带源项浅水波方程的高分辨率熵稳定格式

张海军; 封建湖; 程晓晗; 李雪

doi:10.21656/1000-0887.380195

带源项浅水波方程的高分辨率熵稳定格式

doi: 10.21656/1000-0887.380195

长安大学理学院, 西安 710064

基金项目: 国家自然科学基金（11601037;11401045;11171043）;中央高校基本科研业务费（310812171002）

详细信息

作者简介:
张海军（1992—），男,硕士生(E-mail: 2397381704@qq.com);封建湖（1960—），男，教授，博士，博士生导师(通讯作者. E-mail: jhfeng@chd.edu.cn).

中图分类号: O354;O241.82
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出版历程
- 收稿日期: 2017-07-13
- 修回日期: 2017-12-07
- 刊出日期: 2018-08-15

An Entropy Stable Scheme for Shallow Water Equations With Source Terms

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

Funds: The National Natural Science Foundation of China（11601037;11401045;11171043）

摘要

摘要: 提出了一种求解带源项浅水波方程的熵稳定格式.新格式利用通量限制函数将一阶熵稳定格式和高阶熵守恒格式结合，具有熵守恒格式和熵稳定格式的优点：在解的光滑区域具有高精度，在解的间断区域避免了非物理现象的产生，同时可以准确地捕捉激波，从而达到高分辨率的效果.利用新格式计算了一维和二维的经典算例，数值结果表明，新格式是模拟带源项浅水波方程的理想方法.
- 浅水波方程 /
- 熵守恒格式 /
- 熵稳定格式 /
- 高分辨率
Abstract: An entropy stable scheme was developed for the shallow water equations with source terms, and a 1st-order entropy stable scheme and a high-order entropy conservation scheme were combined with a flux limiter function. The new entropy scheme preserves advantages of both the entropy conservation scheme and the entropy stable scheme, having higher accuracy in the regions of the smooth solutions and capturing shocks accurately while avoiding non-physical phenomena in the regions of the discontinuous solutions, thus achieves high resolution. The new scheme was successfully applied to calculate the classical 1D and 2D problems. The numerical results show that the new scheme does be an ideal method to simulate the shallow water equations with source terms.
- shallow water equations /
- entropy conservation scheme /
- entropy stable scheme /
- high resolution

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参考文献(16)

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