Abstract: In this study, we are interesting to the numeric al simulation of the turbulent natural convection in a square cavity, with differentially heated vertical walls and with adiabatic horizontal ones. The selected problem has been broadly studied due to many applications in engineering, such as solar collectors, conservation of energy in buildings and cooling electronic devices. Turbulence is modelled by the low Reynolds number k- model of Launder (1974). The equations controlling the flow are discretized using the finite volumes method. The SIMPLER algorithm is used for the Pressure-Velocity coupling and the sweeping method with the algorithm of Thomas (TDMA) is used for the iterative solution of the systems of the equations. For the 2 selected Rayleigh numbers: Ra=1.58*10⁹ and Ra=4.9*10¹⁰, the numerical results obtained concerning the dynamic field, the thermal field and the various turbulent quantities, show a good agreement with the experimental results of Tian and with the numerical results of Sharif and those of Hsieh.