CCWENO型高阶熵稳定格式的保平衡性

doi:10.19596/j.cnki.1001-246x.8744

计算物理 ›› 2024, Vol. 41 ›› Issue (4): 453-462.DOI: 10.19596/j.cnki.1001-246x.8744

CCWENO型高阶熵稳定格式的保平衡性

刘沙沙(), 郑素佩(), 张成治, 封建湖

长安大学理学院，陕西西安 710064

收稿日期:2023-04-11 出版日期:2024-07-25 发布日期:2024-08-24
通讯作者: 郑素佩
作者简介:刘沙沙(2000-)，女，硕士研究生，主要从事科学与工程中的高性能计算，E-mail：liushasha2017@163.com
基金资助:
国家自然科学基金(11971075);国家自然科学基金(12101073)

Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations

Shasha LIU(), Supei ZHENG(), Chengzhi ZHANG, Jianhu FENG

School of Science, Chang'an University, Xi'an, Shaanxi 710064, China

Received:2023-04-11 Online:2024-07-25 Published:2024-08-24
Contact: Supei ZHENG

摘要/Abstract

摘要：

针对带源项的底部非平坦浅水波方程，本文对高阶紧致中心加权基本无振荡(CCWENO)型熵稳定格式的保平衡性进行研究，证明了格式的保平衡性，通过一维和二维数值算例进行验证。数值结果表明：高阶CCWENO型熵稳定格式具有保平衡性，即便在较粗网格下也能够准确捕捉解的微小扰动。

关键词: 保平衡性, 熵稳定格式, 浅水波方程, CCWENO重构, 静水稳态

Abstract:

The shallow water equations with source term have steady-state solution. The numerical scheme for solving this kind of equations must have well-balanced property, otherwise it will cause oscillation. For the bottom-non-flat shallow water with source term, this paper studies the well-balanced property of the high order compact central weighted essentially non-oscillatory (CCWENO) entropy stable scheme, and proves its well-balanced property. The theory is verified by one- and two-dimensional numerical examples. The numerical results show that the high order CCWENO scheme has the well-balanced property and can accurately capture the small perturbation of the solution even based on the coarse grid.

Key words: well-balanced, entropy stable scheme, shallow water equations, CCWENO reconstruction, hydrostatic equilibrium state

中图分类号:

O354
O241.82

刘沙沙, 郑素佩, 张成治, 封建湖. CCWENO型高阶熵稳定格式的保平衡性[J]. 计算物理, 2024, 41(4): 453-462.

Shasha LIU, Supei ZHENG, Chengzhi ZHANG, Jianhu FENG. Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations[J]. Chinese Journal of Computational Physics, 2024, 41(4): 453-462.

图/表 5

图1 复杂底部的静水问题

Fig.1 Problems of still water with complex bottom

图2 (a) t=0时水位和底部地形; (b)三者比较

Fig.2 (a) Initial surface level and bottom topography; (b) Results of the three schemes

图3 (a) t=0时水位和底部地形; (b)三者比较图

Fig.3 (a)Initial surface level and bottom topography; (b) Results of the three schemes

图4 (a) t=0时水位和底部地形; (b)三者比较图

Fig.4 Initial surface level and bottom topography; (b) Results of the three schemes

图5 不同时刻水面变化情况(a) 100 × 50；(b)200 × 100

Fig.5 Contours of surface at different times (a) 100 × 50;(b)200 × 100

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CCWENO型高阶熵稳定格式的保平衡性

Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations

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