{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T10:29:18Z","timestamp":1768991358530,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T00:00:00Z","timestamp":1673913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Sanya Science and Education Innovation Park of Wuhan University of Technology","award":["2021KF0023"],"award-info":[{"award-number":["2021KF0023"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A general single-node second-order Dirichlet boundary condition for curved boundaries for the convection\u2013diffusion equation based on the lattice Boltzmann method has been developed. The boundary condition simply utilizes the bounce back rule for the temperature distribution and linear interpolation. The developed boundary condition is quite general and stable. The asymptotic analysis indicates that the proposed boundary scheme is of second-order accuracy. The comparison in terms of L2-norm between the simulation results and the analytical solutions confirms that it is indeed second-order accurate for 2D and 3D symmetric flows comprising straight and curved boundaries. Moreover, the Nusselt numbers for a spherical particle in uniform flow obtained by current simulations agree very well with the predictions of empirical correlations and the data of previous direct numerical simulations with a maximal relative deviation within 8%.<\/jats:p>","DOI":"10.3390\/sym15020265","type":"journal-article","created":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T01:57:57Z","timestamp":1674007077000},"page":"265","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A General Single-Node Second-Order Dirichlet Boundary Condition for the Convection\u2013Diffusion Equation Based on the Lattice Boltzmann Method"],"prefix":"10.3390","volume":"15","author":[{"given":"Yong","family":"Chen","sequence":"first","affiliation":[{"name":"School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China"}]},{"given":"Xiangyang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China"}]},{"given":"Hanhua","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4756","DOI":"10.1038\/s41467-021-25021-8","article-title":"Global catastrophic risk from lower magnitude volcanic eruptions","volume":"12","author":"Mani","year":"2021","journal-title":"Nat. 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