{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T10:14:31Z","timestamp":1772792071235,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T00:00:00Z","timestamp":1659657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministerio de Economia y Competitividad","award":["PID2019-106099RB-C44"],"award-info":[{"award-number":["PID2019-106099RB-C44"]}]},{"name":"Ministerio de Economia y Competitividad","award":["T32 20R"],"award-info":[{"award-number":["T32 20R"]}]},{"name":"Gobierno de Aragon\/FEDER-UE","award":["PID2019-106099RB-C44"],"award-info":[{"award-number":["PID2019-106099RB-C44"]}]},{"name":"Gobierno de Aragon\/FEDER-UE","award":["T32 20R"],"award-info":[{"award-number":["T32 20R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper compares two strategies to compute buoyancy-driven flows using stabilized methods. Both formulations are based on a unified approach for solving compressible and incompressible flows, which solves the continuity, momentum, and total energy equations in a coupled entropy-consistent way. The first approach introduces the variable density thermodynamics of the liquid or gas without any artificial buoyancy terms, i.e., without applying any approximate models into the Navier\u2013Stokes equations. Furthermore, this formulation holds for flows driven by high temperature differences. Further advantages of this formulation are seen in the fact that it conserves the total energy and it lacks the incompressibility inconsistencies due to volume changes induced by temperature variations. The second strategy uses the Boussinesq approximation to account for temperature-driven forces. This method models the thermal terms in the momentum equation through a temperature-dependent nonlinear source term. Computer examples show that the thermodynamic approach, which does not introduce any artificial terms into the Navier\u2013Stokes equations, is conceptually simpler and, with the incompressible stabilization matrix, attains similar residual convergence with iteration count to methods based on the Boussinesq approximation. For the Boussinesq model, the SUPG and SGS methods are compared, displaying very similar computational behavior. Finally, the VMS a posteriori error estimator is applied to adapt the mesh, helping to achieve better accuracy for the same number of degrees of freedom.<\/jats:p>","DOI":"10.3390\/a15080278","type":"journal-article","created":{"date-parts":[[2022,8,7]],"date-time":"2022-08-07T21:03:50Z","timestamp":1659906230000},"page":"278","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Simulation of Low-Speed Buoyant Flows with a Stabilized Compressible\/Incompressible Formulation: The Full Navier\u2013Stokes Approach versus the Boussinesq Model"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7802-3411","authenticated-orcid":false,"given":"Guillermo","family":"Hauke","sequence":"first","affiliation":[{"name":"Instituto de Ingenier\u00eda de Arag\u00f3n\u2014Universidad de Zaragoza, Area de Mec\u00e1nica de Fluidos, Escuela de Ingenier\u00eda y Arquitectura, C\/Mar\u00eda de Luna 3, 50018 Zaragoza, Spain"}]},{"given":"Jorge","family":"Lanzarote","sequence":"additional","affiliation":[{"name":"Repsol, DE Qu\u00edmica, C\/Mendez Alvaro, 44, 28045 Madrid, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0360-1323(94)90022-1","article-title":"Development of a robust finite element CFD procedure for predicting indoor room air motion","volume":"29","author":"Baker","year":"1994","journal-title":"Build. 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