Numerical investigations of the compressible Navier-Stokes system
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 “follow...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2021-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2021/01/proc2107001.pdf |
| _version_ | 1797968402606718976 |
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| author | Al-Taki Bilal Atsou Kevin Casanova Jean-Jéróme Goudon Thierry Lafitte Pauline Lagoutière Frédéric Minjeaud Sebastian |
| author_facet | Al-Taki Bilal Atsou Kevin Casanova Jean-Jéróme Goudon Thierry Lafitte Pauline Lagoutière Frédéric Minjeaud Sebastian |
| author_sort | Al-Taki Bilal |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T02:45:14Z |
| format | Article |
| id | doaj.art-34de5b69db8048ec837aa534b1a879f9 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T02:45:14Z |
| publishDate | 2021-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-34de5b69db8048ec837aa534b1a879f92023-01-02T17:57:56ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592021-01-017011310.1051/proc/202107001proc2107001Numerical investigations of the compressible Navier-Stokes systemAl-Taki Bilal0Atsou Kevin1Casanova Jean-Jéróme2Goudon Thierry3Lafitte Pauline4Lagoutière Frédéric5Minjeaud Sebastian6B.I.C.M.R, Peking UniversityUniversité Côte d’Azur, Inria, CNRS, LJADCeremade, Université Paris Dauphine, PSL, CNRSUniversité Côte d’Azur, Inria, CNRS, LJADCentraleSupelec, Fédération de Mathématiques FR CNRS 3487, Laboratoire MICSInstitut Camille Jordan, Université Claude BernardUniversité Côte d’Azur, Inria, CNRS, LJADIn 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.https://www.esaim-proc.org/articles/proc/pdf/2021/01/proc2107001.pdf |
| spellingShingle | Al-Taki Bilal Atsou Kevin Casanova Jean-Jéróme Goudon Thierry Lafitte Pauline Lagoutière Frédéric Minjeaud Sebastian Numerical investigations of the compressible Navier-Stokes system ESAIM: Proceedings and Surveys |
| title | Numerical investigations of the compressible Navier-Stokes system |
| title_full | Numerical investigations of the compressible Navier-Stokes system |
| title_fullStr | Numerical investigations of the compressible Navier-Stokes system |
| title_full_unstemmed | Numerical investigations of the compressible Navier-Stokes system |
| title_short | Numerical investigations of the compressible Navier-Stokes system |
| title_sort | numerical investigations of the compressible navier stokes system |
| url | https://www.esaim-proc.org/articles/proc/pdf/2021/01/proc2107001.pdf |
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