The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate

doi:10.1088/1674-1056/22/5/050206

Abstract In this paper, a Petrov-Galerkin scheme named Runge-Kutta control volume (RKCV) discontinuous finite element method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preserving the local conservation and a high resolution. Compared with the Runge-Kutta discontinuous Galerkin (RKDG) method, the RKCV method is easier to be implemented. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.

Keywords: compressible Euler equations Runge-Kutta control volume discontinuous finite element method Lagrangian coordinate

Received: 13 September 2012
Revised: 18 November 2012
Accepted manuscript online:

PACS:	02.70.Dh	(Finite-element and Galerkin methods)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035 and 11171038), the Science Research Foundation of the Institute of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ12198), and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102).

Corresponding Authors: Zhao Guo-Zhong
E-mail: zhaoguozhongbttc@sina.com

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Zhao Guo-Zhong (赵国忠), Yu Xi-Jun (蔚喜军), Guo Peng-Yun (郭鹏云) The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate 2013 Chin. Phys. B 22 050206

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The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate

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