二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法

计算物理 ›› 2017, Vol. 34 ›› Issue (3): 294-308.

二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法

赵国忠¹, 蔚喜军², 郭怀民¹

1. 包头师范学院数学科学学院, 包头 014030;
2. 北京应用物理与计算数学研究所计算物理实验室, 北京 100088

收稿日期:2016-03-18 修回日期:2016-06-15 出版日期:2017-05-25 发布日期:2017-05-25
作者简介:ZHAO Guozhong(1977-),male,PhD,professor,research in computational fluid dynamics,E-mail address:zhaoguozhongbttc@sina.com

A Discontinuous Petrov-Galerkin Method for Two-dimensional Compressible Gas Dynamic Equations in Lagrangian Coordinates

ZHAO Guozhong¹, YU Xijun², GUO Huaimin¹

1. Faculty of Mathematics, Baotou Teachers' College, Baotou 014030, China;
2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2016-03-18 Revised:2016-06-15 Online:2017-05-25 Published:2017-05-25
Supported by:
National Natural Science Foundation of China (11261035,11571002), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-15-A07), Natural Science Foundation of Inner Mongolia Autonomous Region, China (2015MS0108, 2012MS0102), Science Research Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region, China (NJZZ12198), Science and Technology Development Foundation of CAEP (2015B0101021) and Defense Industrial Technology Development Program(B1520133015)

摘要/Abstract

摘要： 构造矩形网格下求解Lagrangian坐标系下气动方程组的单元中心型格式. 空间离散采用控制体积间断Petrov-Galerkin方法，时间离散采用二阶TVD Runge-Kutta方法. 利用限制器来抑制非物理震荡并保证RKCV算法的稳定性. 构造的算法可以保证物理量的局部守恒. 与Runge-Kutta间断Galerkin（RKDG）方法相比较，RKCV方法的计算公式少一项积分项使得计算较简单. 给出一些数值算例验证了算法的可靠性及效率.

关键词: 可压缩气动方程组, RKCV间断有限元方法, Lagrangian坐标系

Abstract: A cell-centered scheme is constructed for two-dimensional gas dynamics equations in Lagrangian coordinates on rectangular grids. Spacial discretizations are accomplished by control volume discontinuous Petrov-Galerkin method and temporal discretization is accomplished by second order total variation diminishing Runge-Kutta method. A limiter is used to maintain stability and non-oscillatory property of Runge-Kutta control volume (RKCV) method. The method preserves local conservation of physical variables. Compared with Runge-Kutta discontinuous Galerkin (RKDG) method, computational formula of RKCV method is simpler since it contains no volume quadrature in RKDG method. Numerical examples are given to demonstrate reliability and efficiency of the algorithm.

Key words: compressible gas dynamic equations, RKCV discontinuous finite element method, Lagrangian coordinate

中图分类号:

O241.82

赵国忠, 蔚喜军, 郭怀民. 二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法[J]. 计算物理, 2017, 34(3): 294-308.

ZHAO Guozhong, YU Xijun, GUO Huaimin. A Discontinuous Petrov-Galerkin Method for Two-dimensional Compressible Gas Dynamic Equations in Lagrangian Coordinates[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(3): 294-308.

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