{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:01Z","timestamp":1760240221669,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,11]],"date-time":"2019-04-11T00:00:00Z","timestamp":1554940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Fujian Provinces","award":["JT180075, 2018J01654"],"award-info":[{"award-number":["JT180075, 2018J01654"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301082"],"award-info":[{"award-number":["11301082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon.<\/jats:p>","DOI":"10.3390\/e21040390","type":"journal-article","created":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T03:46:37Z","timestamp":1555040797000},"page":"390","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model"],"prefix":"10.3390","volume":"21","author":[{"given":"Demei","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huilin","family":"Lai","sequence":"additional","affiliation":[{"name":"College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baochang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.cam.2004.11.032","article-title":"Variational iteration method for solving Burger\u2019s and coupled Burger\u2019s equations","volume":"181","author":"Abdou","year":"2005","journal-title":"J. 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