Sensitivity of unsteady collapsible channel flows to modelling assumptions

We investigate the influences of modelling assumptions on the dynamic behaviour of collapsible channel flows. The elastic wall is modelled in various different ways: as a large strain Bernoulli-Euler beam, as a small strain Timoshenko beam, and as a 2D-solid model derived from a general virtual work approach, using small strain or large strain assumptions. Different inlet boundary conditions are also considered. The in-house finite element codes and the commercial finite element package ADINA 8.4 are used. The steady results agree very well when using the different models/approaches. The unsteady results, on the other hand, can be quite different. The dynamic behaviour of the system is analysed for a set of chosen parameters, using the full numerical solvers, the linear stability analysis, and the Fourier transform. It is found that the system stability is highly sensitive to the solid modelling assumptions used, numerical solvers adopted, or the boundary conditions imposed. Accuracy of the numerical schemes also has an impact on the system's unsteady behaviour. However, despite the high sensitivity of the unsteady solutions to the modelling assumptions, a cascade stability structure previously revealed by the authors seems to exist when different numerical approaches are used.