“…Hence, various techniques have been developed in order to reconstruct fields coming from a boundary on the computation domain (i.e. the computation of the velocity imposed by the IB in our case) or the contrary (reconstruction of the stress tensor on the envelop of an airfoil to compute aerodynamic forces, for instance [12]) such as: mollifier functions (used in the original IBM to approximate the Dirac delta functions [13,14]), extrapolation outside the computation domain (used in ghost cells techniques [15,16]), interpolation (widely used in all kind of fictitious domain methods [5,4]). In the case of infinitely thin obstacles, the eXtended (or Generalized) Finite Element Method (X-FEM), which is often used in the field of fracture mechanics [17,18], provides some advantages: it is capable to deal with discontinuous quantities (typically tangential velocities on each side of an infinitely thin obstacle with slip conditions) while preserving the standard finite element properties elsewhere.…”