{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T14:11:37Z","timestamp":1780927897039,"version":"3.54.1"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,15]],"date-time":"2025-06-15T00:00:00Z","timestamp":1749945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Mississippi NASA EPSCoR program"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this study, we introduce a novel 2-step compact scheme-based high-order correction method for computational fluid dynamics (CFD). Unlike traditional single-formula-based schemes, our proposed approach refines flux function values by leveraging results from high-order compact schemes on the same stencils, provided a certain smoothness condition is met. By applying this method, we achieve a more stable and efficient compact corrected Weighted Essentially Non-Oscillatory (WENO) scheme. The results demonstrate significant improvements across all enhanced schemes, particularly in capturing shock waves sharply and maintaining stability in complex scenarios, such as two interacting blast waves, as validated through 1D benchmark tests. In addition, error analysis is also provided for the two different correction configurations based on WENO.<\/jats:p>","DOI":"10.3390\/a18060364","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T06:40:27Z","timestamp":1750056027000},"page":"364","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Two-Step High-Order Compact Corrected WENO Scheme"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4726-8998","authenticated-orcid":false,"given":"Yong","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Mathematics, West Texas A&M University, Canyon, TX 79016, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Caixia","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shiming","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2786-3474","authenticated-orcid":false,"given":"Yonghua","family":"Yan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0021-9991(89)90183-6","article-title":"TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems","volume":"84","author":"Cockburn","year":"1989","journal-title":"J. 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