Development of POD reduced-order model and its closure scheme for 2D Rayleigh–Bénard convection

Abstract

• It is the first time to investigate Rayleigh–Bénard convection at high Ra flow based on POD-Galerkin method. • The reduced-order model with a closure model is built for Rayleigh–Bénard convection. • It is the first time to study the short-time and long-time prediction of Rayleigh–Bénard convection. Reduced-order model (ROM) based on proper orthogonal decomposition (POD) is a fast computational fluid dynamics (CFD) method and has been widely applied to pure flow or heat conduction problems in the past. In this paper, the typical 2D Rayleigh–Bénard convection (RBC) in a square cavity was set as a research target. Firstly, the POD-ROM of 2D RBC problem was constructed at Ra = 10 7 , Pr = 0.71. Combining with direct numerical simulation (DNS) databases, a closure model (CM) was then proposed to correct the evolution process of POD-ROM. Based on the proposed CM, we realized the prediction of flow evolution for a new flow case under the parameters different from that used to get its POD eigenmodes. It showed that the proposed POD-ROM with CM could be able to predict the dynamics of new flow cases. Moreover, the corresponding method proposed in the present study can be also easily extended to other types of flow-heat coupling problems, such as natural heat convection, etc.