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A ‘well-balanced’ finite volume scheme for blood flow simulation

Authors

  • O. Delestre,

    Corresponding author
    • CNRS and UPMC Université Paris 06, UMR 7190, 4 place Jussieu, Institut Jean Le Rond d'Alembert, Boîte 162, Paris, France
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    • Presently at: Laboratoire de Mathématiques J.A. Dieudonné (UMR CNRS 7351) – Polytech Nice-Sophia, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice cedex 02, France

  • P.-Y. Lagrée

    1. CNRS and UPMC Université Paris 06, UMR 7190, 4 place Jussieu, Institut Jean Le Rond d'Alembert, Boîte 162, Paris, France
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Correspondence to: O. Delestre, CNRS and UPMC Université Paris 06, UMR 7190, 4 place Jussieu, Institut Jean Le Rond d'Alembert, Boîte 162, F-75005 Paris, France.

E-mail: Delestre@unice.fr

SUMMARY

We are interested in simulating blood flow in arteries with a one-dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme, which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On the contrary, the proposed scheme is ‘well-balanced’: it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism. Copyright © 2012 John Wiley & Sons, Ltd.

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