Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures

In this paper we introduce a Nitsche-XFEM method for fluid–structure interaction problems involving a thin-walled elastic structure (Lagrangian formalism) immersed in an incompressible viscous fluid (Eulerian formalism). The fluid domain is discretized with an unstructured mesh not fitted to the solid mid-surface mesh. Weak and strong discontinuities across the interface are allowed for the velocity and pressure, respectively. The fluid–solid coupling is enforced consistently using a variant of Nitsche’s method with cut-elements. Robustness with respect to arbitrary interface intersections is guaranteed through suitable stabilization. Several coupling schemes with different degrees of fluid–solid time splitting (implicit, semi-implicit and explicit) are investigated. A series of numerical test in 2D, involving static and moving interfaces, illustrates the performance of the different methods proposed.