Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement

TL;DR

This paper introduces a new stable and accurate partitioned numerical scheme for fluid-structure interaction in blood flow, allowing for non-zero longitudinal displacement of arterial walls, with promising performance and modularity.

Contribution

A novel loosely coupled scheme using modified Lie splitting for FSI in blood flow that handles longitudinal wall displacement with improved accuracy and stability.

Findings

Scheme is unconditionally stable.

Accuracy comparable to monolithic schemes.

Retains advantages of partitioned methods.

Abstract

We present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. Arterial walls are modeled by a {linearly viscoelastic, cylindrical Koiter shell model capturing both radial and longitudinal displacement}. Fluid flow is modeled by the Navier-Stokes equations for an incompressible, viscous fluid. The two are fully coupled via kinematic and dynamic coupling conditions. Our numerical scheme is based on a new modified Lie operator splitting that decouples the fluid and structure sub-problems in a way that leads to a loosely coupled scheme which is {unconditionally} stable. This was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub-problems, leading to an implicit coupling between the fluid and structure velocities. The proposed scheme is a modification of the recently introduced "kinematically coupled scheme" for which the newly proposed modified Lie splitting significantly increases the accuracy. The performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme. It was shown that the accuracy of our scheme was comparable to that of the monolithic scheme, while our scheme retains all the main advantages of partitioned schemes, such as modularity, simple implementation, and low computational costs.