Comparative analysis of nondimensionalization approaches for solving the 2‐D differentially heated cavity problem
This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2‐D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting...
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| Veröffentlicht in: | International journal for numerical methods in fluids 2024-07, Vol.96 (7), p.1276-1303 |
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| container_title | International journal for numerical methods in fluids |
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| creator | Molina‐Herrera, F. I. Quemada‐Villagómez, L. I. Navarrete‐Bolaños, J. L. Jiménez‐Islas, H. |
| description | This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2‐D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 10
3
and 10
8
, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem. |
| doi_str_mv | 10.1002/fld.5285 |
| format | Article |
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3
and 10
8
, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.</description><identifier>ISSN: 0271-2091</identifier><identifier>EISSN: 1097-0363</identifier><identifier>DOI: 10.1002/fld.5285</identifier><language>eng</language><publisher>Bognor Regis: Wiley Subscription Services, Inc</publisher><subject>Aspect ratio ; Comparative analysis ; Computation ; Fluid flow ; Newton-Raphson method ; Polynomials ; Prandtl number</subject><ispartof>International journal for numerical methods in fluids, 2024-07, Vol.96 (7), p.1276-1303</ispartof><rights>2024 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c216t-1fd63147be8b89b6b46b58a1f277139d32c9cb31e800fcee07bb5e22f3c55d5f3</cites><orcidid>0000-0002-1084-5520</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Molina‐Herrera, F. I.</creatorcontrib><creatorcontrib>Quemada‐Villagómez, L. I.</creatorcontrib><creatorcontrib>Navarrete‐Bolaños, J. L.</creatorcontrib><creatorcontrib>Jiménez‐Islas, H.</creatorcontrib><title>Comparative analysis of nondimensionalization approaches for solving the 2‐D differentially heated cavity problem</title><title>International journal for numerical methods in fluids</title><description>This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2‐D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 10
3
and 10
8
, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.</description><subject>Aspect ratio</subject><subject>Comparative analysis</subject><subject>Computation</subject><subject>Fluid flow</subject><subject>Newton-Raphson method</subject><subject>Polynomials</subject><subject>Prandtl number</subject><issn>0271-2091</issn><issn>1097-0363</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNotkMtKAzEUhoMoWC_gIwTcuJl6kjRzWUq9QsGNrockc2JTZiZjMi2MKx_BZ_RJTKmrAz_fOT_nI-SKwZwB8FvbNnPJS3lEZgyqIgORi2MyA16wjEPFTslZjBsAqHgpZiQufTeooEa3Q6p61U7RReot7X3fuA776HxK3VcifE_VMASvzBojtT7Q6Nud6z_ouEbKf79_7mnjrMWA_ehU2050jWrEhhq1c-NE065usbsgJ1a1ES__5zl5f3x4Wz5nq9enl-XdKjOc5WPGbJMLtig0lrqsdK4XuZalYpYXBRNVI7ipjBYMSwBrEKHQWiLnVhgpG2nFObk-3E29n1uMY73x25C-ibWAfCFk8iESdXOgTPAxBrT1EFynwlQzqPdK66S03isVf92lbMI</recordid><startdate>20240701</startdate><enddate>20240701</enddate><creator>Molina‐Herrera, F. 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The simulations were performed for Rayleigh numbers between 10
3
and 10
8
, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.</abstract><cop>Bognor Regis</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/fld.5285</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0002-1084-5520</orcidid></addata></record> |
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| subjects | Aspect ratio Comparative analysis Computation Fluid flow Newton-Raphson method Polynomials Prandtl number |
| title | Comparative analysis of nondimensionalization approaches for solving the 2‐D differentially heated cavity problem |
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