On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
MOX - Modelling and Scientific Computing,
Department of Mathematics, Politecnico di Milano,
Italy. firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
Revised: 19 March 2007
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