几种复合型数值方法的算法模拟与性能比较  

A Comparative Study of Several Composite Schemes for Shallow Water Equations Computation

作　　者：李付鹏[1] 汪继文[1] 

机构地区：[1]安徽大学计算智能与信号处理教育部重点实验室,安徽合肥230039

出　　处：《微机发展》2004年第1期12-14,共3页Microcomputer Development

基　　金：安徽省自然科学基金资助项目(03046101)

摘　　要：浅水波问题的数值模拟一直是计算数学、计算流体力学的研究热点之一,采用低阶方法和高阶方法相复合的数值方法引起了人们的注意,并在水力学的数值模拟中取得了很大的成功。文中对三种复合型的数值方法,即Lax-Wendroff(LW)格式与Lax-Friedrichs(LF)格式的复合算法,Upwind格式与Lax-Wendroff(LW)格式的复合算法,WENO格式与LW格式的复合算法,进行了分析比较和改进,并就计算流体力学中的一维浅水波方程的两个算例分别做了数值对比试验,在解的光滑性、锐利性,计算速度等几个方面做了比较,模拟结果表明三种方法均能准确捕捉激波又不产生非物理震荡。The study on the shallow water wave problems by the numerical method is one of the most active topics in computational mathematics, computational fluid mechanics. In recent years, composite methods combined first-order-accurate and second-order-accurate methods have attracted quite a lot of attention and got a seriesof successes in the numerical simulation of shallow water wave problems. In this paper, three new composite methods, namely, Lax-Wendroff and Lax-Friedrichs composite scheme, Upwind and Lax-Wendroff composite scheme, WENO and Lax-Wendroff composite scheme, are investigated and compared. By testing on the smooth and discontinuous problems, computational efficiency of one-dimensional shallow water equations in computational hydraulicsis compared, the result shows the three methods can capture shock accurately and have no oscillatory.

关 键 词：复合型数值方法 算法模拟 水力学 浅水波 

分 类 号：TV131.4[水利工程—水力学及河流动力学]