双曲型守恒律方程的熵稳定格式的一些讨论

doi:10.12286/jssx.j2021-0798

计算数学 ›› 2021, Vol. 43 ›› Issue (4): 413-425.DOI: 10.12286/jssx.j2021-0798

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双曲型守恒律方程的熵稳定格式的一些讨论

汤华中

北京大学数学科学学院, 北京 100871

收稿日期:2021-04-08 出版日期:2021-11-14 发布日期:2021-11-12
基金资助:
本工作部分得到了国家重点研发计划资助（2020YFA0712000），国家自然科学基金（12171227），和中德合作研究小组项目（GZ1465）的资助.

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汤华中. 双曲型守恒律方程的熵稳定格式的一些讨论[J]. 计算数学, 2021, 43(4): 413-425.

Tang Huazhong. SOME DISCUSSIONS ON ENTROPY STABLE SCHEMES FOR SCALAR HYPERBOLIC CONSERVATION LAWS[J]. Mathematica Numerica Sinica, 2021, 43(4): 413-425.

SOME DISCUSSIONS ON ENTROPY STABLE SCHEMES FOR SCALAR HYPERBOLIC CONSERVATION LAWS

Tang Huazhong

School of Mathematical Sciences, Peking University, Beijing 100871, China

Received:2021-04-08 Online:2021-11-14 Published:2021-11-12

本文讨论双曲型守恒律方程的熵稳定格式.对于给定的熵对，格式所满足的熵条件中的数值熵通量是不唯一的.Tadmor的充分条件可以唯一地确定标量方程的熵守恒通量，但不能唯一确定方程组的熵守恒通量，却可以给出方程组的空间一阶精度的熵守恒格式.也讨论了在熵守恒通量上添加数值粘性得到的显式熵稳定格式需要满足的条件及常见的时间离散对熵守恒和熵稳定的影响.

关键词： 熵稳定格式, 熵守恒格式, 数值粘性, 熵对, 双曲型守恒律

This paper studies the entropy stable schemes for hyperbolic conservation laws. The numerical entropy flux is not unique in the entropy condition for the given entropy pair. According to Tadmor's sufficient condition, the entropy conservative flux for the scalar equation can be uniquely determined, but the entropy conservative flux for the system can not be uniquely given. For the system, the entropy conservative schemes of spatial first order accuracy can be given. The sufficient condition for numerical viscosity and the ratio of time and space stepsizes of the explicit entropy stable schemes for the scalar equation and the influence of some time discretizations on the entropy conservation and entropy stability are also discussed.

Key words: entropy stable schemes, entropy conservative schemes, numerical viscosity, entropy pair, hyperbolic conservation law

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双曲型守恒律方程的熵稳定格式的一些讨论

SOME DISCUSSIONS ON ENTROPY STABLE SCHEMES FOR SCALAR HYPERBOLIC CONSERVATION LAWS

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