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Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

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Abstract

In this paper, we propose a finite volume Hermite weighted essentially non-oscillatory (HWENO) method based on the dimension by dimension framework to solve hyperbolic conservation laws. It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears, and it is compact which will be good for giving the numerical boundary conditions. Furthermore, it avoids complicated least square procedure when we implement the genuine two dimensional (2D) finite volume HWENO reconstruction, and it can be regarded as a generalization of the one dimensional (1D) HWENO method. Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.

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Acknowledgements

The authors would like to thank Ph.D. candidate Jiayin Li in Xiamen University and anonymous referees for their comments on this paper.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, Fujian, China

    Feng Zheng

  2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling & High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, China

    Jianxian Qiu

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  1. Feng Zheng
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Correspondence to Jianxian Qiu.

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Conflict of Interest

Jianxian Qiu is an editorial board member for Communications on Applied Mathematics and Computation and was not involved in the editorial review or the decision to publish this article. On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

The research of Feng Zheng is partially supported by the NSFC grant 12101128.

The research of Jianxian Qiu is partially supported by the NSFC grant 12071392.

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Zheng, F., Qiu, J. Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws. Commun. Appl. Math. Comput. 6, 605–624 (2024). https://doi.org/10.1007/s42967-023-00279-5

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  • DOI: https://doi.org/10.1007/s42967-023-00279-5

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