Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T13:08:51.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of Vlasov solversfor spacecraft charging simulation

Published online by Cambridge University Press:  16 December 2009

Nicolas Vauchelet ,
Jean-Paul Dudon ,
Christophe Besse  and
Thierry Goudon
Nicolas Vauchelet
Affiliation:
Project-Team SIMPAF, INRIA Lille Nord Europe Research Centre, 40 Avenue Halley, Park Plazza, 59650 Villeneuve D'Ascq, France. Current address: Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, Université Paris 6, 75005 Paris, France. [email protected]
Jean-Paul Dudon
Affiliation:
Thales Alenia Space, 100 bd. du Midi, 06156 Cannes La Bocca Cedex, France. [email protected]
Christophe Besse
Affiliation:
Project-Team SIMPAF, INRIA Lille Nord Europe Research Centre, 40 Avenue Halley, Park Plazza, 59650 Villeneuve D'Ascq, France. Laboratoire Paul Painlevé UMR 8524 CNRS–Université des Sciences et Technologies de Lille, France. [email protected]; [email protected]
Thierry Goudon
Affiliation:
Project-Team SIMPAF, INRIA Lille Nord Europe Research Centre, 40 Avenue Halley, Park Plazza, 59650 Villeneuve D'Ascq, France. Laboratoire Paul Painlevé UMR 8524 CNRS–Université des Sciences et Technologies de Lille, France. [email protected]; [email protected]
Get access

Abstract

The modelling and the numerical resolution of the electrical charging of aspacecraft 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.

Keywords

Vlasov-Poisson equationsparticles methodsfinite volume methodssemi-Lagrangian methods
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 1 , January 2010 , pp. 109 - 131
Copyright
© EDP Sciences, SMAI, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Belaouar, R., Crouseilles, N., Degond, P. and Sonnendrücker, E., An asymptotically stable semi-lagrangian scheme in the quasi-neutral limit. J. Sci. Comput. 41 (2009) 341–365. CrossRef
C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation. Institute of Physics Publishing, Bristol and Philadelphia (1991).
Carrillo, J.A. and Vecil, F., Non-oscillatory interpolation methods applied to Vlasov-based models. SIAM J. Sci. Comput. 29 (2007) 1179–1206. CrossRef
Chane-Yook, M., Clerc, S. and Piperno, S., Space charge and potential distribution around a spacecraft in a isotropic plasma. J. Geophys. Res. - Space Physics 111 (2006) A04211. CrossRef
O. Chanrion, 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).
J.-P. Chehab, A. Cohen, D. Jennequin, J.J. Nieto, Ch. Roland and J.-R. Roche, 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.
M. Cho, Arcing on high voltage solar arrays in low earth orbit: theory and computer particle simulation. Ph.D. Thesis, Massachusetts Institute of Technology, USA (1992).
S. Clerc, S. Brosse and M. Chane-Yook, Sparcs: an advanced software for spacecraft charging analysis, in 8th Spacecraft Charging Tech. Conf., Huntsville, USA (2003).
G.-H. Cottet and P.-A. Raviart, Particle methods for the one-dimensional Vlasov–Poisson equations. SIAM J. Numer. Anal. 21 (1984) 52–76.
P. Crispel, 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).
Crispel, P., Degond, P. and Vignal, M.-H., Quasi-neutral fluid models for current-carrying plasmas. J. Comput. Phys. 205 (2005) 408–438. CrossRef
Crouseilles, N. and Filbet, F., Numerical approximation of collisional plasma by high order methods. J. Comp. Phys. 201 (2004) 546–572. CrossRef
Crouseilles, N., Latu, G. and Sonnendrücker, E., Hermite spline interpolation on patches for parallely solving the Vlasov-Poisson equation. Int. J. Appl. Math. Comput. Sci. 17 (2007) 101–115. CrossRef
P. Degond, F. Deluzet and L. Navoret, 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.
Filbet, F. and Sonnendrücker, E., Comparison of Eulerian Solver. Comput. Phys. Comm. 150 (2003) 247–266. CrossRef
Filbet, F., Sonnendrücker, E. and Bertrand, P., Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172 (2001) 166–187. CrossRef
Forest, J., Hilgers, A., Thiebault, B., Eliasson, L., Berthelier, J.-J. and de Feraudy, H., An open-source spacecraft plasma interaction simulation code PicUp3D: tests and validations. IEEE Trans. Plasma Sci. 34 (2006) 2103–2113. CrossRef
Ghizzo, A., Bertrand, P., Shoucri, M., Johnston, T.W., Filjakow, E. and Feix, M.R., Vlasov, A code for the numerical simulation of stimulated Raman scattering. J. Comput. Phys. 90 (1990) 431. CrossRef
Grandgirard, V., Brunetti, M., Bertrand, P., Besse, N., Garbet, X., Ghendrih, P., Manfredi, G., Sarazin, Y., Sauter, O., Sonnendrücker, E., Vaclavik, J. and Villard, L., A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation. J. Comput. Phys. 217 (2006) 395–423. CrossRef
R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics – ETH-Zurich. Birkhauser-Verlag, Basel, Switzerland (1990).
L. Lévy, 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).
M.J. Mandell, V.A. Davies and L.G. Mikelides, NASCAP-2K Preliminary Documentation. Science Applications International Corp. San Diego, USA, Scientific rept. no. 2, A555024 (2002).
Mandell, M.J., Davies, V.A., Cooke, D.L., Wheelock, A.T. and Roth, C.J., Nascap-2k spacecraft charging code overview. IEEE Trans. Plasma Sci. 34 (2006) 2084–2093. CrossRef
A.P. Plokhikh, V.G. Malko and V.A. Semenov, 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).
Roussel, J.-F., Spacecraft plasma environment and contamination simulation code: description and first tests. J. Spacecr. Rockets 35 (1998) 205–211.
J.-F. Roussel, 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).
J.F. Roussel, F. Rogier, M. Lemoine, D. Volpert, G. Rousseau, G. Sookahet, P. Sng and A. Hilgers, 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).
Shoucri, M. and Knorr, G., Numerical integration of the Vlasov equation. J. Comput. Phys. 14 (1974) 84–92. CrossRef
E. Sonnendrücker, 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).
Sonnendrücker, E., Roche, J., Bertrand, P. and Ghizzo, A., The semi-lagrangian method for the numerical resolution of the Vlasov equation. J. Comput. Phys. 149 (1999) 201–220. CrossRef