Application of Method of Lines on the Bifurcation Analysis of a Horizontal Rijke Tube

In this study, Method of Lines is implemented for the bifurcation analysis of a horizontal Rijke tube. Different from the conventional approach by the Galerkin method, a dynamic system is naturally built up by discretizing the acoustic momentum and energy equations incorporating appropriate boundary conditions using a finite difference method. Additionally, a modified form of King’s law is used to model the interaction of Rijke tube velocity with oscillatory heat. A comparison of the numerical results with experimental data and the reported calculations reveals that the current approach can yield very good predictions. Furthermore, subcritical Hopf bifurcations and fold bifurcations are captured with the evolution of different system parameters to gain an understanding of the intrinsic nonlinear behaviors.