求解二维浅水波方程的旋转混合格式  

A Rotated Mixed Scheme for Solving 2D Shallow Water Equations

作　　者：郑素佩[1] 李霄 赵青宇 封建湖[1] ZHENG Supei;LI Xiao;ZHAO Qingyu;FENG Jianhu(School of Sciences,Chang’an University,Xi’an 710064,P.R.China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《应用数学和力学》2022年第2期176-186,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(面上项目)(11971075);陕西省自然科学基金(2020JQ-338,2019JM-243)。

摘　　要：针对二维浅水波方程数值求解问题,构造了一种旋转通量混合格式.空间方向上,该算法利用浅水波方程通量函数的旋转不变性,在单元界面法线方向及单元界面切线方向上采用可消除红斑现象的HLL与满足热力学第二定律的熵稳定加权混合数值通量函数,时间方向上采用三阶强稳定Runge-Kutta法.数值结果表明,该混合格式对于二维浅水波方程数值求解具有分辨率高的良好特性.A rotated flux mixed scheme was proposed for solving 2D shallow water equations.Spatially,the algorithm uses the rotation invariance of the shallow water equations.In the normal direction and tangent direction of the element interface,both the HLL,which can eliminate the carbuncle,and the entropy stable weighted hybrid numerical flux function satisfying the 2nd law of thermodynamics,were applied to give fine numerical results.Temporally,the 3rd-order strongly stable Runge-Kutta method was used.The numerical results show that,the new scheme has high resolution for solving 2D shallow water equations.

关 键 词：旋转不变性 熵稳定格式 HLL格式 有限体积法 RUNGE-KUTTA法 

分 类 号：O354[理学—流体力学]