A POD-Galerkin reduced-order model for two-dimensional Rayleigh-Bénard convection with viscoelastic fluid

Reduced-order model (ROM) based on proper orthogonal decomposition (POD) has been widely used in different fields, such as optimization design and flow control, etc., which needs to get calculation results quickly. Most of present studies about POD-ROM focus on the Newtonian fluid flows, whereas, few studies are related with viscoelastic fluid flows. In this paper, POD-ROM is the first time developed for viscoelastic fluid flow by considering a typical two-dimensional thermal fluid problem: Rayleigh-Benard convection (RBC). Three different cases are chosen to simulate viscoelastic RBC flow at Rayleigh number of 108, Prandtl number of 7.0 and Weissenberg number of 0.1, 0.2 and 0.3, respectively. It is found that phase portraits under different POD modes share the same trend as that for DNS. By introducing ‘intrinsic stabilization scheme’ closure model, it shows that the relative errors of fluctuation velocity, temperature and conformation tensor fields decrease greatly, i.e., POD-ROM with closure model can perform better than POD-ROM without closure model for long-time prediction.