A Reduced-order Extrapolation Model Based on Proper Orthogonal Decomposition Technique for Rayleigh-Bénard convection

Abstract

In order to quickly calculate the flow characteristics in the simulated two-dimensional Rayleigh-Bénard convection model, a reduced-order extrapolation difference model for solving two-dimensional Rayleigh-Bénard is established based on the Proper Orthogonal Decomposition (POD) method. Firstly, the classical difference format is used to calculate the flow field on the initial time span, the sample data is to construct the POD basis, and the truncation error generated in the process of constructing the POD base is analysed. Then, the two-dimensional reduced-order extrapolation Rayleigh-Bénard model is constructed by combining the SVD and POD methods. By numerical examples, the classical difference model and the reduced-order extrapolation model are numerically simulated under the given initial boundary value. The reliability and effective of the reduced-order method are verified by comparing the flow field temperature cloud maps in the two calculation stages.