Natural Convection in a Square Enclosure by a Finite-Element, Penalty Function Method Using Primitive Fluid Variables

Abstract

Numerical solutions for the problem of laminar natural convection in a square enclosure using the penalty function, finite-element method are presented. Solutions are obtained for values of the Rayleigh number up to 10⁷ using primitive fluid variables, and the efficacy of the method is demonstrated through a qualitative and quantitative evaluation of the results. The simplicity and general applicability of the method are shown especially in the context of extensions to three-dimensional geometries and irregular computational grids.