Abstract. In the present work, a numerical method for solving the problem of free convection in enclosures with complex geometries is developed. This development is executed by the combination of projection and Galerkin nite-element methods. Ninenode (quadratic) quadrilateral elements are used to generate the grid for the eld of the problem. The results show that the convergence of this method is acceptable while there is no necessity to use upwind schemes. Increasing the numbers of nodes and decreasing the time increment yield a more accurate solution. The advantages of this numerical method are the ability to model any complex geometry and no necessity to use upwind schemes.

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