  In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model,
applied to natural convection problems in a variable height cavity, in which
the buoyancy forces are involved. We take into account in this problem both
physical and geometrical parametrizations, considering the Rayleigh number as a
parameter, so as the height of the cavity. We perform an Empirical
Interpolation Method to approximate the sub-grid eddy viscosity term that let
us obtain an affine decomposition with respect to the parameters. We construct
an a posterior error estimator, based upon the Brezzi-Rappaz-Raviart theory,
used in the greedy algorithm for the selection of the basis functions. Finally
we present several numerical tests for different parameter configuration.
