A Nitsche-XFEM method and splitting schemes for the simulation of thin-walled structures immersed in an incompressible fluid

The use of fictitious domain/immersed boundary methods for the numerical simulation of fluid-structure interaction problems has recently seen a surge of interest.
In this work we consider the extension of the Nitsche-XFEM method to fluid-structure interaction problems involving a thin-walled elastic structure (Lagrangian formalism) immersed in an incompressible fluid (Eulerian formalism). The fluid domain is discretized with an unstructured mesh not fitted to the solid one. Weak and strong discontinuities across the interface are allowed for the velocity and pressure respectively. The kinematic/kinetic fluid-solid coupling is enforced consistently using a variant of Nitsche’s method involving cut elements. Robustness with respect to arbitrary interface/element intersections is guaranteed through a ghost penalty stabilization.
For the temporal discretization, several coupling schemes with different degrees of fluid-solid splitting (implicit, semi-implicit and explicit) are investigated.
The stability and convergence properties of the methods proposed are rigorously analyzed in a representative linear setting.
Several numerical examples, involving static and moving interfaces, illustrate the performance of the methods.

contact: luca.formaggia@polimi.it