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 (FSI) algorithm with an anisotropic remeshingstrategy for thin rigid structures is presented in two-dimensions. One specific feature of the algorithmconsists 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 remeshingis performed locally. Furthermore, constraints between the fluid and the solid may be directly enforcedwith 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 isotropicmeshes - may be unstable on anisotropic ones. We specifically focus on a proper finite element pair choice.As for the time advancing of the FSI solver, we perform a geometrical linearization with a sequential solutionof fluid and structure in a backward Euler framework.Using the proposed methodology we extensively address the motion of a hinged rigid leaflet. Numericaltests demonstrate that some finite element pairs are inf-sup unstable with our algorithm, in particular with adiscontinuous pressure.