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Pressure boundary conditions for blood flows

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Abstract

Simulations of blood flows in arteries require numerical solutions of fluidstructure interactions involving Navier-Stokes equations coupled with large displacement visco-elasticity for the vessels.

Among the various simplifications which have been proposed, the surface pressure model leads to a hierarchy of simpler models including one that involves only the pressure. The model exhibits fundamental frequencies which can be computed and compared with the pulse. Yet unconditionally stable time discretizations can be constructed by combining implicit time schemes with Galerkin-characteristic discretization of the convection terms in the Navier-Stokes equations. Such problems with prescribed pressure on the walls will be shown to be efficient and accurate as an approximation of the full fluid structure interaction problem.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, V5A 1S6, BC, Canada

    Kirill P. Gostaf

  2. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Place Jussieu, Boite 187, Paris, 75252, France

    Olivier Pironneau

Authors
  1. Kirill P. Gostaf
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  2. Olivier Pironneau
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Correspondence to Kirill P. Gostaf.

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In Honor of the Scientific Contributions of Professor Luc Tartar

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Gostaf, K.P., Pironneau, O. Pressure boundary conditions for blood flows. Chin. Ann. Math. Ser. B 36, 829–842 (2015). https://doi.org/10.1007/s11401-015-0983-8

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  • DOI: https://doi.org/10.1007/s11401-015-0983-8

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