中山大学学报自然科学版 ›› 2012, Vol. 51 ›› Issue (1): 19-24.

• 研究论文 • 上一篇    下一篇

求解二维浅水波方程的群速度修正法

周超红,姚清河,朱庆勇
  

  1. (中山大学应用力学与工程系,广东 广州 510275)
  • 收稿日期:2011-11-01 修回日期:1900-01-01 出版日期:2012-01-25 发布日期:2012-01-25
  • 通讯作者: 朱庆勇

The Modified Finite Difference Schemes with Group Velocity Control for Solving 2D Shallow Water Equations

ZHOU Chaohong, YAO Qinghe, ZHU Qingyong   

  1. (Department of Applied Mechanics and Engineering, Sun Yatsen University, Guangzhou 510275, China)
  • Received:2011-11-01 Revised:1900-01-01 Online:2012-01-25 Published:2012-01-25

摘要: 研究了利用群速度控制法的思想构造二维浅水波方程高分辨率格式。利用群速度修正的思想,得到了三阶迎风群速度控制格式、四阶群速度控制格式等多种高分辨率格式;通过引入色散度量以及各向异性度量的概念,为评估差分算子对微分算子的逼近程度提供了标准。

关键词: 高分辨率格式, 群速度控制法, 2D浅水波方程

Abstract:

The general method of constructing high-resolution schemes to solve 2D shallow water equations is studied. Using the technique of group velocity control, some high-resolution schemes are obtained, such as three-order upwind group velocity control schemes and four-order group velocity control schemes. Using the dispersion and anisotropy measurement, a criterion to evaluate approximation degree of difference operators to differential operators is obtained.

Key words: high-resolution schemes, group velocity control, 2D shallow water equations

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