Numerical investigations of the compressible Navier-Stokes system
ESAIM. Proceedings, Tome 70 (2021), pp. 1-13
Cet article a éte moissonné depuis la source EDP Sciences
In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations:a staggered scheme based on the Rusanov one for the inviscid (Euler) system,a staggered pseudo-Lagrangian scheme in which the mesh “follows” the fluid,the Eulerian projection (on a fixed mesh) of the preceding scheme.All these schemes only involve the resolution of linear systems (all the nonlinear terms are solved in an explicit way). We propose numerical illustrations of their behaviors on particular solutions in which the density has discontinuities (hereafter called Hoff solutions). We show that the three schemes seem to converge to the same solutions, and we compare the evolution of the amplitude of the discontinuity of the numerical solution (with the pseudo-Lagrangian scheme) with the one predicted by Hoff and observe a good agreement.
Affiliations des auteurs :
Bilal Al-Taki 1 ; Kevin Atsou 2 ; Jean-Jéróme Casanova 3 ; Thierry Goudon 2 ; Pauline Lafitte 4 ; Frédéric Lagoutière 5 ; Sebastian Minjeaud 2
@article{EP_2021_70_a1,
author = {Bilal Al-Taki and Kevin Atsou and Jean-J\'er\'ome Casanova and Thierry Goudon and Pauline Lafitte and Fr\'ed\'eric Lagouti\`ere and Sebastian Minjeaud},
title = {Numerical investigations of the compressible {Navier-Stokes} system},
journal = {ESAIM. Proceedings},
pages = {1--13},
year = {2021},
volume = {70},
doi = {10.1051/proc/202107001},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202107001/}
}
TY - JOUR AU - Bilal Al-Taki AU - Kevin Atsou AU - Jean-Jéróme Casanova AU - Thierry Goudon AU - Pauline Lafitte AU - Frédéric Lagoutière AU - Sebastian Minjeaud TI - Numerical investigations of the compressible Navier-Stokes system JO - ESAIM. Proceedings PY - 2021 SP - 1 EP - 13 VL - 70 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202107001/ DO - 10.1051/proc/202107001 LA - en ID - EP_2021_70_a1 ER -
%0 Journal Article %A Bilal Al-Taki %A Kevin Atsou %A Jean-Jéróme Casanova %A Thierry Goudon %A Pauline Lafitte %A Frédéric Lagoutière %A Sebastian Minjeaud %T Numerical investigations of the compressible Navier-Stokes system %J ESAIM. Proceedings %D 2021 %P 1-13 %V 70 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202107001/ %R 10.1051/proc/202107001 %G en %F EP_2021_70_a1
Bilal Al-Taki; Kevin Atsou; Jean-Jéróme Casanova; Thierry Goudon; Pauline Lafitte; Frédéric Lagoutière; Sebastian Minjeaud. Numerical investigations of the compressible Navier-Stokes system. ESAIM. Proceedings, Tome 70 (2021), pp. 1-13. doi: 10.1051/proc/202107001
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