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

作     者：Hanghang Ma Xin Zheng Yue Wang Jianping Chen Hongna Zhang Weihua Cai 

作者机构：School of Energy Science and Engineering Harbin Institute of Technology Harbin 150001 China School of Municipal and Environmental Engineering Harbin Institute of Technology Harbin 150001 China Universite de Lyon CNRS INSA-Lyon Universite Claude Bernard Lyon 1 CETHIL UMR5008 F-69621 Villeurbanne France 

出 版 物：《Journal of Harbin Institute of Technology(New Series)》 (哈尔滨工业大学学报（英文版）)

年 卷 期：2018年第25卷第1期

页      面：67-78页

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Sponsored by the National Natural Science Foundation of China(Grant o.51576051) 

主　　题：Rayleigh-Bénard convection proper orthogonal decomposition(POD) low-dimensional model POD-Galerkin direct numerical simulation(DNS) 

摘      要：Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 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.