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An improved third‐order finite difference weighted essentially nonoscillatory scheme for hyperbolic conservation laws
Author(s) -
Li Guodong,
Li Xiaogang,
Li Pengfen,
Cai Dandan
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4847
Subject(s) - conservation law , mathematics , boundary (topology) , third order , smoothness , order (exchange) , convergence (economics) , truncation error , scheme (mathematics) , polynomial , finite difference , mathematical analysis , law , economic growth , finance , political science , economics
Summary In this article, we present an improved third‐order finite difference weighted essentially nonoscillatory (WENO) scheme to promote the order of convergence at critical points for the hyperbolic conservation laws. The improved WENO scheme is an extension of WENO‐ZQ scheme. However, the global smoothness indicator has a little different from WENO‐ZQ scheme. In this follow‐up article, a convex combination of a second‐degree polynomial with two linear polynomials in a traditional WENO fashion is used to compute the numerical flux at cell boundary. Although the same three‐point information is adopted by the improved third‐order WENO scheme, the truncation errors are smaller than some other third‐order WENO schemes in L ∞ and L 2 norms. Especially, the convergence order is not declined at critical points, where the first and second derivatives vanish but not the third derivative. At last, the behavior of improved scheme is proved on a variety of one‐ and two‐dimensional standard numerical examples. Numerical results demonstrate that the proposed scheme gives better performance in comparison with other third‐order WENO schemes.