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

An immersed finite element fluid-structure interaction algorithm with an anisotropic remeshing strategy for thin rigid structures is presented in two dimensions. One specific feature of the algorithm consists of remeshing only the fluid elements that are cut by the solid such that they fit the solid geometry. This approach allows to keep the initial (given) fluid mesh during the entire simulation while remeshing is performed locally. Furthermore, constraints between the fluid and the solid may be directly enforced with both an essential treatment and elements allowing the stress to be discontinuous across the structure. Remeshed elements may be strongly anisotropic. Classical interpolation schemes - inf-sup stable on isotropic meshes - may be unstable on anisotropic ones. We specifically focus on a proper finite element pair choice. As for the time advancing of the fluid-structure interaction solver, we perform a geometrical linearization with a sequential solution of fluid and structure in a backward Euler framework. Using the proposed methodology, we extensively address the motion of a hinged rigid leaflet. Numerical tests demonstrate that some finite element pairs are inf-sup unstable with our algorithm, in particular with a discontinuous pressure.