Bifurcations in two‐dimensional differentially heated cavity

Abstract

In this work, we propose a numerical analysis of a bidimensional instationary naturalconvection in a square cavity filled with air and inclined 45 degree versus to horizontal. The verticalwalls are subjected to non‐uniform temperatures while the horizontal walls are adiabatic. Theequations based on the formulation vorticity‐stream function are solved using the AlternatingDirections Implicit scheme (ADI) and Gauss elimination method. We analyze the influence ofRayleigh number on the roads to chaos borrowed by the natural convection developed in thiscavity, and we are looking for stable solutions representing the nonlinear dynamic system. Acorrelation between the Nusselt number and the Rayleigh number is proposed. We have analyzedthe vicinity of the critical point. The transition of the point attractor to another limit cycleattractor is characterized by the Hopf bifurcation.