Geodesic
Numerical investigations of the compressible Navier-Stokes system
Bilal Al-Taki1 ; Kevin Atsou2 ; Jean-Jéróme Casanova3 ; Thierry Goudon2 ; Pauline Lafitte4 ; Frédéric Lagoutière5 ; Sebastian Minjeaud2
1B.I.C.M.R, Peking University, Beijing, China
2Université Côte d’Azur, Inria, CNRS, LJAD
3Ceremade, Université Paris Dauphine, PSL, CNRS
4CentraleSupelec, Fédération de Mathématiques FR CNRS 3487, Laboratoire MICS
5Institut Camille Jordan, Université Claude Bernard, Lyon
ESAIM. Proceedings, Tome 70 (2021), pp. 1-13
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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.
DOI : 10.1051/proc/202107001

Bilal Al-Taki  1   ; Kevin Atsou  2   ; Jean-Jéróme Casanova  3   ; Thierry Goudon  2   ; Pauline Lafitte  4   ; Frédéric Lagoutière  5   ; Sebastian Minjeaud  2

1 B.I.C.M.R, Peking University, Beijing, China
2 Université Côte d’Azur, Inria, CNRS, LJAD
3 Ceremade, Université Paris Dauphine, PSL, CNRS
4 CentraleSupelec, Fédération de Mathématiques FR CNRS 3487, Laboratoire MICS
5 Institut Camille Jordan, Université Claude Bernard, Lyon 
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     title = {Numerical investigations of the compressible {Navier-Stokes} system},
     journal = {ESAIM. Proceedings},
     pages = {1--13},
     year = {2021},
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     doi = {10.1051/proc/202107001},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202107001/}
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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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