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Issue ESAIM: M2AN
Volume 41, Number 4, July-August 2007
Page(s) 743 - 769
DOI 10.1051/m2an:2007039
Published online 04 October 2007

M2AN, Vol. 41, N°4, pp. 743-769
DOI: 10.1051/m2an:2007039

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

Luca Formaggia, Alexandra Moura and Fabio Nobile

MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Italy. luca.formaggia@polimi.it; alexandra.moura@polimi.it; fabio.nobile@polimi.it

(Received November 15, 2006. Revised March 19, 2007. Published online 4 October 2007.)

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.


Mathematics Subject Classification. 65M12, 65M60, 92C50, 74F10, 76Z05.

Key words: Fluid-structure interaction, 3D-1D FSI coupling, energy estimate, multiscale models.


© EDP Sciences, SMAI 2007


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