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Pré-publication, Document de travail

Numerical staggered schemes for the free-congested Navier-Stokes equations

Abstract : In this paper we analyze two numerical staggered schemes, one fully implicit, the other semiimplicit, for the compressible Navier-Stokes equations with a singular pressure law; system which degenerates towards the free-congested Navier-Stokes equations with the density constraint 0 ≤ ρ ≤ 1 as the intensity of the pressure, ε, tends to 0. The two schemes are shown to "preserve" the limit ε → 0, in the following sense: via discrete energy and pressure estimates we control uniformly with respect to ε the discrete density, velocity and pressure; and, as ε → 0, the limit pressure is shown to be activated only in the congested region where the discrete limit density is maximal, equal to 1. Finally, the semi-implicit scheme is implemented via the software CALIF 3 S on 1D and 2D test cases and the numerical solutions are shown to capture well the transition between the congested regions {ρ = 1} and the free regions {ρ < 1}.
Type de document :
Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-03300103
Contributeur : Charlotte Perrin <>
Soumis le : lundi 26 juillet 2021 - 19:25:38
Dernière modification le : samedi 31 juillet 2021 - 09:07:05