|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 $3$D problem and show how the 3D-1D coupling depends on them.
Several comparative numerical tests illustrating the coupling are presented.|
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Formaggia, L.; Moura, A.; Nobile, F. , On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations , M2AN, 2007, 41, 743-769