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Artificial boundaries and formulations for the incompressible Navier–Stokes equations: applications to air and blood flows

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Abstract

We deal with numerical simulations of incompressible Navier–Stokes equations in truncated domain. In this context, the formulation of these equations has to be selected carefully in order to guarantee that their associated artificial boundary conditions are relevant for the considered problem. In this paper, we review some of the formulations proposed in the literature, and their associated boundary conditions. Some numerical results linked to each formulation are also presented. We compare different schemes, giving successful computations as well as problematic ones, in order to better understand the difference between these schemes and their behaviours dealing with systems involving Neumann boundary conditions. We also review two stabilization methods which aim at suppressing the instabilities linked to these natural boundary conditions.

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Acknowledgments

The author wants to thank Céline Grandmont and Sébastien Martin for valuable discussions and for their very helpful feedbacks on the manuscript, and Bertrand Maury for his fruitful remarks. The present work has been partially supported by the Agence Nationale de la Recherche (ANR) through the projects ANR-11-TECS-006 (OxHelease) and ANR-08-JCJC-013-01 (M3RS).

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  1. Laboratoire de Mathématiques d’Orsay, Université Paris-Sud 11, 91405 , Orsay Cedex, France

    Justine Fouchet-Incaux

  2. INRIA-Paris-Rocquencourt, EPC REO, Domaine de Voluceau, BP105, 78153,  Le Chesnay Cedex, France

    Justine Fouchet-Incaux

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Fouchet-Incaux, J. Artificial boundaries and formulations for the incompressible Navier–Stokes equations: applications to air and blood flows. SeMA 64, 1–40 (2014). https://doi.org/10.1007/s40324-014-0012-y

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