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

In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high re...

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Bibliographic Details
Published in:Chinese physics B 2013-05, Vol.22 (5), p.96-103
Main Author: 赵国忠 蔚喜军 郭鹏云
Format: Article
Language:English
Subjects:
Algorithms
Compressibility
Conservation
Euler equations
Finite element method
Galerkin methods
Mathematical analysis
Mathematical models
Runge-Kutta method
一维
伽辽金法
可压缩Euler方程
拉格朗日坐标
拉格朗日方法
控制体积
有限元素法
间断
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Summary:In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. 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.
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/5/050206