Geodesic
Entropy stable discontinuous Galerkin method for two-dimensional Euler equations
Matematičeskoe modelirovanie, Tome 33 (2021) no. 2, pp. 125-140

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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.
Mots-clés : Euler equations
Keywords: the discontinuous Galerkin method, slope limiter, entropic inequality. 
@article{MM_2021_33_2_a8,
     author = {M. D. Bragin and Y. A. Kriksin and V. F. Tishkin},
     title = {Entropy stable discontinuous {Galerkin} method for two-dimensional {Euler} equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {125--140},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_2_a8/}
}
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M. D. Bragin; Y. A. Kriksin; V. F. Tishkin. Entropy stable discontinuous Galerkin method for two-dimensional Euler equations. Matematičeskoe modelirovanie, Tome 33 (2021) no. 2, pp. 125-140. http://geodesic.mathdoc.fr/item/MM_2021_33_2_a8/