Numerical Study of the Transition Toward Chaos of Two-Dimensional Natural Convection within a Square Cavity

ABSTRACT

The authors present the results of a numerical study involving unsteady natural convection inside an air-filled square cavity, heated from two opposite sides and cooled from the other two sides. The behavior of the system with increasing Rayleigh number is analyzed. Results obtained using centered finite differences (CFD), Patankar, and QUICK methods are compared. The last method has been found to yield results similar to the other two but with much less computational effort. This article confirms and expands our previously published study, in which the CFD method was used. Using the QUICK method, the authors show that the system transits from a fixed point toward chaos via a limit cycle, a period-doubling cascade, periodic windows, and tangential bifurcations.