TECHNIQUE FOR RAPID CONVERGENCE OF THE PENALTY FINITE-ELEMENT METHOD WITH A MODIFIED GALERKIN SCHEME AND ITS APPLICATION TO NATURAL CONVECTION

Abstract

This paper describes an efficient scheme for convergence of calculations using the penalty finite-element method. Sample calculations were carried out for laminar natural convection in a square channel and in a horizontal layer of fluid. The penalty parameter was initially set at a small value and then increased to larger values in discrete steps. This procedure decreased the computing time to 5% or less of that required for a single large value of the penalty parameter while producing less than 2% difference in the final value of the average Nusselt number. Extrapolation of the computed Nusselt numbers to zero element size resulted in a good agreement with prior experimental and numerical results.