Geodesic
Entropy stable discontinuous Galerkin method for Euler equations using non-conservative variables
Matematičeskoe modelirovanie, Tome 32 (2020) no. 9, pp. 87-102

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A conservative version of the entropy stable discontinuous Galerkin method for Euler equations is proposed in variables: density, momentum density, and pressure. A special difference approximation in time, conservative in total energy is constructed for the equation describing the dynamics of the average pressure in a finite element. The entropic inequality and the requirements for the monotonicity of the numerical solution are ensured by a special slope limiter. The method developed has been successfully tested on a number of model gasdynamic problems. In particular, the quality of numerical calculation the specific internal energy has been significantly improved for the Einfeldt problem.
Mots-clés : gasdynamic equations
Keywords: discontinuous Galerkin method, tilt limiter, entropic inequality. 
@article{MM_2020_32_9_a5,
     author = {Y. A. Kriksin and V. F. Tishkin},
     title = {Entropy stable discontinuous {Galerkin} method for {Euler} equations using non-conservative variables},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {87--102},
     publisher = {mathdoc},
     volume = {32},
     number = {9},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_9_a5/}
}
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Y. A. Kriksin; V. F. Tishkin. Entropy stable discontinuous Galerkin method for Euler equations using non-conservative variables. Matematičeskoe modelirovanie, Tome 32 (2020) no. 9, pp. 87-102. http://geodesic.mathdoc.fr/item/MM_2020_32_9_a5/