一种维持Saint-Venant方程组移动稳态解的中心格式

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 891-903.

一种维持Saint-Venant方程组移动稳态解的中心格式

罗一鸣¹(),李订芳¹(),刘敏¹(),董建^2,*()

¹ 武汉大学数学与统计学院武汉 430072
² 国防科技大学文理学院长沙 410073

收稿日期:2021-01-11 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 董建 E-mail:luoyiming@whu.edu.cn;dfli@whu.edu.cn;liumin@whu.edu.cn;j.dong@whu.edu.cn
作者简介:罗一鸣, E-mail: luoyiming@whu.edu.cn|李订芳, E-mail: dfli@whu.edu.cn|刘敏, E-mail: liumin@whu.edu.cn
基金资助:
国家重点研发计划项目(2017YFC0405901)

Moving-Water Equilibria Preserving Central Scheme for the Saint-Venant System

Yiming Luo¹(),Dingfang Li¹(),Min Liu¹(),Jian Dong^2,*()

¹ School of Mathematics and Statistics, Wuhan University, Wuhan 430072
² College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073

Received:2021-01-11 Online:2022-06-26 Published:2022-05-09
Contact: Jian Dong E-mail:luoyiming@whu.edu.cn;dfli@whu.edu.cn;liumin@whu.edu.cn;j.dong@whu.edu.cn
Supported by:
the National Key Research and Development Project(2017YFC0405901)

摘要/Abstract

摘要：

针对Saint-Venant方程组提出了一种具有二阶精度的非交错中心有限体积格式.相较于经典中心格式为维持静稳态解选择重构守恒变量和水位值，但在求解移动稳态问题时会产生巨大误差，格式通过重构守恒变量和能量值，以及一种新的源项离散方法能够精确维持移动稳态解并捕捉其小扰动.最后，通过一些经典数值算例验证了格式的收敛性，谐性以及稳健性.

关键词: Saint-Venant方程组, 非交错中心格式, 移动稳态

Abstract:

In this paper, we propose a second-order unstaggered central finite volume scheme for the Saint-Venant system. Classical central scheme can preserve still-water steady state solution by reconstructing conservative variables and the water level, but generates enormous numerical oscillation when considering moving-water steady state. We choose to reconstruct conservative variables and the energy, and design a new discretization of the source term to preserve moving-water equilibria and capture its small perturbations. In the end, several classical numerical experiments are performed to verify the proposed scheme which is convergent, well-balanced and robust.

Key words: Saint-Venant system, Unstaggered central scheme, Moving-water equilibria

中图分类号:

O241.82

罗一鸣,李订芳,刘敏,董建. 一种维持Saint-Venant方程组移动稳态解的中心格式[J]. 数学物理学报, 2022, 42(3): 891-903.

Yiming Luo,Dingfang Li,Min Liu,Jian Dong. Moving-Water Equilibria Preserving Central Scheme for the Saint-Venant System[J]. Acta mathematica scientia,Series A, 2022, 42(3): 891-903.

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参考文献 17

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网格数	$L^1$误差	收敛阶
50	$6.26*10^{-4}$	-
100	$1.57*10^{-4}$	2.00
200	$3.90*10^{-5}$	2.01
400	$9.73*10^{-6}$	2.00