We present two dimensional numerical simulations of circulation induced by a heat island in an unbounded domain. The flow is thermally stratified in the vertical direction. Boussinesq equations in a closed domain are used to describe the flow variables. For this problem, very elongated computational domain have to be used in order to obtain accurate solutions. A term, whose effect is to smoothly damp the convective terms in a layer close to the vertical boundaries, is introduced in the temperature equation. Therefore, shorter domains can be considered. This method is investigated through the numerical simulations of the stationary solutions at Rayleigh number Ra=10^5 and 2.5x10^5. Time periodic solutions at Ra=5x10^5 and 10^6 are also reported and analyzed.