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

作　　者：赵国忠 蔚喜军 郭鹏云 

机构地区：[1]Faculty of Mathematics,Baotou Teachers' College [2]Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics

出　　处：《Chinese Physics B》2013年第5期96-103,共8页中国物理B（英文版）

基　　金：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);the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102)

摘　　要：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.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.

关 键 词：compressible Euler equations Runge-Kutta control volume discontinuous finite element method Lagrangian coordinate 

分 类 号：O241.82[理学—计算数学]