A time-periodic approach for fluid-structure interaction in distensible vessels

The analysis of periodic unsteady incompressible flow inside compliant vessels is of considerable interest for the simulation of blood flow in arteries. Weakly coupled fluid-structure interaction (FSI) models seem to be most suitable for this purpose. For weakly coupled solution methods, however, often convergence may not be achieved for compliant vessels with an axial length scale that is large compared to the characteristic radius. In this study, a time-periodic method for weakly coupled FSI models is presented. Approximate solutions of subsequent time-periods are obtained using the solution of the previous time-period as an initial solution. For the first period, not only suitable boundary conditions are derived from a 1-D wave propagation model, but also the initial axial pressure distribution. The time-periodic method was successfully applied to straight, curved and bifurcating geometries. The new approach proves to have a far better computational stability than weakly coupled methods based on timestep-wise coupling, especially in vessels with a length that is an order of magnitude larger than the radius.