A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

doi:10.1007/s42967-020-00112-3

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (1): 3-30.doi: 10.1007/s42967-020-00112-3

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A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

Kunlei Zhao^1,2, Yulong Du³, Li Yuan^1,2

1 State Key Laboratory of Scientific and Engineering Computing(LSEC) and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
3 School of Mathematical Sciences, Beihang University, Beijing 100191, China

收稿日期:2020-09-04 修回日期:2020-11-19 出版日期:2023-03-20 发布日期:2023-03-08
通讯作者: Li Yuan,E-mail:lyuan@lsec.cc.ac.cn;Kunlei Zhao,E-mail:klzhao@lsec.cc.ac.cn;Yulong Du,E-mail:kunyu0918@163.com E-mail:lyuan@lsec.cc.ac.cn;klzhao@lsec.cc.ac.cn;kunyu0918@163.com
基金资助:
This work is supported by the National Natural Science Foundation of China (91641107, 91852116, 12071470) and Fundamental Research of Civil Aircraft (MJ-F-2012-04) of Ministry of Industrialization and Information of China.

A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

Kunlei Zhao^1,2, Yulong Du³, Li Yuan^1,2

1 State Key Laboratory of Scientific and Engineering Computing(LSEC) and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
3 School of Mathematical Sciences, Beihang University, Beijing 100191, China

Received:2020-09-04 Revised:2020-11-19 Online:2023-03-20 Published:2023-03-08
Contact: Li Yuan,E-mail:lyuan@lsec.cc.ac.cn;Kunlei Zhao,E-mail:klzhao@lsec.cc.ac.cn;Yulong Du,E-mail:kunyu0918@163.com E-mail:lyuan@lsec.cc.ac.cn;klzhao@lsec.cc.ac.cn;kunyu0918@163.com
Supported by:
This work is supported by the National Natural Science Foundation of China (91641107, 91852116, 12071470) and Fundamental Research of Civil Aircraft (MJ-F-2012-04) of Ministry of Industrialization and Information of China.

摘要/Abstract

摘要： In this paper, we develop a new sixth-order WENO scheme by adopting a convex combination of a sixth-order global reconstruction and four low-order local reconstructions. Unlike the classical WENO schemes, the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals one. Further, a very simple smoothness indicator for the global stencil is proposed. The new scheme can achieve sixthorder accuracy in smooth regions. Numerical tests in some one- and two-dimensional benchmark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme, and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

关键词: Global smoothness indicator, Linear weights, Sixth-order accuracy, WENO

Abstract: In this paper, we develop a new sixth-order WENO scheme by adopting a convex combination of a sixth-order global reconstruction and four low-order local reconstructions. Unlike the classical WENO schemes, the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals one. Further, a very simple smoothness indicator for the global stencil is proposed. The new scheme can achieve sixthorder accuracy in smooth regions. Numerical tests in some one- and two-dimensional benchmark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme, and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

Key words: Global smoothness indicator, Linear weights, Sixth-order accuracy, WENO

中图分类号:

Kunlei Zhao, Yulong Du, Li Yuan. A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws[J]. Communications on Applied Mathematics and Computation, 2023, 5(1): 3-30.

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A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

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