A new global smoothness indicator of WENO scheme for hyperbolic conservation laws

A new global smoothness indicator of WENO scheme for hyperbolic conservation laws | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 9 October 2025 V1 Latest version Share on A new global smoothness indicator of WENO scheme for hyperbolic conservation laws Authors : Lingling Zhang 0000-0001-9532-6596 [email protected] and Chunlong Yu Authors Info & Affiliations https://doi.org/10.22541/au.176002593.31063562/v1 141 views 97 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, we propose a novel improved fifth-order WENO-Z scheme, referred to as the WENO-ZT scheme. This scheme is specifically designed to achieve and maintain fifth-order accuracy, even in the presence of critical points. By incorporating the high-order information from the classical WENO-Z scheme, we develop a new global smoothness indicator to evaluate the local smoothness of the function across the stencil, while simultaneously reducing computational cost. The performance of the proposed WENO-ZT scheme is evaluated through several test cases, including the linear advection equation and one-dimensional and two-dimensional compressible Euler equations. Both theoretical analysis and numerical experiments confirm that, compared to the WENO-JS, WENO-M, and WENO-Z schemes, the WENO-ZT scheme exhibits superior capability in resolving complex flow structures, achieving fifth-order accuracy, and reducing numerical dissipation. Supplementary Material File (manuscript.pdf) Download 63.03 MB Information & Authors Information Version history V1 Version 1 09 October 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords precision analysis smoothness indicator stencil reorganization weno scheme Authors Affiliations Lingling Zhang 0000-0001-9532-6596 [email protected] Taiyuan University of Technology School of Mathematics View all articles by this author Chunlong Yu Taiyuan University of Technology School of Mathematics View all articles by this author Metrics & Citations Metrics Article Usage 141 views 97 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Lingling Zhang, Chunlong Yu. A new global smoothness indicator of WENO scheme for hyperbolic conservation laws. Authorea . 09 October 2025. DOI: https://doi.org/10.22541/au.176002593.31063562/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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