ESAIM: Mathematical Modelling and Numerical Analysis

Table of Contents - November 2008 - Volume 42 - Issue06

Research Article

Numerical simulation of blood flows through a porous interface

Fernández, Miguel A.a1, Gerbeau, Jean-Frédérica1 and Martin, Vincenta2

a1 INRIA Paris-Rocquencourt, BP 105, 78153 Le Chesnay, France. Miguel.Fernandez@inria.fr; Jean-Frederic.Gerbeau@inria.fr

a2 University of Technology of Compiègne, LMAC, GI, Royallieu, BP 20529, 60205 Compiègne, France. Vincent.Martin@utc.fr

Abstract

We propose a model for a medical device, called a stent, designed for the treatment of cerebral aneurysms. The stent consists of a grid, immersed in the blood flow and located at the inlet of the aneurysm. It aims at promoting a clot within the aneurysm. The blood flow is modelled by the incompressible Navier-Stokes equations and the stent by a dissipative surface term. We propose a stabilized finite element method for this model and we analyse its convergence in the case of the Stokes equations. We present numerical results for academical test cases, and on a realistic aneurysm obtained from medical imaging.

(Received February 5 2007)

(Online publication August 12 2008)

Key Words:

  • Stabilized finite element;
  • sieve problem;
  • blood flow;
  • terminal aneurysm;
  • stent;
  • fluid-structure interaction.

Mathematics Subject Classification:

  • 65M60;
  • 74K25;
  • 76D05;
  • 76Z05
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