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

Published online by Cambridge University Press:  03 June 2015

Zhenzhen Li*
Affiliation:
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
Xijun Yu*
Affiliation:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R. China
Jiang Zhu*
Affiliation:
National Laboratory for Scientific Computing, LNCC/MCTI, Avenida Getúlio Vargas 333, 25651-075 Petrópolis, RJ, Brazil
Zupeng Jia*
Affiliation:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R. China
*
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Abstract

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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2014

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