FINITE-ELEMENT SOLUTION OF STEADY NATURAL-CONVECTION EQUATIONS BY A FALSE DIFFUSION METHOD

Use of upwind finite element methods was so far confined to forced con vection problems. The present work is devoted to the application of fa lse diffusion techniques to phenomena involving natural convection. A range of Rayleigh numbers in which the discretization by the conventio nal Galerkin scheme fails is considered. A false diffusion method simi lar to the Streamline upwind technique has been employed to avoid cros s-wind diffusion. The upwind parameter is changed continually until a true solution is obtained. The present scheme provides convenient mean s for obtaining gradually improved guesses from which a more accurate solution can be obtained using the conventional Galerkin method. The c riterion for the determination of a true solution is established, and hot-wall Nusselt number values are documented in tabular form.