High Rayleigh number variational multiscale large eddy simulations of Rayleigh-B\'{e}nard Convection
The variational multiscale (VMS) formulation is used to develop residual-based VMS large eddy simulation (LES) models for Rayleigh-B\'{e}nard convection. The resulting model is a mixed model that incorporates the VMS model and an eddy viscosity model. The Wall-Adapting Local Eddy-viscosity (WALE) model is used as the eddy viscosity model in this work. The new LES models were implemented in the finite element code Drekar. Simulations are performed using continuous, piecewise linear finite elements. The simulations ranged from $Ra = 10^6$ to $Ra = 10^{14}$ and were conducted at $Pr = 1$ and $Pr = 7$. Two domains were considered: a two-dimensional domain of aspect ratio 2 with a fluid confined between two parallel plates and a three-dimensional cylinder of aspect ratio $1/4$. The Nusselt number from the VMS results is compared against three dimensional direct numerical simulations and experiments. In all cases, the VMS results are in good agreement with existing literature.