Stable loosely-coupled-type algorithm for fluid–structure interaction in blood flow

Abstract

We introduce a novel loosely coupled-type algorithm for fluid–structure interaction between blood flow and thin vascular walls. This algorithm successfully deals with the difficulties associated with the “added mass effect”, which is known to be the cause of numerical instabilities in fluid–structure interaction problems involving fluid and structure of comparable densities. Our algorithm is based on a time-discretization via operator splitting which is applied, in a novel way, to separate the fluid sub-problem from the structure elastodynamics sub-problem. In contrast with traditional loosely-coupled schemes, no iterations are necessary between the fluid and structure sub-problems; this is due to the fact that our novel splitting strategy uses the “added mass effect” to stabilize rather than to destabilize the numerical algorithm. This stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub-problem. The stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable. Due to the crucial role played by the kinematic lateral boundary condition, the proposed algorithm is named the “kinematically coupled scheme”.