{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T21:14:27Z","timestamp":1767215667388,"version":"3.48.0"},"reference-count":45,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12461076"],"award-info":[{"award-number":["12461076"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>A linear BDF2 numerical scheme is proposed to solve the Boussinesq system. By using the exponential scalar auxiliary variable (E-SAV) approach, we explicitly deal with the nonlinear terms of the Boussinesq system, and decouple the velocity and temperature in the numerical simulation. These numerical scheme is unconditionally stable. We give rigorous error analysis for the velocity and temperature. Numerical experiment is performed to verify the proposed numerical scheme.<\/jats:p>","DOI":"10.1515\/cmam-2024-0155","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T11:47:14Z","timestamp":1760096834000},"page":"89-107","source":"Crossref","is-referenced-by-count":0,"title":["Error Analysis of BDF2 Scheme for the Boussinesq System Based on Exponential Scalar Auxiliary Variable"],"prefix":"10.1515","volume":"26","author":[{"given":"Huanhuan","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics , 71206 Guizhou University , Guiyang 550025 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , 71206 Guizhou University , Guiyang 550025 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0414-7504","authenticated-orcid":false,"given":"Xianbing","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , 71206 Guizhou University , Guiyang 550025 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2025,10,11]]},"reference":[{"key":"2025123121115001035_j_cmam-2024-0155_ref_001","doi-asserted-by":"crossref","unstructured":"M.  Akbas, S.  Kaya and L. G.  Rebholz,\nOn the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems,\nNumer. Methods Partial Differential Equations 33 (2017), no. 4, 999\u20131017.","DOI":"10.1002\/num.22061"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_002","unstructured":"J.  Boussinesq,\nTh\u00e9orie des ondes et des remous qui se propagent le long d\u2019un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond,\nJ. Math. Pures Appl. (2) 17 (1872), 55\u2013108."},{"key":"2025123121115001035_j_cmam-2024-0155_ref_003","doi-asserted-by":"crossref","unstructured":"C.  Chen and T.  Zhang,\nUnconditional stability of first and second orders implicit\/explicit schemes for the natural convection equations,\nComput. Math. Appl. 139 (2023), 152\u2013172.","DOI":"10.1016\/j.camwa.2022.06.020"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_004","doi-asserted-by":"crossref","unstructured":"A. J.  Chorin,\nNumerical solution of the Navier\u2013Stokes equations,\nMath. Comp. 22 (1968), 745\u2013762.","DOI":"10.1090\/S0025-5718-1968-0242392-2"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_005","doi-asserted-by":"crossref","unstructured":"A.  \u00c7\u0131b\u0131k and S.  Kaya,\nA projection-based stabilized finite element method for steady-state natural convection problem,\nJ. Math. Anal. Appl. 381 (2011), no. 2, 469\u2013484.","DOI":"10.1016\/j.jmaa.2011.02.020"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_006","doi-asserted-by":"crossref","unstructured":"B.  Du, H.  Su and X.  Feng,\nTwo-level variational multiscale method based on the decoupling approach for the natural convection problem,\nInt. Commun. Heat. Mass. 61 (2015), 128\u2013139.","DOI":"10.1016\/j.icheatmasstransfer.2014.12.004"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_007","doi-asserted-by":"crossref","unstructured":"W.  E and J.-G.  Liu,\nGauge method for viscous incompressible flows,\nCommun. Math. Sci. 1 (2003), no. 2, 317\u2013332.","DOI":"10.4310\/CMS.2003.v1.n2.a6"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_008","doi-asserted-by":"crossref","unstructured":"J. L.  Guermond and J.  Shen,\nVelocity-correction projection methods for incompressible flows,\nSIAM J. Numer. Anal. 41 (2003), no. 1, 112\u2013134.","DOI":"10.1137\/S0036142901395400"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_009","doi-asserted-by":"crossref","unstructured":"J. L.  Guermond and J.  Shen,\nOn the error estimates for the rotational pressure-correction projection methods,\nMath. Comp. 73 (2004), no. 248, 1719\u20131737.","DOI":"10.1090\/S0025-5718-03-01621-1"},{"key":"2025123121115001035_j_cmam-2024-0155_ref_010","doi-asserted-by":"crossref","unstructured":"Y.  He and H.  Chen,\nEfficient algorithm and convergence analysis of conservative SAV compact difference scheme for Boussinesq paradigm equation,\nComput. Math. 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T.  Gu,\nFinite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation,\nAppl. Math. 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