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

Author

Listed:
  • Jesús Cortés

    (Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
    These authors contributed equally to this work.)

  • Henar Herrero

    (Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
    These authors contributed equally to this work.)

  • Francisco Pla

    (Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Jesús Cortés & Henar Herrero & Francisco Pla, 2022. "A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem," Mathematics, MDPI, vol. 10(6), pages 1-31, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:905-:d:769221
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    References listed on IDEAS

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    1. Chemseddine Maatki, 2021. "Three-Dimensional Numerical Study of the Effect of Protective Barrier on the Dispersion of the Contaminant in a Building," Mathematics, MDPI, vol. 9(10), pages 1-29, May.
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    Cited by:

    1. Darío Martínez & Henar Herrero & Francisco Pla, 2022. "2D Newton Schwarz Legendre Collocation Method for a Convection Problem," Mathematics, MDPI, vol. 10(19), pages 1-25, October.

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