Rayleigh-Benard convection of viscoelastic fluids in three-dimension finite cavity

The Rayleigh-Benard convection (RBC) with viscoelastic fluids has captured wide attention in the past decades, caused by its ubiquitous uses in the heat transfer process. However, the numerical technique for simulating the viscoelastic fluid flows developed slowly until recent years because of the numerical instability raised by the hyperbolic characteristics of the viscoelastic constitutive equation. In the present work, a novel numerical scheme was developed to simulate the three-dimension (3D) RBC with viscoelastic fluids, where the quasi-linear treatment was applied to the hyperbolic terms of the momentum equation and the viscoelastic constitutive equation. The in-house solver was also optimized in the aspect of time cost. The results show that the critical value of convection onset in 3D is near to that in the two-dimension (2D); however, the flow pattern displays the wave characteristics in the horizontal direction. The viscoelastic kinetic energy budget of oscillating convection in 3D still conforms to the energy transport law of that in 2D [Zheng et al., Phys. Rev. Fluids 8, 023303 (2023)].