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Matem. Mod., 2015, Volume 27, Number 2, Pages 129–138 (Mi mm3576)  

This article is cited in 6 scientific papers (total in 6 papers)

On convergence rate of WENO schemes behind a shock front

N. A. Mikhailov

Russian Federal Nuclear Center Zababakhin All-Russia Research Institute of Technical Physics

Abstract: The numerical analysis has shown that high order finite-volume WENO schemes have only the first order of convergence in the smooth part of weak solution behind a shock front. The order of integral convergence of difference solution is found to estimate accuracy of translation of Rankine–Hugoniot conditions through the shock.

Keywords: finite-volume WENO schemes, Rankine–Hugoniot conditions, integral convergence, order of convergence.

Full text: PDF file (384 kB)
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English version:
Mathematical Models and Computer Simulations, 2015, 7:5, 467–474

UDC: 519-63
Received: 26.08.2013

Citation: N. A. Mikhailov, “On convergence rate of WENO schemes behind a shock front”, Matem. Mod., 27:2 (2015), 129–138; Math. Models Comput. Simul., 7:5 (2015), 467–474

Citation in format AMSBIB
\Bibitem{Mik15}
\by N.~A.~Mikhailov
\paper On convergence rate of WENO schemes behind a shock front
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 2
\pages 129--138
\mathnet{http://mi.mathnet.ru/mm3576}
\elib{https://elibrary.ru/item.asp?id=23421477}
\transl
\jour Math. Models Comput. Simul.
\yr 2015
\vol 7
\issue 5
\pages 467--474
\crossref{https://doi.org/10.1134/S2070048215050075}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84941903187}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. A. Kovyrkina, V. V. Ostapenko, “On the construction of combined finite-difference schemes of high accuracy”, Dokl. Math., 97:1 (2018), 77–81  crossref  mathscinet  zmath  isi  scopus
    2. M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, V. F. Tishkin, “Issledovanie tochnosti razryvnogo metoda Galerkina pri raschete reshenii s udarnymi volnami”, Preprinty IPM im. M. V. Keldysha, 2018, 195, 20 pp.  mathnet  crossref  elib
    3. O. Kovyrkina, V. Ostapenko, “High order combined finite-difference schemes”, International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2017), AIP Conf. Proc., 1978, Amer. Inst. Phys., 2018, 470027-1  crossref  mathscinet  isi  scopus
    4. N. A. Zyuzina, O. A. Kovyrkina, V. V. Ostapenko, “Monotone finite-difference scheme preserving high accuracy in regions of shock influence”, Dokl. Math., 98:2 (2018), 506–510  crossref  mathscinet  zmath  isi  scopus
    5. M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, V. F. Tishkin, “On the accuracy of the discontinuous Galerkin method in calculation of shock waves”, Comput. Math. Math. Phys., 58:8 (2018), 1344–1353  mathnet  crossref  crossref  isi  elib
    6. Ostapenko V.V., Khandeeva N.A., “The Accuracy of Finite-Difference Schemes Calculating the Interaction of Shock Waves”, Dokl. Phys., 64:4 (2019), 197–201  crossref  isi
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