Geodesic
Numerical approximation of Knudsen layer for the Euler-Poisson system
Fréderique Charles1 ; Nicolas Vauchelet1 ; Christophe Besse2, 3 ; Thierry Goudon2, 3 ; Ingrid Lacroix–Violet2, 3 ; Jean-Paul Dudon4 ; Laurent Navoret5
1 Laboratoire Jacques-Louis Lions - UMR 7598 CNRS & Université Pierre et Marie Curie, Paris VI, France
2 Project Team SIMPAF, INRIA Lille Nord Europe, France
3 Labo Paul Painlevé UMR 8524, CNRS & USTLille, France
4 Thales Alenia Space, Cannes, France
5 Institut Mathématique de Toulouse CNRS & Université Paul Sabatier, Toulouse, France
ESAIM. Proceedings, Tome 32 (2011), pp. 177-194.

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In this work, we consider the computation of the boundary conditions for the linearized Euler–Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the boundary layers. In this paper, we will extend these techniques in the case of the coupled Euler-Poisson system.
DOI : 10.1051/proc/2011020

Fréderique Charles 1 ; Nicolas Vauchelet 1 ; Christophe Besse 2, 3 ; Thierry Goudon 2, 3 ; Ingrid Lacroix–Violet 2, 3 ; Jean-Paul Dudon 4 ; Laurent Navoret 5

1 Laboratoire Jacques-Louis Lions - UMR 7598 CNRS & Université Pierre et Marie Curie, Paris VI, France
2 Project Team SIMPAF, INRIA Lille Nord Europe, France
3 Labo Paul Painlevé UMR 8524, CNRS & USTLille, France
4 Thales Alenia Space, Cannes, France
5 Institut Mathématique de Toulouse CNRS & Université Paul Sabatier, Toulouse, France 
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     author = {Fr\'ederique Charles and Nicolas Vauchelet and Christophe Besse and Thierry Goudon and Ingrid Lacroix{\textendash}Violet and Jean-Paul Dudon and Laurent Navoret},
     title = {Numerical approximation of {Knudsen} layer for the {Euler-Poisson} system},
     journal = {ESAIM. Proceedings},
     pages = {177--194},
     publisher = {mathdoc},
     volume = {32},
     year = {2011},
     doi = {10.1051/proc/2011020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2011020/}
}
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%A Nicolas Vauchelet
%A Christophe Besse
%A Thierry Goudon
%A Ingrid Lacroix–Violet
%A Jean-Paul Dudon
%A Laurent Navoret
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Fréderique Charles; Nicolas Vauchelet; Christophe Besse; Thierry Goudon; Ingrid Lacroix–Violet; Jean-Paul Dudon; Laurent Navoret. Numerical approximation of Knudsen layer for the Euler-Poisson system. ESAIM. Proceedings, Tome 32 (2011), pp. 177-194. doi : 10.1051/proc/2011020. http://geodesic.mathdoc.fr/articles/10.1051/proc/2011020/

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