Commun. Comput. Phys., 15 (2014), pp. 1184-1206.

A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions

Zhenzhen Li 1, Xijun Yu 2*, Jiang Zhu 3, Zupeng Jia 2

1 School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P.R. China; Graduate School, China Academy of Engineering Physics, Beijing 100088, P.R. China.
2 Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R. China.
3 National Laboratory for Scientific Computing, LNCC/MCTI, Avenida Getulio Vargas 333, 25651-075 Petropolis, RJ, Brazil.

Received 21 March 2013; Accepted (in revised version) 18 December 2013
Available online 21 January 2014


This paper presents a new Lagrangian type scheme for solving the Euler equations of compressible gas dynamics. In this new scheme the system of equations is discretized by Runge-Kutta Discontinuous Galerkin (RKDG) method, and the mesh moves with the fluid flow. The scheme is conservative for the mass, momentum and total energy and maintains second-order accuracy. The scheme avoids solving the geometrical part and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the non-oscillatory property of the scheme.

AMS subject classifications: 65M60, 76M10

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Key words: Lagrangian type scheme, compressible Euler equations, RKDG method, conservative scheme.

*Corresponding author.
Email: (Z. Z. Li), (X. J. Yu), (J. Zhu), (Z. P. Jia)

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