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
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.
Euler equations, the discontinuous Galerkin method, slope limiter, entropic
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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
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\by M.~D.~Bragin, Y.~A.~Kriksin, V.~F.~Tishkin
\paper Entropy stable discontinuous Galerkin method for two-dimensional Euler equations
\jour Matem. Mod.
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