Low-Dissipation 5th-Order Entropy Stable Schemes

LIU Jiahao; ZHENG Supei; CHEN Mengying; GUO Yilin

doi:10.21656/1000-0887.450091

Volume 46 Issue 4

Apr. 2025

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LIU Jiahao, ZHENG Supei, CHEN Mengying, GUO Yilin. Low-Dissipation 5th-Order Entropy Stable Schemes[J]. Applied Mathematics and Mechanics, 2025, 46(4): 528-541. doi: 10.21656/1000-0887.450091

Citation:

LIU Jiahao, ZHENG Supei, CHEN Mengying, GUO Yilin. Low-Dissipation 5th-Order Entropy Stable Schemes[J]. Applied Mathematics and Mechanics, 2025, 46(4): 528-541. doi: 10.21656/1000-0887.450091

Citation:

LIU Jiahao, ZHENG Supei, CHEN Mengying, GUO Yilin. Low-Dissipation 5th-Order Entropy Stable Schemes[J]. Applied Mathematics and Mechanics, 2025, 46(4): 528-541. doi: 10.21656/1000-0887.450091

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Low-Dissipation 5th-Order Entropy Stable Schemes

doi: 10.21656/1000-0887.450091

School of Sciences, Chang'an University, Xi'an 710064, P.R.China

Received Date: 2024-04-08
Rev Recd Date: 2024-09-27
Publish Date: 2025-04-01

Abstract

Abstract

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.
- entropy stability,
- TENO reconstruction,
- hyperbolic conservation law,
- sign-preserving property,
- TeCNO scheme

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References(18)

References

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