Numerical method is developed which is capable of computing the buoyancy driven flows within an enclosure with large temperature differences. Numerical procedure is constructed on the system of truncated equations which is derived from the assumption that the flow Mach number is small. Numerical results are compared with available bench mark solutions for natural convection within a square enclosure and it is found that the outcome is highly satisfactory. Based on the confirmation of the accuracy and efficiency of the present methodology, exemplary computations are performed on the natural convection flows within enclosures with various complex configuration, in order to exhibit the applicability of the present computational method. Present numerical method will be extended to include turbulence modeling in the future studies toward the practical goal of simulating the flows associated with room fire.