  We present two dimensional numerical simulations of a natural convection
problem in an unbounded domain. A thermal stratification is applied in the
vertical direction and the flow circulation is induced by a heat island located
on the ground. For this problem, thermal perturbations are convected in the
horizontal direction far from the heated element so that very elongated
computational domains have to be used in order to compute accurate numerical
solutions. To avoid this difficulty thermal sponge layers are added at the
vertical boundaries. With this approach, stationary solutions at $Ra\le 10^5$
are investigated. Boussinesq equations are discretized with a second-order
finite volume scheme on a staggered grid combined with a second-order
projection method for the time integration.
