A fluid–structure interaction method with solid-rigid contact for heart valve dynamics

A computational method is proposed for problems where fluid–structure interaction is combined with solid-rigid contact. This combination is particularly important for the dynamics and impact of heart valves. The Navier–Stokes equation in an Eulerian setting is coupled to a Neo-Hookean solid model using a Lagrangian description. A fictitious domain method extended with a local mesh adaptation algorithm provides the required flexibility with respect to the motion and deformation of the valve. In addition, it ensures the solids ability of sustaining pressures present in the fluid. Making use of the fact that the fluid and solid mesh are not required to be connected conformingly, it is shown that the model can be extended with a contact algorithm without introducing meshing complications near the contact surfaces.