We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh-Bénard convection (RBC) for Rayleigh numbers ranging from 106 to 1015 and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. (2020), albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at Ra = 1013, we use grids that are 1/120 times the grid-resolution as that of the DNS (Iyer et al. 2020). The Reynolds numbers in our simulations span 3 orders of magnitude from 1,000 to 1,700,000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as Nu ∼ Ra0.321 and Re ∼ Ra0.495. We also perform LES of RBC with periodic side-walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477 respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers, and hence enable us to test the transition to ultimate convection regime.
Bibliographical noteKAUST Repository Item: Exported on 2022-09-14
Acknowledgements: Our numerical simulations were performed on Cray XC40 (Shaheen II) of KAUST supercomputing laboratory, Saudi Arabia, through Project k1416. Some simulations were also performed on the High Performance Computing facility at IIT Kanpur, funded by the DST and IITK.
ASJC Scopus subject areas
- Condensed Matter Physics