Combination of projection and Galerkin finite element methods to solve the problem of free convection in enclosures with complex geometries

Abstract

In the present work, a numerical method to solve the problem of free convec-tion in enclosures with complex geometries is developed. This development isexecuted by the combination of projection and Galerkin nite element methods.Nine-node (quadratic) quadrilateral elements are used to generate the grid forthe eld of the problem. The results show that the convergence of this methodis acceptable, while there is no necessity to use upwind schemes. Increasingthe numbers of nodes and decreasing the time increment yield a more accuratesolution. The advantages of this numerical method are the ability to model anycomplex geometry and no necessity to use upwind schemes.