A computational local reduced-order method for a Rayleigh-Benard problem

  • Herrero, Henar (Universidad de Castilla-La Mancha)
  • Cortés, Jesús (Universidad de Castilla-La Mancha)
  • Pla, Francisco (Universidad de Castilla-La Mancha)

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In this work a local reduced-order method is applied to a 2D Rayleigh-Benard bifurcation problem. Local refers to the selection of the best POD basis for each value of the Rayleigh number through a k-means algorithm. The reduced-order method is a Galerkin projection of the incompressible Navier-Stokes and heat equations onto the local bases. Pressure is recovered through an enrichment of the velocity space. The local reduced-order method is used to compute several bifurcation diagrams of the problem for R in the interval 1000-3000. The method is benchmarked against a Legendre collocation scheme. Errors between the solutions of both methods are optimal. The local method is also compared to a standard global reduced-order method. In the performed numerical results, the local reduced-order method runs about 2.5 times faster than the global reduced-order method and 400 times faster than the Legendre collocation scheme.