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

Kunlei Zhao; Yulong Du; Li Yuan

doi:10.1007/s42967-020-00112-3

Communications on Applied Mathematics and Computation ›› 2021, Vol. 5 ›› Issue (1) : 3-30. DOI: 10.1007/s42967-020-00112-3

Original Paper

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

Kunlei Zhao¹^,² ,
Yulong Du³ ,
Li Yuan¹^,²^,c

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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 sixth-order 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.

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Kunlei Zhao, Yulong Du, Li Yuan. A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws. Communications on Applied Mathematics and Computation, 2021, 5(1): 3‒30 https://doi.org/10.1007/s42967-020-00112-3

Funding

National Natural Science Foundation of China (CN)(91852116); National Natural Science Foundation of China (CN)(12071470); Great Project of Ministry of Industrialization and Information of China(MJ-F-2012-04)