On the Stability of the Coupling of 3d and 1d Fluid-structure Interaction Models for Blood Flow Simulations

We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluidstructure 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 3D1D 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. Mathematics Subject Classification. 65M12, 65M60, 92C50, 74F10, 76Z05. Received November 15, 2006. Revised March 19, 2007.