A locally anisotropic fluid-structure interaction remeshing strategy for thin structures with application to a hinged rigid leaflet

SUMMARY An immersed finite element Fluid-Structure Interaction (FSI) algorithm with an anisotropic remeshing strategy for thin rigid structures is presented in two-dimensions. The algorithm consists in remeshing only the fluid elements that are cut by the solid such that they fit the solid geometry. This approach allows to keep the initially provided fluid mesh vertexes fixed during the whole simulation. Furthermore, essential constraints between the fluid and the solid may be directly enforced in the finite element spaces and elements allowing the stress to be discontinuous across the structure may be employed. However, remeshed elements may be strongly anisotropic while the adopted interpolation schemes, always stable on isotropic meshes, may be unstable on anisotropic ones. Therefore a proper element choice needs to be done, which is one of the focuses of the present work. Regarding the FSI algorithm, the fluid and the solid are strongly coupled within a time advancing implicit Euler scheme. In the numerical tests, we focus on inf-sup stability of several mixed finite elements and we numerically show that some elements might not be suitable for such an FSI algorithm, in particular the mixed elements having a discontinuous pressure. Using the proposed methodology, we carefully address the motion of a hinged rigid leaflet, a problem already discussed in the literature but for which we propose a detailed analysis.