Abstract:
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.
Citation:
Y. A. Kriksin, V. F. Tishkin, “Entropy stable discontinuous Galerkin method for Euler equations using non-conservative variables”, Mat. Model., 32:9 (2020), 87–102; Math. Models Comput. Simul., 13:3 (2021), 416–425
This publication is cited in the following 4 articles:
Y. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method in conservative variables for three-dimensional Euler equations”, Math. Models Comput. Simul., 16:6 (2024), 843–852
Yu. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method for two-dimensional Euler equations in triangulated domains”, Math. Models Comput. Simul., 15:5 (2023), 781–791
E. V. Shilnikov, I. R. Khaytaliev, “Application of the local discontinuous Galerkin method to the solution of the quasi-gas dynamic equation system”, Math. Models Comput. Simul., 15:1 suppl. (2023), S111–S122
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method in conservative variables for two-dimensional Euler equations”, Math. Models Comput. Simul., 14:4 (2022), 578–589
Citation in format AMSBIB
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