Pla, Francisco; Herrero, Henar; Vega, José M. A flexible symmetry-preserving Galerkin/POD reduced order model applied to a convective instability problem. (English) Zbl 1390.76348 Comput. Fluids 119, 162-175 (2015). Summary: A flexible Galerkin method based on proper orthogonal decomposition (POD) is described to construct the bifurcation diagram, as the Rayleigh number \(R\) is varied, in the Rayleigh-Bénard convection in a rectangular box for large Prandtl number. The bifurcation diagram is approximated using the POD modes resulting from unconverged snapshots for just one specific value of \(R\), calculated in either Newton iterations or time-dependent runs converging to steady states. Moreover, the selection of the specific value of \(R\) is quite flexible. In addition, a horizontal reflection symmetry is taken into account to construct a symmetry-preserving Galerkin system. The resulting un-symmetric and symmetric low-dimensional systems are combined with a basic continuation method, which provide the bifurcation diagram at a quite low computational cost. Cited in 8 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 76E15 Absolute and convective instability and stability in hydrodynamic stability Keywords:reduced order models; proper orthogonal decomposition; Rayleigh Bénard instability; geophysical flows PDFBibTeX XMLCite \textit{F. Pla} et al., Comput. Fluids 119, 162--175 (2015; Zbl 1390.76348) Full Text: DOI Link References: [1] Allgower, E. L.; Georg, K., Introduction to numerical continuation methods, SIAM classics in applied mathematics, vol. 45, (2003), SIAM · Zbl 1036.65047 [2] Alonso, D.; Velazquez, A.; Vega, J. 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