Geodesic
Application of the local discontinuous Galerkin method to the solution of the quasi-gas dynamic equation system
Matematičeskoe modelirovanie, Tome 35 (2023) no. 8, pp. 51-66

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In this paper we consider the solution of quasi-gas dynamic (QGD) system of equations by the local discontinuous Galerkin method (LDG). One-dimensional Riemann discontinuity problems with known exact solutions are solved. Strong discontinuities are present in the solutions of the problems. Therefore, to ensure the monotonicity of the solution obtained by the LDG method, the so-called slope limiters, or limiters, were introduced. A "moment" limiter was chosen that preserved as high an order as possible. The limiter was modified to smooth the oscillations in the solution constancy areas.
Keywords: regularized gas dynamics equations, Riemann problem, solution accuracy, contact discontinuity, local discontinuous Galerkin method, numerical flux. 
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     title = {Application of the local discontinuous {Galerkin} method to the solution of the quasi-gas dynamic equation system},
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E. V. Shilnikov; I. R. Khaytaliev. Application of the local discontinuous Galerkin method to the solution of the quasi-gas dynamic equation system. Matematičeskoe modelirovanie, Tome 35 (2023) no. 8, pp. 51-66. http://geodesic.mathdoc.fr/item/MM_2023_35_8_a3/