{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:58:32Z","timestamp":1760147912455,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T00:00:00Z","timestamp":1678752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2018YFA0703300","20200201278JC"],"award-info":[{"award-number":["2018YFA0703300","20200201278JC"]}]},{"name":"Natural Science Foundation of Jilin Province, China","award":["2018YFA0703300","20200201278JC"],"award-info":[{"award-number":["2018YFA0703300","20200201278JC"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary\u2013lattice Boltzmann method (IB-LBM) to solve the fluid\u2013structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies.<\/jats:p>","DOI":"10.3390\/axioms12030298","type":"journal-article","created":{"date-parts":[[2023,3,15]],"date-time":"2023-03-15T05:22:59Z","timestamp":1678857779000},"page":"298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force"],"prefix":"10.3390","volume":"12","author":[{"given":"Bowen","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiping","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"337","DOI":"10.4208\/cicp.291210.290411s","article-title":"Numerical methods for fluid-structure interaction\u2014A review","volume":"12","author":"Hou","year":"2012","journal-title":"Commun. 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