自适应大时间步长格式在一维浅水方程中的应用  

Application of Adaptive Large Time Step Scheme in One-dimensional Shallow Water Equation

作　　者：王冬旭 李玉星[1] 李爽 WANG Dong-xu;LI Yu-xing;LI Shuang(College of Pipeline and Civil Engineering,China University of Petroleum(East China),Qingdao 266580,China)

机构地区：[1]中国石油大学(华东)储运与建筑工程学院,青岛266580

出　　处：《科学技术与工程》2020年第23期9597-9602,共6页Science Technology and Engineering

基　　金：国家自然科学基金面上项目(51774313);国家重点研发计划(2016YFC0802104)。

摘　　要：针对一维浅水方程提出了一种自适应大时间步长格式,依据波头与波尾传播速度差的绝对值,确定稀疏波近似波数。当波头与波尾速度相近时,稀疏波采用双波近似,以提高计算效率;当波头与波尾速度差距较大时,稀疏波采用十波近似,以获得较高计算精度。同时通过数值结果对比发现随机选取法(random choice method,RCM)可以有效抑制平台区域的震荡,但随着Courant-Friedrichs-Lewy(CFL)数和时间的增加,RCM对间断处短波震荡抑制效果逐渐减弱。In order to achieve higher computational accuracy and efficiency, an adaptive large time step(LTS) scheme relative to the one-dimensional shallow water equation was proposed. In this scheme, the approximate wave number of the rarefaction wave was determined in accordance with the absolute value of the velocity difference between head and tail of the wave. When the wave head was close to the wave tail, double wave approximation was employed by rarefaction wave to improve the calculation efficiency. On the other hand, when the wave head was far from the wave tail, ten wave approximation was adopted by the rarefaction wave to obtain higher calculation accuracy. At the same time, the comparison of numerical results shows that random choice method(RCM) method can effectively suppress the shock in the platform area, but with the increase of Courant-Friedrichs-Lewy(CFL) number, RCM method has less effect on the short-wave shock suppression at the discontinuity.

关 键 词：自适应 大时间步长 浅水方程 数值震荡 CFL数 

分 类 号：TV131[水利工程—水力学及河流动力学]