{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T18:13:19Z","timestamp":1772129599414,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,27]],"date-time":"2019-12-27T00:00:00Z","timestamp":1577404800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Program Funded by Shaanxi Province Education Department","award":["19JK0905"],"award-info":[{"award-number":["19JK0905"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this article, a lattice Boltzmann (LB) method for studying microchannel gas flows is developed in the framework of the cascaded collision operator. In the cascaded lattice Boltzmann (CLB) method, the Bosanquet-type effective viscosity is employed to capture the rarefaction effects, and the combined bounce-back\/specular-reflection scheme together with the modified second-order slip boundary condition is adopted so as to match the Bosanquet-type effective viscosity. Numerical simulations of microchannel gas flow with periodic and pressure boundary conditions in the transition flow regime are carried out to validate the CLB method. The predicted results agree well with the analytical, numerical, and experimental data reported in the literature.<\/jats:p>","DOI":"10.3390\/e22010041","type":"journal-article","created":{"date-parts":[[2019,12,27]],"date-time":"2019-12-27T11:42:47Z","timestamp":1577446967000},"page":"41","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Numerical Modelling of Microchannel Gas Flows in the Transition Flow Regime Using the Cascaded Lattice Boltzmann Method"],"prefix":"10.3390","volume":"22","author":[{"given":"Qing","family":"Liu","sequence":"first","affiliation":[{"name":"School of Resources Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}]},{"given":"Xiang-Bo","family":"Feng","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Safety and Durability of Concrete, Xijing University, Xi\u2019an 710123, Shaanxi, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1146\/annurev.fluid.30.1.579","article-title":"Micro-electro-mechanical-systems (MEMS) and fluid flows","volume":"30","author":"Ho","year":"1998","journal-title":"Annu. 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