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Matematicheskoe modelirovanie, 2021, Volume 33, Number 2, Pages 125–140
DOI: https://doi.org/10.20948/mm-2021-02-09 (Mi mm4266) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Entropy stable discontinuous Galerkin method for two-dimensional Euler equations

M. D. Bragin, Y. A. Kriksin, V. F. Tishkin

Keldysh Institute of Applied Mathematics RAS, Moscow
Full-text PDF (574 kB) Citations (6)
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DOI: https://doi.org/10.20948/mm-2021-02-09
Abstract: A two-dimensional version of the conservative entropy stable discontinuous Galerkin method for the Euler equations is proposed in the variables: density, momentum density and pressure. For the equation describing the dynamics of the mean pressure in a finite element, the approximation is constructed that is conservative in total energy. The special slope limiter ensures the fulfillment of the entropy inequality and the two-dimensional analogue of the monotonicity conditions for the numerical solution. The developed method is tested on some model gasdynamic problems.
Keywords: Euler equations, the discontinuous Galerkin method, slope limiter, entropic inequality.
Funding agency Grant number
Russian Science Foundation 17-71-30014
Received: 22.10.2020
Revised: 22.10.2020
Accepted: 30.11.2020
English version:
Mathematical Models and Computer Simulations, 2021, Volume 13, Issue 5, Pages 897–906
DOI: https://doi.org/10.1134/S2070048221050069
Document Type: Article
Language: Russian
Citation: M. D. Bragin, Y. A. Kriksin, V. F. Tishkin, “Entropy stable discontinuous Galerkin method for two-dimensional Euler equations”, Mat. Model., 33:2 (2021), 125–140; Math. Models Comput. Simul., 13:5 (2021), 897–906
Citation in format AMSBIB
\Bibitem{BraKriTis21}
\by M.~D.~Bragin, Y.~A.~Kriksin, V.~F.~Tishkin
\paper Entropy stable discontinuous Galerkin method for two-dimensional Euler equations
\jour Mat. Model.
\yr 2021
\vol 33
\issue 2
\pages 125--140
\mathnet{http://mi.mathnet.ru/mm4266}
\crossref{https://doi.org/10.20948/mm-2021-02-09}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 5
\pages 897--906
\crossref{https://doi.org/10.1134/S2070048221050069}
Linking options:
  • https://www.mathnet.ru/eng/mm4266
  • https://www.mathnet.ru/eng/mm/v33/i2/p125
    • This publication is cited in the following 6 articles:
    1. V. N. Litvinov, A. E. Chistyakov, A. V. Nikitina, A. M. Atayan, I. Yu. Kuznetsova, “Matematicheskoe modelirovanie gidrodinamicheskikh protsessov Azovskogo morya na mnogoprotsessornoi vychislitelnoi sisteme”, Kompyuternye issledovaniya i modelirovanie, 16:3 (2024), 647–672  mathnet  crossref
    2. A.I. Sukhinov, A.E. Chistyakov, A.V. Nikitina, A.M. Atayan, V.N. Litvinov, M.V. Porksheyan, “Construction of parallel algorithms for modeling hydrodynamic processes in the Azov sea based on hybrid MPI+OpenMP technology”, Comp. Contin. Mech., 16:1 (2023), 17  crossref
    3. Yu. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method for two-dimensional Euler equations in triangulated domains”, Math. Models Comput. Simul., 15:5 (2023), 781–791  mathnet  crossref  crossref  mathscinet
    4. A. E. Chistyakov, A. V. Nikitina, I. Yu. Kuznetsova, E. O. Rakhimbaeva, M. V. Porksheyan, “Investigation of the Approximation Error of the Difference Scheme for the Mathematical Model of Hydrodynamics”, Lobachevskii J Math, 44:5 (2023), 1839  crossref
    5. A. I. Sukhinov, A. E. Chistyakov, I. Y. Kuznetsova, A. M. Atayan, A. V. Nikitina, “Regularized difference scheme for solving hydrodynamic problems”, Math. Models Comput. Simul., 14:5 (2022), 745–754  mathnet  crossref  crossref  mathscinet
    6. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method in conservative variables for two-dimensional Euler equations”, Math. Models Comput. Simul., 14:4 (2022), 578–589  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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