POD Analysis and Low-Dimensional Model Based on POD-Galerkin for Two-Dimensional Rayleigh-Bénard Convection

Abstract

Direct numerical simulation based on OpenFOAM is carried out for two-dimensional Rayleigh-Benard (RB) convection in a square domain at high Rayleigh number of 10 7 and Pr =0.71. Proper orthogonal decomposition (POD) is used to analyze the flow and temperature characteristics from POD energy spectrum and eigenmodes. The results show that the energy spectrum converges fast and the scale of vortex structures captured by eigenmodes becomes smaller as the eigenmode order increases. Meanwhile, a low-dimensional model (LDM) for RB convection is derived based on POD eigenmodes used as a basis of Galerkin project of Navier-Stokes-Boussinesq equations. LDM is built based on different number of eigenmodes and through the analysis of phase portraits, streamline and isothermal predicted by LDM, it is suggested that the error between LDM and DNS is still large.