Artificial boundaries and formulations for the incompressible Navier-Stokes equations. Applications to air and blood flows.

Justine Fouchet-Incaux 1, 2, *
* Corresponding author
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
2 ANEDP
LM-Orsay - Laboratoire de Mathématiques d'Orsay
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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Justine Fouchet-Incaux. Artificial boundaries and formulations for the incompressible Navier-Stokes equations. Applications to air and blood flows.. SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2014, pp.40. ⟨10.1007/s40324-014-0012-y⟩. ⟨hal-00926273⟩

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