On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 4, pp. 743-769.

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.

DOI : 10.1051/m2an:2007039
Classification : 65M12, 65M60, 92C50, 74F10, 76Z05
Mots clés : fluid-structure interaction, 3D-1D FSI coupling, energy estimate, multiscale models
Formaggia, Luca 1 ; Moura, Alexandra  ; Nobile, Fabio 

1 Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy.
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Formaggia, Luca; Moura, Alexandra; Nobile, Fabio. On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 4, pp. 743-769. doi : 10.1051/m2an:2007039. http://archive.numdam.org/articles/10.1051/m2an:2007039/

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