摘要
双曲守恒律方程间断解的存在使其对数值求解格式的精度、分辨率等要求很高.Tadmor等构造的熵稳定(entropy stable,ES)格式,其数值解收敛到具有物理意义的唯一解,但耗散大,抹平严重,空间精度只有一阶.因此,将具有低数值耗散的TENO(targeted essentially non-oscillatory)重构引入到TeCNO框架中,构造出低耗散五阶TENO型熵稳定格式.证明了重构的熵变量在单元交界面处的跳跃满足保号性及所构造格式的熵稳定性.最后通过多种不同数值算例,检验五阶TENO型熵稳定格式的低数值耗散、高收敛阶、高分辨率及良好的数值鲁棒性.
The existence of intermittent solutions to hyperbolic conservation law equations requires high accuracy and resolution of the numerical solution schemes.The entropy stable schemes constructed by Tadmor et al.has numerical solutions that converge to physically meaningful unique solutions,but with severe dissipation large smearing effects and only 1st-order spatial accuracy.Therefore,the TENO(targeted essentially non-oscillatory)reconstruction with low numerical dissipation was introduced into the TeCNO framework,and a low-dissipation 5th-order TENO-type entropy stable scheme was constructed.It was proved that the jumps of the reconstructed entropy variables at the cell interfaces satisfy the sign-preserving property and the entropy stability of the constructed schemes.Finally,the low numerical dissipation,high convergence order,high resolution and good numerical robustness of the 5th-order TENO-type entropy stable scheme,were verified through various numerical examples.
作者
刘佳豪
郑素佩
陈梦莹
郭依琳
LIU Jiahao;ZHENG Supei;CHEN Mengying;GUO Yilin(School of Sciences,Chang’an University,Xi’an 710064,P.R.China)
出处
《应用数学和力学》
北大核心
2025年第4期528-541,共14页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11971075)
陕西省自然科学基础研究计划(2024JC-ZDXM-23)。
关键词
熵稳定
TENO重构
双曲守恒律方程
保号性
TeCNO格式
entropy stability
TENO reconstruction
hyperbolic conservation law
sign-preserving property
TeCNO scheme
