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On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations

Luca Formaggia, Alexandra Moura, Fabio Nobile

ESAIM Mathematical Modelling and Numerical Analysis · 2007 · 86 citations · 31 references

Open access

TL;DR

The study examines coupling between three‑dimensional and one‑dimensional fluid‑structure interaction models for blood flow in compliant vessels. The authors aim to derive an energy estimate for the fully coupled 3D‑1D FSI system. They employ a hyperbolic 1D model, a Navier‑Stokes 3D model with vessel wall dynamics, a non‑standard Navier‑Stokes formulation for appropriate coupling boundary conditions, and investigate several vessel‑wall mechanics to assess coupling dependence. An energy estimate for the coupled system is obtained, the dependence of the coupling on vessel‑wall mechanics is demonstrated, and comparative numerical tests illustrate the coupling behavior.

Abstract

We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the coupling of the models. With this we derive an energy estimate for the fully 3D-1D FSI coupling. We consider several possible models for the mechanics of the vessel wall in the 3D problem and show how the 3D-1D coupling depends on them. Several comparative numerical tests illustrating the coupling are presented.