A POD Reduced Order Method Applied to an Instability Problem of Rayleigh–Bénard Convection

Abstract

The application of a proper orthogonal decomposition (POD) reduced order method to a two-dimensional instability problem of Rayleigh–Bénard convection is described in this work. The partial differential equations that model the problem along with the corresponding eigenvalue problems of the linear stability analysis of stationary solutions are numerically solved for different values of the bifurcation parameter, i.e. the Rayleigh number [Formula: see text]. The POD reduced order method considers spaces derived from different stationary solutions depending on [Formula: see text] as snapshots. The eigenvalue with the largest real part and its corresponding eigenfunction are calculated for the POD solutions. The resulting matrices of the eigenvalue problems are low-dimensional. There is a drastic reduction in the computational cost.