Abstract
A numerical procedure to solve unsteady natural convection flow problems is presented. The governing equations in primitive variables are made non-dimensional to a well balanced form and transformed into generalized coordinates to treat flow problems with a wide range of parameters and complex geometry. The solution procedure of finite difference is applied in such a way that the viscous terms are calculated by central differences and the convective terms by the Generalized QUICK method. The time integration is performed by a two-step method with the second order accuracy to give a proper solution at every time step. The pressure is obtained by solving the Poisson equation with a modified source, which improves the convergence of iterations. As a key point in this study, pressure boundary conditions and pressure distributions are carefully investigated. The natural convection flow in a square cavity heated below is selected as a test problem. Three cases were calculated : Pr=0.72, 10 and 100 for Gr=106, where a steady solution for Pr=0.72 and unsteady solutions for Pr=10 and 100 were obtained.
