Evaluation of a new Implicit Coupling Algorithm for the Partitioned Fluid-Structure Interaction Simulation of Bileaflet Mechanical Heart Valves

We present a newly developed Fluid-Structure Interaction coupling algorithm to simulate Bileaflet Mechanical Heart Valves dynamics in a partitioned way. The coupling iterations between the flow solver and the leaflet motion solver are accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet acceleration. This Jacobian is used in the leaflet motion solver when new positions of the leaflets are computed during the coupling iterations. The Jacobian is numerically derived from the flow solver by applying leaflet perturbations. Instead of calculating this Jacobian every time step, the Jacobian is extrapolated from previous time steps and a recalculation of the Jacobian is only done when needed. The efficiency of our new algorithm is subsequently compared to existing algorithms which use fixed relaxation and dynamic Aitken Delta(2) relaxation in the coupling iterations when the new positions of the leaflets are computed. Results show that dynamic Aitken Delta(2) relaxation outperforms fixed relaxation. Moreover, during the opening phase of the valve, our new algorithm needs fewer subiterations per time step to achieve convergence than the method with Aitken Delta(2) relaxation. Thus, our newly developed FSI coupling scheme outperforms the existing coupling schemes.