On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 4, pp. 743-769.

We consider the coupling between three-dimensional ($3$D) and one-dimensional ($1$D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The $1$D model is a hyperbolic system of partial differential equations. The $3$D 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 $3$D-$1$D FSI coupling. We consider several possible models for the mechanics of the vessel wall in the $3$D problem and show how the $3$D-$1$D coupling depends on them. Several comparative numerical tests illustrating the coupling are presented.

DOI : https://doi.org/10.1051/m2an:2007039
Classification : 65M12,  65M60,  92C50,  74F10,  76Z05
Mots clés : fluid-structure interaction, 3D-1D FSI coupling, energy estimate, multiscale models
@article{M2AN_2007__41_4_743_0,
author = {Formaggia, Luca and Moura, Alexandra and Nobile, Fabio},
title = {On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {743--769},
publisher = {EDP-Sciences},
volume = {41},
number = {4},
year = {2007},
doi = {10.1051/m2an:2007039},
zbl = {1139.92009},
mrnumber = {2362913},
language = {en},
url = {www.numdam.org/item/M2AN_2007__41_4_743_0/}
}
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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 4, pp. 743-769. doi : 10.1051/m2an:2007039. http://www.numdam.org/item/M2AN_2007__41_4_743_0/

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