On the Jump Conditions for an Immersed Interface Method

An Unfitted Formulation for the Interaction of an Incompressible Fluid with a Thick Structure via an XFEM/DG Approach

“…A different approach consists in considering unfitted meshes, where the fluid mesh is fixed on the background while the structure one is free to move independently. Within these methods, the immersed boundary (IB) [34,35,5,31,6,23,25,4] and the fictitious domain (FD) methods [25,22] are two effective techniques that were successfully employed in the case of thin valve leaflets; see, e.g., [43,14,36,3,8,24]. A more recent methodology is based on an unfitted formulation that allows one to treat nonconforming, overlapping/unfitted meshes by writing the weak formulation of fluid and structure problems in their physical domains.…”