.~Bragin, B.~V.~Rogov
\paper Combined monotone bicompact scheme of higher order accuracy in domains of influence of nonstationary shock waves
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 492
\pages 79--84
\mathnet{http://mi.mathnet.ru/danma77}
\crossref{https://doi.org/10.31857/S2686954320020071}
\zmath{https://zbmath.org/?q=an:7424598}
\elib{https://elibrary.ru/item.asp?id=42930020}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 239--243
\crossref{https://doi.org/10.1134/S1064562420020076}
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  • https://www.mathnet.ru/eng/danma/v492/p79
    • This publication is cited in the following 8 articles:
    1. M. D. Bragin, “Actual Accuracy of Linear Schemes of High-Order Approximation in Gasdynamic Simulations”, Comput. Math. and Math. Phys., 64:1 (2024), 138  crossref  mathscinet
    2. M. D. Bragin, “Realnaya tochnost lineinykh skhem vysokogo poryadka approksimatsii v zadachakh gazovoi dinamiki”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:1 (2024)  crossref
    3. V. V. Ostapenko, E. I. Polunina, N. A. Khandeeva, “On increasing the accuracy of difference schemes when calculating centered rarefaction waves”, Matem. Mod., 36:6 (2024), 119–134  mathnet  mathnet  crossref
    4. M. D. Bragin, “A comparison of two approaches to construct combined schemes for multidimensional Euler equations”, Matem. Mod., 36:6 (2024), 74–88  mathnet  mathnet  crossref
    5. M. D. Bragin, O. A. Kovyrkina, M. E. Ladonkina, V. V. Ostapenko, V. F. Tishkin, N. A. Khandeeva, “Combined numerical schemes”, Comput. Math. Math. Phys., 62:11 (2022), 1743–1781  mathnet  mathnet  crossref  crossref  mathscinet
    6. O. A. Kovyrkina, V. V. Ostapenko, “On accuracy of MUSCL type scheme when calculating discontinuous solutions”, Math. Models Comput. Simul., 13:5 (2021), 810–819  mathnet  mathnet  crossref  crossref  mathscinet  mathscinet
    7. M. E. Ladonkina, O. A. Nekliudova, V. V. Ostapenko, V. F. Tishkin, “On increasing the stability of the combined scheme of the discontinuous Galerkin method”, Math. Models Comput. Simul., 13:6 (2021), 979–985  mathnet  mathnet  crossref  crossref  mathscinet
    8. M. D. Bragin, B. V. Rogov, “Combined multidimensional bicompact scheme with higher order accuracy in domains of influence of nonstationary shock waves”, Dokl. Math., 102:2 (2020), 360–363  mathnet  crossref  crossref  zmath  elib
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