A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem

Jesús Cortés, Henar Herrero and Francisco Pla
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Jesús Cortés: Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
Henar Herrero: Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
Francisco Pla: Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain

Mathematics, 2022, vol. 10, issue 6, 1-31

Abstract: 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 R 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 R 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.

Keywords: reduced-order models; proper orthogonal decomposition; spectral methods; Rayleigh–Bénard instability; geophysical flows (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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