{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T21:39:48Z","timestamp":1792445988816,"version":"4.5.0"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["2021JYCXJJ010"],"award-info":[{"award-number":["2021JYCXJJ010"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12072127"],"award-info":[{"award-number":["12072127"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["51836003"],"award-info":[{"award-number":["51836003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2022,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This study constructs a new diffuse-domain (DD) lattice Boltzmann (LB) method for two-phase flows in complex geometries. We first coupled the DD method with the consistent and conservative phase-field (CCPF) method which can be described by the DD-CC Navier\u2013Stokes\u2013Cahn\u2013Hilliard (NSCH) equations with the consistency of reduction, the consistency of mass and momentum transport, and the consistency of mass conservation. Then we conducted a matched asymptotic analysis and found that the DD-CCNSCH equations would converge to the CCNSCH equations as the thickness of the DD interface approaches to zero. Since the boundary conditions imposed on the complex geometries are incorporated into the DD-CCNSCH equations as the source terms, the system can be implemented more readily in a large and regular domain, and there is no need to treat the complex boundary conditions specially. We further developed a DD-CCPFLB method, and through the Chapman\u2013Enskog analysis, the DD-CCPFLB method can correctly recover the DD-CCNSCH equations for two-phase flows in complex geometries. To quantitatively validate the DD-CCPFLB method, three benchmark problems are considered, and the numerical results are in agreement with those obtained through directly solving the CCNSCH equations combined with the original boundary conditions, the analytical solution, or the reported data. Finally, the present method is used to study the problems of two-phase flows in complex geometries, including the droplet dynamics in the Y-shaped channel and a droplet passing through cylindrical obstacles. The effects of the wettability and viscosity ratio are mainly investigated, and it is found that these two factors have significant impacts on the droplet dynamics.<\/jats:p>","DOI":"10.1137\/22m1475120","type":"journal-article","created":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T17:25:40Z","timestamp":1670520340000},"page":"1411-1436","source":"Crossref","is-referenced-by-count":39,"title":["A Diffuse-Domain Phase-Field Lattice Boltzmann Method for Two-Phase Flows in Complex Geometries"],"prefix":"10.1137","volume":"20","author":[{"given":"Xi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1169-6133","authenticated-orcid":true,"given":"Zhenhua","family":"Chai","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China; Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China; Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chengjie","family":"Zhan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baochang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China; Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China; Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,12,5]]},"reference":[{"key":"ref1","first-page":"77","volume":"57","author":"Aland S.","year":"2010","journal-title":"CMES Comput. Model. Eng. 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Singap. 22, World Scientific, Hackensack, NJ, 2012.","DOI":"10.1142\/9789814360906_0003"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/61"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198503989.001.0001"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1155"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.830"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(92)90307-K"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.26804\/capi.2019.03.01"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.013309"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109174"},{"key":"ref36","doi-asserted-by":"crossref","unstructured":"C. J. Zhan , \nZ. H. Chai , and \nB. C. Shi , Consistent and conservative phase-field based lattice Boltzmann method for incompressible two-phase flows, Phys. Rev. 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