{"title":"Sixth-order perturbed WENO interpolation-based AWENO and WCNS-E schemes for hyperbolic conservation laws","authors":"","doi":"10.1016/j.aml.2024.109230","DOIUrl":null,"url":null,"abstract":"<div><p>The weighted essentially non-oscillatory (WENO) interpolation-based schemes (the alternative WENO (AWENO) scheme and the explicit weighted compact nonlinear (WCNS-E) scheme) are limited to the fifth-order despite the sixth-order Taylor expansion of the numerical flux used. This order reduction is due to the fifth-order accuracy inherent in the WENO interpolation. We investigate the perturbed WENO interpolation with a free parameter and affine-invariant WENO weights to recover sixth-order accuracy in smooth regions. A cutoff function of the free parameter with a threshold, determined by approximate dispersion relation analysis, is applied to enhance the ENO property. The proposed schemes perform better in accuracy, dissipation, resolution, shock-capturing, and efficiency in 1D and 2D benchmark problems.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002507","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The weighted essentially non-oscillatory (WENO) interpolation-based schemes (the alternative WENO (AWENO) scheme and the explicit weighted compact nonlinear (WCNS-E) scheme) are limited to the fifth-order despite the sixth-order Taylor expansion of the numerical flux used. This order reduction is due to the fifth-order accuracy inherent in the WENO interpolation. We investigate the perturbed WENO interpolation with a free parameter and affine-invariant WENO weights to recover sixth-order accuracy in smooth regions. A cutoff function of the free parameter with a threshold, determined by approximate dispersion relation analysis, is applied to enhance the ENO property. The proposed schemes perform better in accuracy, dissipation, resolution, shock-capturing, and efficiency in 1D and 2D benchmark problems.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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