{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:02:11Z","timestamp":1760144531482,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T00:00:00Z","timestamp":1713052800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11972362","11372342"],"award-info":[{"award-number":["11972362","11372342"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Based on a 5-point stencil and three 3-point stencils, a nonlinear multi-order weighted method adaptive to 5-3-3-3 stencils for shock capturing is presented in this paper. The form of the weighting function is the same as JS (Jiang\u2013Shu) weighting; however, the smoothness indicator of the 5-point stencil adopts a special design with a higher-order leading term similar to the \u03c4 in Z weighting. The design maintains that the nonlinear weights satisfy sufficient conditions for the scheme to avoid degradation even near extreme points. By adjusting the linear weights to a specific value and using the \u03c4 in Z weighting, the method can be degraded to Z weighting. Analysis of linear weights shows that they do not affect the accuracy in the smooth region, and they can also adjust the resolution and discontinuity-capturing capability. Numerical tests of different hyperbolic conservation laws are conducted to test the performance of the newly designed nonlinear weights based on the weighted compact nonlinear scheme. The numerical results show that there are no obvious oscillations near the discontinuity, and the resolution of both the discontinuity and smooth regions is better than that of Z weights.<\/jats:p>","DOI":"10.3390\/e26040334","type":"journal-article","created":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T10:24:26Z","timestamp":1713176666000},"page":"334","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improvement of Z-Weighted Function Based on Fifth-Order Nonlinear Multi-Order Weighted Method for Shock Capturing of Hyperbolic Conservation Laws"],"prefix":"10.3390","volume":"26","author":[{"given":"Jinwei","family":"Bai","sequence":"first","affiliation":[{"name":"Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China"}]},{"given":"Zhenguo","family":"Yan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China"}]},{"given":"Meiliang","family":"Mao","sequence":"additional","affiliation":[{"name":"Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China"}]},{"given":"Yankai","family":"Ma","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China"}]},{"given":"Dingwu","family":"Jiang","sequence":"additional","affiliation":[{"name":"Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1002\/fld.3767","article-title":"High-order CFD methods: Current status and perspective","volume":"72","author":"Wang","year":"2013","journal-title":"Int. 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