高阶保号熵稳定格式

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1296-1310.

高阶保号熵稳定格式

郑素佩(),徐霞*(),封建湖(),贾豆()

^{长安大学理学院西安 710064}

收稿日期:2020-05-27 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 徐霞 E-mail:zsp2008@chd.edu.cn;xuxiachina@163.com;jhfeng@chd.edu.cn;1429594854@qq.com
作者简介:郑素佩, E-mail: zsp2008@chd.edu.cn|封建湖, E-mail: jhfeng@chd.edu.cn|贾豆, E-mail: 1429594854@qq.com
基金资助:
国家自然科学基金(11971075);陕西省自然科学基金(2020JQ-338);陕西省自然科学基金(2019JM-243)

High Order Sign Preserving Entropy Stable Schemes

Supei Zheng(),Xia Xu*(),Jianhu Feng(),Dou Jia()

^{College of Science, Chang'an University, Xi'an 710064}

Received:2020-05-27 Online:2021-10-26 Published:2021-10-08
Contact: Xia Xu E-mail:zsp2008@chd.edu.cn;xuxiachina@163.com;jhfeng@chd.edu.cn;1429594854@qq.com
Supported by:
the NSFC(11971075);the NSF of Shaanxi Province(2020JQ-338);the NSF of Shaanxi Province(2019JM-243)

摘要/Abstract

摘要：

高阶熵稳定格式构造的一个核心任务是如何保证熵变量在进行高阶重构前后的符号不变.该文构造了高阶保号熵稳定格式（熵守恒通量采用Fjordholm方案，耗散部分的熵变量采用三阶紧致CWENO重构），证明了基于该重构的熵变量在跳跃间断处满足保号性.数值结果表明，该格式达到三阶精度、分辨率高、鲁棒性强且无振荡产生.

关键词: 保号性, 紧致CWENO重构, 熵稳定格式

Abstract:

Ensuring the sign preserving on entropy variable after the high-order reconstruction is fundamental in constructing the high-order entropy stable schemes. In this paper, we construct the 3rd order compact CWENO-type entropy stable schemes (Fjordholm's the 3rd order entropy conservative schemes with sign preserving compact CWENO reconstruction for the entropy variable) and prove the sign preserving on entropy variable with the 3rd order compact CWENO reconstruction. Numerical results show that the schemes can achieve third-order accuracy, and have high resolution, robustness and non-oscillation.

Key words: Sign preserving, Compact CWENO reconstruction, Entropy stable schemes

中图分类号:

O354

郑素佩,徐霞,封建湖,贾豆. 高阶保号熵稳定格式[J]. 数学物理学报, 2021, 41(5): 1296-1310.

Supei Zheng,Xia Xu,Jianhu Feng,Dou Jia. High Order Sign Preserving Entropy Stable Schemes[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1296-1310.

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N	L¹ error	Rate	L^∞ error	Rate
40	0.001979313043305		3.629516311932702e-04
80	2.726027476503843e-04	2.86	7.092855086397350e-05	2.36
160	3.522356279884232e-05	2.95	9.975669895746602e-06	2.83
320	4.405706993699641e-06	3.00	1.260137438287312e-06	2.99
640	5.373835462491922e-07	3.01	1.576597490888024e-07	3.00

N	L¹ error	Rate	L^∞ error	Rate
40	1.827054747602715e-04		1.448773504797440e-04
80	2.851024314352313e-05	2.68	1.785661053588239e-05	3.02
160	3.845862448196772e-06	2.89	2.226299234296333e-06	3.00
320	4.929538860536765e-07	2.96	2.782109209450295e-07	3.00
640	6.139221843903657e-08	3.01	3.478015911254420e-08	3.00