An Efficient Equal-Order Finite-Element Method for Natural Convection in Complex Enclosures

Abstract

In this article, an efficient and accurate equal-order finite-element method is developed and then incorporated into the finite-element program, ANSYS/FLOTRAN, release 6.0. In this method the systems of linear algebraic equations resulting from the finite-element formulation of the momentum and energy equations are solved implicitly using a fast and robust preconditioned BiCGStab( l ) algorithm. Further, the linkage between the momentum and continuity equations is enhanced through improved pressure-velocity coupling. As a result, no under-relaxation is needed for the pressure equation and large values of under-relaxation are possible for the momentum and energy equations, resulting in a marked improvement in convergence. Both efficiency and accuracy of this method are demonstrated for buoyancy-driven flows in square, semicircular, and triangular cavities at various Rayleigh numbers.