Lagrange坐标系下二维气动方程组的RKDG有限元方法

计算物理 ›› 2012, Vol. 29 ›› Issue (2): 166-174.

Lagrange坐标系下二维气动方程组的RKDG有限元方法

赵国忠^1,2, 蔚喜军¹, 张荣培¹

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

收稿日期:2011-04-19 修回日期:2011-08-08 出版日期:2012-03-25 发布日期:2012-03-25
作者简介:赵国忠(1977-),男,博士,讲师,研究方向为计算流体力学,E-mail:zhaoguozhongbttc@sina.com
基金资助:
国家自然科学基金(10771019,11171038)资助项目

RKDG Finite Element Method for Two-dimensional Gas Dynamic Equations in Lagrangian Coordinate

ZHAO Guozhong^1,2, YU Xijun¹, ZHANG Rongpei¹

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

Received:2011-04-19 Revised:2011-08-08 Online:2012-03-25 Published:2012-03-25

摘要/Abstract

摘要： 构造Lagrange坐标系下二维可压缩气动方程组的RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法.将流体力学方程组和几何守恒律统-求解,所有计算都在固定的网格上进行,计算过程中不需要网格节点的速度信息.对几个数值算例进行数值模拟,得到较好的数值模拟结果.

关键词: Lagrange坐标, RKDG有限元方法, 二维气动方程组

Abstract: We construct a Runge-Kutta discontinuous Galerkin (RKDG) finite element method for two-dimensional compressible gas dynamic equations in Lagrangian coordinate.The equations for fluid dynamics and geometry conservation laws are solved simultaneously.All calculations can be done on fixed meshes.Information of grid velocities are not needed in calculation.Several numerical examples are used to evaluate efficiency and reliability of the scheme.It shows that the algorithm works well.

Key words: Lagrangian coordinate, RKDG finite element method, two-dimensional gas dynamic equations

中图分类号:

O241.82

赵国忠, 蔚喜军, 张荣培. Lagrange坐标系下二维气动方程组的RKDG有限元方法[J]. 计算物理, 2012, 29(2): 166-174.

ZHAO Guozhong, YU Xijun, ZHANG Rongpei. RKDG Finite Element Method for Two-dimensional Gas Dynamic Equations in Lagrangian Coordinate[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 29(2): 166-174.

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[2]	陈荣三, 蔚喜军. 二维多介质可压缩流的RKDG有限元方法[J]. 计算物理, 2006, 23(6): 699-705.
[3]	陈荣三, 蔚喜军. 一维多介质可压缩Euler方程的高精度RKDG有限元方法[J]. 计算物理, 2006, 23(1): 43-49.
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