The modelling and the numerical resolution of the electrical charging of a spacecraft in interaction with the Earth magnetosphere is considered. It involves the Vlasov-Poisson system, endowed with non standard boundary conditions. We discuss the pros and cons of several numerical methods for solving this system, using as benchmark a simple 1D model which exhibits the main difficulties of the original models.
Mots-clés : Vlasov-Poisson equations, particles methods, finite volume methods, semi-lagrangian methods
@article{M2AN_2010__44_1_109_0,
author = {Vauchelet, Nicolas and Dudon, Jean-Paul and Besse, Christophe and Goudon, Thierry},
title = {Comparison of {Vlasov} solvers for spacecraft charging simulation},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {109--131},
publisher = {EDP-Sciences},
volume = {44},
number = {1},
year = {2010},
doi = {10.1051/m2an/2009042},
mrnumber = {2647755},
zbl = {1193.82046},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2009042/}
}
TY - JOUR AU - Vauchelet, Nicolas AU - Dudon, Jean-Paul AU - Besse, Christophe AU - Goudon, Thierry TI - Comparison of Vlasov solvers for spacecraft charging simulation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 109 EP - 131 VL - 44 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2009042/ DO - 10.1051/m2an/2009042 LA - en ID - M2AN_2010__44_1_109_0 ER -
%0 Journal Article %A Vauchelet, Nicolas %A Dudon, Jean-Paul %A Besse, Christophe %A Goudon, Thierry %T Comparison of Vlasov solvers for spacecraft charging simulation %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 109-131 %V 44 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2009042/ %R 10.1051/m2an/2009042 %G en %F M2AN_2010__44_1_109_0
Vauchelet, Nicolas; Dudon, Jean-Paul; Besse, Christophe; Goudon, Thierry. Comparison of Vlasov solvers for spacecraft charging simulation. ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 1, pp. 109-131. doi : 10.1051/m2an/2009042. http://archive.numdam.org/articles/10.1051/m2an/2009042/
[1] , , and , An asymptotically stable semi-lagrangian scheme in the quasi-neutral limit. J. Sci. Comput. 41 (2009) 341-365. | Zbl
[2] and , Plasma Physics via Computer Simulation. Institute of Physics Publishing, Bristol and Philadelphia (1991).
[3] and , Non-oscillatory interpolation methods applied to Vlasov-based models. SIAM J. Sci. Comput. 29 (2007) 1179-1206. | Zbl
[4] , and , Space charge and potential distribution around a spacecraft in a isotropic plasma. J. Geophys. Res. - Space Physics 111 (2006) A04211.
[5] , Simulation de l'influence de la propulsion plasmique sur la charge électrostatique d'un satellite en milieu magnétosphérique. Ph.D. Thesis, École nationale des ponts et chaussées, France (2001).
[6] , , , , and , An adaptive particle-in-cell method using multi-resolution analysis, in Numerical methods for hyperbolic and kinetic problems, IRMA Lect. Math. Theor. Phys. 7, S. Cordier, T. Goudon, M. Gutnic and E. Sonnendrücker Eds., Eur. Math. Soc., Zürich, Switzerland (2005) 29-42.
[7] , Arcing on high voltage solar arrays in low earth orbit: theory and computer particle simulation. Ph.D. Thesis, Massachusetts Institute of Technology, USA (1992).
[8] , and , Sparcs: an advanced software for spacecraft charging analysis, in 8th Spacecraft Charging Tech. Conf., Huntsville, USA (2003).
[9] and , Particle methods for the one-dimensional Vlasov-Poisson equations. SIAM J. Numer. Anal. 21 (1984) 52-76. | Zbl
[10] , Modélisation mathématique et simulation de la transition d'une décharge électrostatique primaire vers un arc électrique secondaire entretenu par la puissance photovoltaïque d'un générateur solaire de satellite. Ph.D. Thesis, Université Paul Sabatier Toulouse III, France (2006).
[11] , and , Quasi-neutral fluid models for current-carrying plasmas. J. Comput. Phys. 205 (2005) 408-438. | Zbl
[12] and , Numerical approximation of collisional plasma by high order methods. J. Comp. Phys. 201 (2004) 546-572. | Zbl
[13] , and , Hermite spline interpolation on patches for parallely solving the Vlasov-Poisson equation. Int. J. Appl. Math. Comput. Sci. 17 (2007) 101-115. | Zbl
[14] , and , An asymptotically stable Particle-In-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality. C. R. Acad. Sci. Paris, Ser. I 343 (2006) 613-618. | Zbl
[15] and , Comparison of Eulerian Solver. Comput. Phys. Comm. 150 (2003) 247-266. | Zbl
[16] , and , Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172 (2001) 166-187. | Zbl
[17] , , , , and , An open-source spacecraft plasma interaction simulation code PicUp3D: tests and validations. IEEE Trans. Plasma Sci. 34 (2006) 2103-2113.
[18] , , , , and , A Vlasov code for the numerical simulation of stimulated Raman scattering. J. Comput. Phys. 90 (1990) 431. | Zbl
[19] , , , , , , , , , , and , A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation. J. Comput. Phys. 217 (2006) 395-423. | Zbl
[20] , Numerical Methods for Conservation Laws, Lectures in Mathematics - ETH-Zurich. Birkhauser-Verlag, Basel, Switzerland (1990). | Zbl
[21] , Charge des matériaux et systèmes en environnement spatial, CERT-ONERA, in Space environment prevention of risks related to spacecraft charging, Éditions Cepaduès, Toulouse, France (1996).
[22] , and , NASCAP-2K Preliminary Documentation. Science Applications International Corp. San Diego, USA, Scientific rept. no. 2, A555024 (2002).
[23] , , , and , Nascap-2k spacecraft charging code overview. IEEE Trans. Plasma Sci. 34 (2006) 2084-2093.
[24] , and , Escape software modeling for the electrostatic charging with electric propulsion in the ionosphere earth. Manuel d'utilisation v-1, Research Institute of Applied Mechanics and Electrodynamics, Moscou, Russia (1998).
[25] , Spacecraft plasma environment and contamination simulation code: description and first tests. J. Spacecr. Rockets 35 (1998) 205-211.
[26] , Modelling of spacecraft plasma environment interactions, in Spacecraft Charging Technology, Proceedings of the Seventh International Conference held 23-27 April, 2001 at ESTEC, Noordwijk, The Netherlands, R.A. Harris Ed., European Space Agency, ESA SP-476 (2001).
[27] , , , , , , and , Design of a new modular spacecraft plasma interaction modeling software (SPIS), in Proceedings of the 8th Spacecraft Charging Tech. Conf., Huntsville, USA, October 20-24 (2003).
[28] and , Numerical integration of the Vlasov equation. J. Comput. Phys. 14 (1974) 84-92. | Zbl
[29] , Méthodes semi-Lagrangiennes pour la résolution numérique de l'équation de Vlasov, in Lecture notes CEA-EDF-INRIA School on “Modèles numériques pour la fusion contrôlée”, Nice, France (2008).
[30] , , and , The semi-lagrangian method for the numerical resolution of the Vlasov equation. J. Comput. Phys. 149 (1999) 201-220. | Zbl
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