A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws
作者机构：State Key Laboratory of Scientific and Engineering Computing(LSEC)and Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100190China School of Mathematical SciencesBeihang UniversityBeijing 100191China
出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)
年 卷 期：2023年第5卷第1期
页 面：3-30页
核心收录：
基 金：the National Natural Science Foundation of China(91641107,91852116,12071470) Fundamental Research of Civil Aircraft(MJ-F-2012-04)of Ministry of Industrialization and Information of China.
主 题：Global smoothness indicator Linear weights Sixth-order accuracy WENO
摘 要：In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion 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 bench-mark 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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