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 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.

Published in:
Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 41, 4, 743-769

 Record created 2012-04-23, last modified 2018-03-13

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