Linear stability analysis of a Level Set model of immersed elastic membrane

We perform a linear stability analysis of an elementary 1D model obtained from a Level Set formulation of the coupling between an immersed elastic interface and the surrounding fluid. Despite the striking simplicity of the studied model, relevant instability regimes are obtained, unifying results obtained in previous studies (Brackbill et al, 1992, Vigneaux et al, 2007). We also present numerical tests on the full model which further illustrate the relevance of this simplified model