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Matematicheskoe modelirovanie, 2019, Volume 31, Number 10, Pages 22–34
DOI: https://doi.org/10.1134/S0234087919100022
(Mi mm4115)
 

This article is cited in 2 scientific papers (total in 2 papers)

Accuracy comparison for discontinuous Galerkin schemes in the case of wave and vortex

I. S. Bosnyakov

Zhukovsky Central Aerohydrodinamic Institute (TsAGI)
Full-text PDF (462 kB) Citations (2)
References:
Abstract: This study considers discontinuous Galerkin schemes with Legendre polynomial basis of degree K=0,,5. The scheme build for convection equation is studied in sense of amplitude and dispersion error. The relation between wave number and cell size is determined to provide the desired solution accuracy in task with wave. The computations for acoustic wave are performed with the solver for full Euler equations. Despite different problem statement, the analytical estimates for the relation prove practical applicability. The other test considers inviscid vortex flow. The practical estimate of mesh density is based on the solution of model vortex flow with viscosity. The relation between scheme order and mesh density is pointed for all testcases. The results of this paper can be used in building meshes for tasks intended to be solved with discontinuous Galerkin approach.
Keywords: discontinuous Galerkin method, convection equation, Euler equations, acoustic wave, vortex.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation RFMEFI62817X0007
Received: 04.03.2019
Revised: 04.03.2019
Accepted: 08.04.2019
English version:
Mathematical Models and Computer Simulations, 2020, Volume 12, Issue 3, Pages 445–452
DOI: https://doi.org/10.1134/S2070048220030096
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. S. Bosnyakov, “Accuracy comparison for discontinuous Galerkin schemes in the case of wave and vortex”, Mat. Model., 31:10 (2019), 22–34; Math. Models Comput. Simul., 12:3 (2020), 445–452
Citation in format AMSBIB
\Bibitem{Bos19}
\by I.~S.~Bosnyakov
\paper Accuracy comparison for discontinuous Galerkin schemes in the case of wave and vortex
\jour Mat. Model.
\yr 2019
\vol 31
\issue 10
\pages 22--34
\mathnet{http://mi.mathnet.ru/mm4115}
\crossref{https://doi.org/10.1134/S0234087919100022}
\elib{https://elibrary.ru/item.asp?id=41137468}
\transl
\jour Math. Models Comput. Simul.
\yr 2020
\vol 12
\issue 3
\pages 445--452
\crossref{https://doi.org/10.1134/S2070048220030096}
Linking options:
  • https://www.mathnet.ru/eng/mm4115
  • https://www.mathnet.ru/eng/mm/v31/i10/p22
  • This publication is cited in the following 2 articles:
    1. I. S. Bosnyakov, A. V. Volkov, “Issledovanie skhemy Galerkina s razryvnymi bazisnymi funktsiyami na primere zadachi ob odnorodnoi i izotropnoi turbulentnosti”, Matem. modelirovanie, 37:1 (2025), 171–183  mathnet  crossref
    2. G. B. Sizykh, “A method for replicating exact solutions of the Euler equations for incompressible Beltrami flows”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 24:4 (2020), 790–798  crossref  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математическое моделирование
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    References:49
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