求解二维浅水波方程的移动网格旋转通量法

郑素佩; 王令; 王苗苗

doi:10.21656/1000-0887.400124

求解二维浅水波方程的移动网格旋转通量法

doi: 10.21656/1000-0887.400124

长安大学理学院, 西安 710064

基金项目: 国家自然科学基金（11401045;11971075）;陕西省科技计划项目（2018JM1033）

详细信息

作者简介:
郑素佩（1978—），女，副教授，博士，硕士生导师(E-mail: zsp2008@chd.edu.cn);王令（1993—），女，硕士生(通讯作者. E-mail: 1099248265@qq.com).

中图分类号: O354|O241.82
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- 文章访问数: 2214
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- PDF下载量: 462
- 被引次数: 0
出版历程
- 收稿日期: 2019-03-26
- 修回日期: 2019-05-31
- 刊出日期: 2020-01-01

Solution of 2D Shallow Water Wave Equations With the Moving-Grid Rotating-Invariance Method

School of Sciences, Chang’an University, Xi’an 710064, P.R.China

Funds: The National Natural Science Foundation of China（11401045; 11971075）

摘要

摘要: 为提高求解二维浅水波方程数值算法的分辨率，拟构造求解该方程的新算法：基于移动网格法，选用熵稳定数值通量函数，利用旋转不变性得到混合数值通量.该算法中，浅水波方程的数值求解和依据解的特性进行自适应疏密分布的网格计算过程交错进行.利用变分原理进行网格重构，新网格上的物理量采用二阶精度的守恒型插值公式计算，最终采用三阶强稳定RungeKutta法与满足热力学第二定律的熵稳定格式实现浅水波方程的数值求解.数值结果表明，新算法具有良好的间断捕捉能力，分辨率高.
- 为提高求解二维浅水波方程数值算法的分辨率，拟构造求解该方程的新算法：基于移动网格法，选用熵稳定数值通量函数，利用旋转不变性得到混合数值通量.该算法中，浅水波方程的数值求解和依据解的特性进行自适应疏密分布的网格计算过程交错进行.利用变分原理进行网格重构，新网格上的物理量采用二阶精度的守恒型插值公式计算，最终采用三阶强稳定RungeKutta法与满足热力学第二定律的熵稳定格式实现浅水波方程的数值求解.数值结果表明，新算法具有良好的间断捕捉能力，分辨率高.
Abstract: In order to improve the resolution of the numerical algorithm for solving the 2D shallow water wave equation, a new algorithm was proposed based on the moving-grid method, with the entropy stable numerical flux function and by means of the mixed numerical flux obtained through the rotating invariance. The numerical solution of the shallow water wave equation and the grid computation process based on the characteristics of the solution were interleaved. The variational principle was used to reconstruct the mesh, and the physical quantity on the new mesh was computed with the 2nd-order precision conservation interpolation formula. The 3rd-order strongly stable Runge-Kutta method and the entropy stable format satisfying the 2nd law of thermodynamics were used to numerically solve the shallow water wave equation. The numerical results show that, the new algorithm has good discontinuity capture ability and high resolution.
- moving-grid method

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参考文献(29)

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求解二维浅水波方程的移动网格旋转通量法

doi: 10.21656/1000-0887.400124

作者简介:
郑素佩（1978—），女，副教授，博士，硕士生导师(E-mail: zsp2008@chd.edu.cn);王令（1993—），女，硕士生(通讯作者. E-mail: 1099248265@qq.com).

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Solution of 2D Shallow Water Wave Equations With the Moving-Grid Rotating-Invariance Method

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留言板

求解二维浅水波方程的移动网格旋转通量法

doi: 10.21656/1000-0887.400124

作者简介: 郑素佩（1978—），女，副教授，博士，硕士生导师(E-mail: zsp2008@chd.edu.cn);王令（1993—），女，硕士生(通讯作者. E-mail: 1099248265@qq.com).

计量

出版历程

Solution of 2D Shallow Water Wave Equations With the Moving-Grid Rotating-Invariance Method

计量

出版历程

目录

作者简介:
郑素佩（1978—），女，副教授，博士，硕士生导师(E-mail: zsp2008@chd.edu.cn);王令（1993—），女，硕士生(通讯作者. E-mail: 1099248265@qq.com).