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

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

中国物理B ›› 2013, Vol. 22 ›› Issue (5): 50206-050206.doi: 10.1088/1674-1056/22/5/050206

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

赵国忠^a, 蔚喜军^b, 郭鹏云^a

a Faculty of Mathematics, Baotou Teachers' College, Baotou 014030, China;
b Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2012-09-13 修回日期:2012-11-18 出版日期:2013-04-01 发布日期:2013-04-01
基金资助:
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).

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

Zhao Guo-Zhong (赵国忠)^a, Yu Xi-Jun (蔚喜军)^b, Guo Peng-Yun (郭鹏云)^a

a Faculty of Mathematics, Baotou Teachers' College, Baotou 014030, China;
b Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2012-09-13 Revised:2012-11-18 Online:2013-04-01 Published:2013-04-01
Contact: Zhao Guo-Zhong E-mail:zhaoguozhongbttc@sina.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: compressible Euler equations, Runge-Kutta control volume discontinuous finite element method, Lagrangian coordinate

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.

Key words: compressible Euler equations, Runge-Kutta control volume discontinuous finite element method, Lagrangian coordinate

中图分类号: (Finite-element and Galerkin methods)

02.70.Dh

02.60.Lj (Ordinary and partial differential equations; boundary value problems)

赵国忠, 蔚喜军, 郭鹏云. The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate[J]. 中国物理B, 2013, 22(5): 50206-050206.

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[J]. Chin. Phys. B, 2013, 22(5): 50206-050206.

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

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

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