Title

运用半离散中心迎风格式计算二维浅水方程的研究

Translated Titles

Study on semi-discrete central-upwind Scheme for the 2-D Shallow Water Equations

Authors

陈建忠(Jian-Zhong Chen);史忠科(Zhong-Ke Shi)

Key Words

二维浅水方程 ; 中心迎风格式 ; 重构 ; 半离散 ; 2-D shallow water equations ; central-upwind difference scheme ; reconstruction ; semi-discrete

PublicationName

水科學進展

Volume or Term/Year and Month of Publication

16卷6期(2005 / 11 / 01)

Page #

853 - 857

Content Language

簡體中文

Chinese Abstract

以三阶中心加权本质无振荡重构为基础,采用一维一维进行计算的方法,给出了求解二维浅水方程的高分辨率三阶半离散中心迎风格式。引入的重构方法既提高了格式的精度,又保证格式是无振荡的。时间的离散用最优的三阶SSP (Strong Stability Preserving) Runge-Kutta方法。源项的离散用辛普森公式。计算方法保持了中心差分格式简单的优点,即不需用黎曼解算器和进行特征分解过程。数值模拟结果与其它方法所得结果一致,表明了方法的有效性和稳定性。

English Abstract

Based on the third-order central weighted essentially non-oscillatory (CWENO) reconstruction, a high-resolution semi-discrete central-upwind difference scheme for solving the 2-D shallow water equations is presented by using the dimension-by-dimension approach. The reconstruction is chosen to improve the accuracy and guarantee the non-oscillatory behavior of the present scheme. The optimal third-order SSP (Strong Stability Preserving) Runge-Kutta method is used for time discrete. Since no Riemann solvers are required and characteristic decomposition can be avoided, the resulting scheme retains all the advantages of central scheme. For the numerical treatment of source terms, the Simpson's quadrature rule is used. The simulated results are shown to be in good agreement with numerical results obtained by other methods. These results demonstrate that the present method is efficient and stable.

Topic Category 工程學 > 水利工程
社會科學 > 經濟學