Analysis of a coupled fluid-structure model with applications to hemodynamics

Tomas Chacon-Rebollo (1) , Vivette Girault (1) , François Murat (1) , Olivier Pironneau (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We propose and analyze a simplified fluid-structure coupled model for flows with compliant walls. As in [F. Nobile and C. Vergara, SIAM J. Sci. Comput., 30 (2008), pp. 731–763], the wall reaction to the fluid is modeled by a small displacement viscoelastic shell where the tangential stress components and displacements are neglected. We show that within this small displacement approximation a transpiration condition can be used which does not require an update of the geometry at each time step, for pipe flow at least. Such simplifications lead to a model which is well posed and for which a semi-implicit time discretization can be shown to converge. We present some numerical results and a comparison with a standard test case taken from hemodynamics. The model is more stable and less computer demanding than full models with moving mesh. We apply the model to a three-dimensional arterial flow with a stent. ------ This paper has been published in SIAM J. Numer. Anal., 54, (2016), pp. 994-1019.

Mots clés: fluid-structure interaction; compliant walls; finite element method; convergence analysis; Navier–Stokes equations; blood flow

Domaines: Analyse numérique [cs.NA]

Tomas Chacon-Rebollo, Vivette Girault, François Murat, Olivier Pironneau. Analysis of a coupled fluid-structure model with applications to hemodynamics. SIAM Journal on Numerical Analysis, 2016. ⟨hal-01003208v2⟩