A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem
A Galerkin/POD reduced-order model from eigenfunctions of non-converged time evolution transitory states in a problem of Rayleigh–Bénard is presented. The problem is modeled in a rectangular box with the incompressible momentum equations coupled with an energy equation depending on the Rayleigh numb...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/6/905 |
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| author | Jesús Cortés Henar Herrero Francisco Pla |
| author_facet | Jesús Cortés Henar Herrero Francisco Pla |
| author_sort | Jesús Cortés |
| collection | DOAJ |
| description | A Galerkin/POD reduced-order model from eigenfunctions of non-converged time evolution transitory states in a problem of Rayleigh–Bénard is presented. The problem is modeled in a rectangular box with the incompressible momentum equations coupled with an energy equation depending on the Rayleigh number <i>R</i> as a bifurcation parameter. From the numerical solution and stability analysis of the system for a single value of the bifurcation parameter, the whole bifurcation diagram in an interval of values of <i>R</i> is obtained. Three different bifurcation points and four types of solutions are obtained with small errors. The computing time is drastically reduced with this methodology. |
| first_indexed | 2024-03-09T13:26:48Z |
| format | Article |
| id | doaj.art-f0e8df6a32944cd6a034aa30d114a360 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:26:48Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-f0e8df6a32944cd6a034aa30d114a3602023-11-30T21:23:49ZengMDPI AGMathematics2227-73902022-03-0110690510.3390/math10060905A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection ProblemJesús Cortés0Henar Herrero1Francisco Pla2Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, SpainDepartamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, SpainDepartamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, SpainA Galerkin/POD reduced-order model from eigenfunctions of non-converged time evolution transitory states in a problem of Rayleigh–Bénard is presented. The problem is modeled in a rectangular box with the incompressible momentum equations coupled with an energy equation depending on the Rayleigh number <i>R</i> as a bifurcation parameter. From the numerical solution and stability analysis of the system for a single value of the bifurcation parameter, the whole bifurcation diagram in an interval of values of <i>R</i> is obtained. Three different bifurcation points and four types of solutions are obtained with small errors. The computing time is drastically reduced with this methodology.https://www.mdpi.com/2227-7390/10/6/905reduced-order modelsproper orthogonal decompositionspectral methodsRayleigh–Bénard instabilitygeophysical flows |
| spellingShingle | Jesús Cortés Henar Herrero Francisco Pla A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem Mathematics reduced-order models proper orthogonal decomposition spectral methods Rayleigh–Bénard instability geophysical flows |
| title | A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem |
| title_full | A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem |
| title_fullStr | A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem |
| title_full_unstemmed | A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem |
| title_short | A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem |
| title_sort | galerkin pod reduced order model from eigenfunctions of non converged time evolution solutions in a convection problem |
| topic | reduced-order models proper orthogonal decomposition spectral methods Rayleigh–Bénard instability geophysical flows |
| url | https://www.mdpi.com/2227-7390/10/6/905 |
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