Numerical simulation of unsteady flow in a two-dimensional collapsible channel

In this study, the time-dependent problem is studied to investigate the instability of the steady solution, and details of the resulting oscillations when it is unstable. For this purpose, a time-dependent simulation of the coupled flow-membrane problem has been developed using the Spine method to treat the moving boundary and a second-order time integration scheme with variable time increments. It is found that the steady solutions become unstable as tension falls below a certain value. As a consequence, steady flow gives way to self-excited oscillations. A sequence of bifurcations going through regular oscillations to irregular oscillations is observed. Additionally, vorticity waves are found downstream of the elastic sections.