Abstract
The variational approach to obtaining equations of the entropy stable discontinuous Galerkin method is generalized. It is shown how the monotonicity property can be incorporated into this approach. As applied to Euler equations, the entropic slope limiter, a new effective approximate method for the studied approach, is designed. It guarantees the monotonicity of the numerical solution, as well as the nonnegativity of the pressure and entropy production for each finite element. This method is successfully tested on some well-known gas dynamics model problems.
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ACKNOWLEDGMENTS
The authors thank the Supercomputer Center RCC of Moscow State University and the Center of Information Technologies of Groningen University (the Netherlands) for providing the possibility to execute the numerical computations.
Funding
This work was supported by the Russian Science Foundation, project no. 17-71-30014.
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Translated by A. Muravnik
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Bragin, M.D., Kriksin, Y.A. & Tishkin, V.F. Discontinuous Galerkin Method with an Entropic Slope Limiter for Euler Equations. Math Models Comput Simul 12, 824–833 (2020). https://doi.org/10.1134/S2070048220050038
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DOI: https://doi.org/10.1134/S2070048220050038