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Matem. Mod., 2014, Volume 26, Number 1, Pages 17–32 (Mi mm3435)  

This article is cited in 10 scientific papers (total in 10 papers)

Application of the RKDG method for gas dynamics problems

M. E. Ladonkina, O. A. Neklyudova, V. F. Tishkin

KIAM RAS

Abstract: In recent years the RKDG method with discontinuous basic functions which is characterized as a higher-order method is widely used. It’s known that for guaranteeing the monotony of solution obtained by this method it is necessary to use limiters especially if the solution contains big instabilities. However, application of limiters can negatively affect the accuracy of the solution. In this paper the way of saving the order of accuracy of the solution and guaranteeing the monotony is explored.

Keywords: discontinuous Galerkin method, limiters, Euler equations.

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English version:
Mathematical Models and Computer Simulations, 2014, 6:4, 397–407

Bibliographic databases:

Document Type: Article
Received: 01.10.2012

Citation: M. E. Ladonkina, O. A. Neklyudova, V. F. Tishkin, “Application of the RKDG method for gas dynamics problems”, Matem. Mod., 26:1 (2014), 17–32; Math. Models Comput. Simul., 6:4 (2014), 397–407

Citation in format AMSBIB
\Bibitem{LadNekTis14}
\by M.~E.~Ladonkina, O.~A.~Neklyudova, V.~F.~Tishkin
\paper Application of the RKDG method for gas dynamics problems
\jour Matem. Mod.
\yr 2014
\vol 26
\issue 1
\pages 17--32
\mathnet{http://mi.mathnet.ru/mm3435}
\zmath{https://zbmath.org/?q=an:06379908}
\transl
\jour Math. Models Comput. Simul.
\yr 2014
\vol 6
\issue 4
\pages 397--407
\crossref{https://doi.org/10.1134/S207004821404005X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925947229}


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    This publication is cited in the following articles:
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    2. A. V. Rodionov, “On correlation between the discontinuous Galerkin method and MUSCL-type schemes”, Math. Models Comput. Simul., 8:3 (2016), 285–300  mathnet  crossref  elib
    3. V. F. Tishkin, V. T. Zhukov, E. E. Myshetskaya, “On justification of the Godunov scheme in multidimensional case”, Math. Models Comput. Simul., 8:5 (2016), 548–556  mathnet  crossref  elib
    4. Voroshchuk D.N., Miryaha V.A., Petrov I.B., Sannikov A.V., “Discontinuous Galerkin Method For Wave Propagation in Elastic Media With Inhomogeneous Inclusions”, Russ. J. Numer. Anal. Math. Model, 31:1 (2016), 41–50  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. M. Krasnov, M. E. Ladonkina, “Razryvnyi metod Galërkina na trëkhmernykh tetraedralnykh setkakh. Primenenie shablonnogo metaprogrammirovaniya yazyka C++”, Preprinty IPM im. M. V. Keldysha, 2016, 024, 23 pp.  mathnet
    6. M. E. Ladonkina, O. A. Neklyudova, V. F. Tishkin, “Ispolzovanie usrednenii dlya sglazhivaniya reshenii v razryvnom metode Galerkina”, Preprinty IPM im. M. V. Keldysha, 2017, 089, 32 pp.  mathnet  crossref
    7. M. E. Ladonkina, O. A. Neklyudova, V. F. Tishkin, “Postroenie limitera dlya razryvnogo metoda Galerkina na osnove usredneniya resheniya”, Matem. modelirovanie, 30:5 (2018), 99–116  mathnet
    8. I. B. Petrov, “Problemy modelirovaniya prirodnykh i antropogennykh protsessov v Arkticheskoi zone Rossiiskoi Federatsii”, Matem. modelirovanie, 30:7 (2018), 103–136  mathnet
    9. M. M. Krasnov, M. E. Ladonkina, V. F. Tishkin, “Realizatsiya razryvnogo metoda Galërkina v programmnom komplekse DGM”, Preprinty IPM im. M. V. Keldysha, 2018, 245, 31 pp.  mathnet  crossref
    10. A. I. Sukhinov, A. E. Chistyakov, “Raznostnaya skhema KABARE s uluchshennymi dispersionnymi svoistvami”, Matem. modelirovanie, 31:3 (2019), 83–96  mathnet  crossref  elib
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