A combined fictitious domain/adaptive meshing method for fluid-structure interaction in heart valves

A new approach for modelling the fluid-structure interaction of flexible heart valves is proposed. Using a finite element method, a Lagrangian description of a non-linear solid and an Eulerian description of a fluid are coupled by a Lagrange multiplier. This multiplier allows the solid and fluid mesh to be non-conform. Solid displacements and fluid velocities are described well in such a fictitious domain approach. However, the accuracy of pressures and shear stresses in the vicinity of the solid are poor. Therefore an inexpensive mesh-adaptation algorithm is applied, which adapts the fluid mesh to the position of the solid mesh every time step. This minor adjustment of the fluid mesh makes it possible to sustain a physiological pressure gradient across a solid leaflet. Furthermore, shear stresses can be computed at both sides of the leaflet. The method is demonstrated for a 2D example, however with a scope to 3D modelling.