{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:17:27Z","timestamp":1760149047037,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T00:00:00Z","timestamp":1687996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Program in Higher Institution of Ningxia","award":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"],"award-info":[{"award-number":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"]}]},{"name":"National Natural Science Foundation of China","award":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"],"award-info":[{"award-number":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"]}]},{"name":"the National Natural Science Foundation of Ningxia","award":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"],"award-info":[{"award-number":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"]}]},{"name":"Key Research and Development Program of Ningxia","award":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"],"award-info":[{"award-number":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"]}]},{"name":"National Youth Top-notch Talent Support Program of Ningxia","award":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"],"award-info":[{"award-number":["NGY2020110","12161067","12001015","12261070","2022AAC02023","2022AAC03313","2022AAC03314","2021BEB04053"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a higher-order blended compact difference (BCD) scheme on nonuniform grids for solving the three-dimensional (3D) convection\u2013diffusion equation with variable coefficients. The BCD scheme has fifth- to sixth-order accuracy and considers the first and second derivatives of the unknown function as unknowns as well. Unlike other schemes that require grid transformation, the BCD scheme does not require any grid transformation and is simple and flexible in grid subdivisions. Concurrently, the corresponding high-order boundary schemes of the first and second derivatives have also been constructed. We tested the BCD scheme on three problems that involve convection-dominated and boundary-layer features. The numerical results show that the BCD scheme has good adaptability and high resolution on nonuniform grids. It outperforms the BCD scheme on uniform grids and the high-order compact scheme on nonuniform grids in the literature in terms of accuracy and resolution.<\/jats:p>","DOI":"10.3390\/axioms12070651","type":"journal-article","created":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T01:14:12Z","timestamp":1688087652000},"page":"651","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Higher-Order Blended Compact Difference Scheme on Nonuniform Grids for the 3D Steady Convection-Diffusion Equation"],"prefix":"10.3390","volume":"12","author":[{"given":"Tingfu","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Lan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongbin","family":"Ge","sequence":"additional","affiliation":[{"name":"School of Science, Dalian Minzu University, Dalian 116600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lili","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Batchelor, G.K. 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