Finite element analysis of unsteady natural convection

In this study, a new finite element method (the MSR-method) is proposed for unsteady three-dimensional thermal-fluid analyses. This method is a combin ation of a modified Galerkin method (MGM) and the SIMPLER formulation. In t he MSR-method the velocity and pressure are computed using the SIMPLER proc edure and the approximate velocity and the energy equation are solved using the MGM. In the MGM, the inertia term and the pressure term are considered explicitly, so only the symmetrical matrixes appear. Then an artificial vi scosity is introduced through an error analysis approach to improve its acc uracy and stability. In this paper, the natural convection problems in a th ree-dimensional cavity are simulated up to the Rayleigh number of 10(8), an d converged solutions are obtained. Authors confirmed that our proposed met hod gives reasonable results for these problems comparing with other resear ch works.