Abstract: A spectral element method for the computation of nature convection in closed square cavity is presented.The incompressible Navier Stokes equations expressed in terms of the primitive variables velocity and pressure,and an additional equation for the temperature,are considered.All the variables are expanded in Chebyshev polynomials.A time splitting method is used with a fourth order Runge Kutta for the nonlinear terms and a semi implicit Crank Nicolson method for the viscous terms.The obtained results show to be in excellent agreement with the accepted benchmark solutions.

Key words: spectral element method, natural convection, Navier Stokes, unsteady flow