Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

doi:10.1007/s42967-023-00279-5

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (1): 605-624.doi: 10.1007/s42967-023-00279-5

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Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

Feng Zheng¹, Jianxian Qiu²

1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, Fujian, China;
2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling & High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, China

收稿日期:2022-08-23 修回日期:2023-03-09 发布日期:2024-04-16
通讯作者: Jianxian Qiu,E-mail:jxqiu@xmu.edu.cn;Feng Zheng,E-mail:fzbz200808-31@163.com E-mail:jxqiu@xmu.edu.cn;fzbz200808-31@163.com
基金资助:
The authors would like to thank Ph.D. candidate Jiayin Li in Xiamen University and anonymous referees for their comments on this paper.

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

Feng Zheng¹, Jianxian Qiu²

1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, Fujian, China;
2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling & High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, China

Received:2022-08-23 Revised:2023-03-09 Published:2024-04-16
Contact: Jianxian Qiu,E-mail:jxqiu@xmu.edu.cn;Feng Zheng,E-mail:fzbz200808-31@163.com E-mail:jxqiu@xmu.edu.cn;fzbz200808-31@163.com
Supported by:
The authors would like to thank Ph.D. candidate Jiayin Li in Xiamen University and anonymous referees for their comments on this paper.

摘要/Abstract

摘要： 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.

关键词: Finite volume, Dimension by dimension, HWENO, Hyperbolic conservation laws

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.

Key words: Finite volume, Dimension by dimension, HWENO, Hyperbolic conservation laws

Feng Zheng, Jianxian Qiu. Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws[J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 605-624.

参考文献

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Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

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