RB (Reduced basis) applied to RB (Rayleigh-Bénard)
2013 - H. Herrero, Y. Maday, F. Pla
Computer Methods in Applied Mechanics and Engineering. 261-262, 132-141 (2013)
The reduced basis approximation is a discretization method that can be implemented for solving parameter-dependent problems in cases of many queries. In this work it is applied to a two dimensional Rayleigh-Bénard problem that depends on the Rayleigh number, which measures buoyancy. For each fixed aspect ratio, multiple steady solutions can be found for different Rayleigh numbers and stable solutions coexist at the same values of external physical parameters. The reduced basis method permits to speed up the computations of these solutions at any value of the Rayleigh number chosen in a fixed interval associated with a single bifurcation branch while maintaining accuracy.