  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.
