{"title":"基于六阶扰动 WENO 插值的双曲守恒定律 AWENO 和 WCNS-E 方案","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":"{\"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}","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
摘要
基于加权本质非振荡（WENO）的插值方案（替代 WENO（AWENO）方案和显式加权紧凑非线性（WCNS-E）方案）尽管使用了六阶泰勒扩展数值通量，但其阶数仅限于五阶。阶次降低的原因是 WENO 插值固有的五阶精度。我们研究了带有自由参数和仿射不变 WENO 权重的扰动 WENO 插值，以恢复平滑区域的六阶精度。通过近似频散关系分析确定自由参数的截止函数和阈值，以增强 ENO 特性。在一维和二维基准问题中，所提出的方案在精度、耗散、分辨率、冲击捕捉和效率方面都有更好的表现。
Sixth-order perturbed WENO interpolation-based AWENO and WCNS-E schemes for hyperbolic conservation laws
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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