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 ≤ 10 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.