浅水波方程的旋转不变性及自适应求解  

Rotational Invariance and Adaptive Solution of Shallow Water Wave Equation

作　　者：李霄 郑素佩[2] 王令 封建湖[2] LI Xiao;ZHENG Supei;WANG Ling;FENG Jianhu(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan 756000,China;School of Science,Chang′an University,Xi′an 710064,China;China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756000 [2]长安大学理学院,陕西西安710064 [3]中国空气动力研究与发展中心,四川绵阳621000

出　　处：《郑州大学学报（理学版）》2023年第4期75-81,共7页Journal of Zhengzhou University:Natural Science Edition

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

摘　　要：针对二维浅水波方程数值求解问题,对该类方程通量函数的旋转不变性进行了理论推导,构造了基于移动网格的混合旋转通量法。基于变分原理的自适应移动网格法能够将网格根据解的特点自适应分布,且网格移动与微分方程数值求解相互独立。混合旋转通量法能够保留熵稳定格式和HLL格式的优点,且克服了因网格扭曲变形造成的计算中断问题。数值结果表明所构造算法所得数值结果分辨率高,算法鲁棒性强。In order to solve the two-dimensional shallow water wave equations,the flux functions of rotational invariance for these equations were derived theoretically,and a hybrid rotating flux method based on moving mesh was proposed.The adaptive moving mesh method based on variational principle could adaptively distribute the mesh according to the characteristics of the solution,and the mesh movement was independent of the differential equation.The hybrid rotating flux method could retain the advantages of the entropy stable scheme and the HLL scheme,and overcome the computational interruption caused by the distortion of the mesh.Numerical results showed that the proposed algorithm had high resolution and strong robustness.

关 键 词：旋转不变性 移动网格法 旋转混合通量 RUNGE-KUTTA法 

分 类 号：O354[理学—流体力学] O241.82[理学—力学]