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Matem. Mod., 2021, Volume 33, Number 2, Pages 125–140 (Mi mm4266)  

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

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


DOI: https://doi.org/10.20948/mm-2021-02-09

Full text: PDF file (574 kB)
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References: PDF file   HTML file

Received: 22.10.2020
Revised: 22.10.2020
Accepted:30.11.2020

Citation: M. D. Bragin, Y. A. Kriksin, V. F. Tishkin, “Entropy stable discontinuous Galerkin method for two-dimensional Euler equations”, Matem. Mod., 33:2 (2021), 125–140

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 Matem. Mod.
\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}


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