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

Luca Formaggia; Alexandra Moura; Fabio Nobile

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 4, page 743-769
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Formaggia, Luca, Moura, Alexandra, and 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 41.4 (2007): 743-769. <http://eudml.org/doc/250040>.

@article{Formaggia2007,
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. },
author = {Formaggia, Luca, Moura, Alexandra, Nobile, Fabio},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Fluid-structure interaction; 3D-1D FSI coupling; energy estimate; multiscale models.},
language = {eng},
month = {10},
number = {4},
pages = {743-769},
publisher = {EDP Sciences},
title = {On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations},
url = {http://eudml.org/doc/250040},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Formaggia, Luca
AU - Moura, Alexandra
AU - Nobile, Fabio
TI - On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/10//
PB - EDP Sciences
VL - 41
IS - 4
SP - 743
EP - 769
AB - 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.
LA - eng
KW - Fluid-structure interaction; 3D-1D FSI coupling; energy estimate; multiscale models.
UR - http://eudml.org/doc/250040
ER -

References

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