Comparison of Vlasov solvers for spacecraft charging simulation

Nicolas Vauchelet; Jean-Paul Dudon; Christophe Besse; Thierry Goudon

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 1, page 109-131
  • ISSN: 0764-583X

Abstract

top
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.

How to cite

top

Vauchelet, Nicolas, et al. "Comparison of Vlasov solvers for spacecraft charging simulation." ESAIM: Mathematical Modelling and Numerical Analysis 44.1 (2010): 109-131. <http://eudml.org/doc/250756>.

@article{Vauchelet2010,
abstract = { 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. },
author = {Vauchelet, Nicolas, Dudon, Jean-Paul, Besse, Christophe, Goudon, Thierry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Vlasov-Poisson equations; particles methods; finite volume methods; semi-Lagrangian methods; Vlasov solvers; spacecraft electrical charging; Vlasov equation; semi-Lagrangian method; back-trajectory method},
language = {eng},
month = {3},
number = {1},
pages = {109-131},
publisher = {EDP Sciences},
title = {Comparison of Vlasov solvers for spacecraft charging simulation},
url = {http://eudml.org/doc/250756},
volume = {44},
year = {2010},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 44
IS - 1
SP - 109
EP - 131
AB - 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.
LA - eng
KW - Vlasov-Poisson equations; particles methods; finite volume methods; semi-Lagrangian methods; Vlasov solvers; spacecraft electrical charging; Vlasov equation; semi-Lagrangian method; back-trajectory method
UR - http://eudml.org/doc/250756
ER -

References

top
  1. R. Belaouar, N. Crouseilles, P. Degond and E. Sonnendrücker, An asymptotically stable semi-lagrangian scheme in the quasi-neutral limit. J. Sci. Comput.41 (2009) 341–365.  
  2. C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation. Institute of Physics Publishing, Bristol and Philadelphia (1991).  
  3. J.A. Carrillo and F. Vecil, Non-oscillatory interpolation methods applied to Vlasov-based models. SIAM J. Sci. Comput.29 (2007) 1179–1206.  
  4. M. Chane-Yook, S. Clerc and S. Piperno, Space charge and potential distribution around a spacecraft in a isotropic plasma. J. Geophys. Res. - Space Physics111 (2006) A04211.  
  5. 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).  
  6. 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.  
  7. 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).  
  8. 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).  
  9. G.-H. Cottet and P.-A. Raviart, Particle methods for the one-dimensional Vlasov–Poisson equations. SIAM J. Numer. Anal. 21 (1984) 52–76.  
  10. 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).  
  11. P. Crispel, P. Degond and M.-H. Vignal, Quasi-neutral fluid models for current-carrying plasmas. J. Comput. Phys.205 (2005) 408–438.  
  12. N. Crouseilles and F. Filbet, Numerical approximation of collisional plasma by high order methods. J. Comp. Phys.201 (2004) 546–572.  
  13. N. Crouseilles, G. Latu and E. Sonnendrücker, Hermite spline interpolation on patches for parallely solving the Vlasov-Poisson equation. Int. J. Appl. Math. Comput. Sci.17 (2007) 101–115.  
  14. 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. I343 (2006) 613–618.  
  15. F. Filbet and E. Sonnendrücker, Comparison of Eulerian Solver. Comput. Phys. Comm.150 (2003) 247–266.  
  16. F. Filbet, E. Sonnendrücker and P. Bertrand, Conservative numerical schemes for the Vlasov equation. J. Comput. Phys.172 (2001) 166–187.  
  17. J. Forest, A. Hilgers, B. Thiebault, L. Eliasson, J.-J. Berthelier and H. de Feraudy, An open-source spacecraft plasma interaction simulation code PicUp3D: tests and validations. IEEE Trans. Plasma Sci.34 (2006) 2103–2113.  
  18. A. Ghizzo, P. Bertrand, M. Shoucri, T.W. Johnston, E. Filjakow and M.R. Feix, A Vlasov code for the numerical simulation of stimulated Raman scattering. J. Comput. Phys.90 (1990) 431.  
  19. V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet, P. Ghendrih, G. Manfredi, Y. Sarazin, O. Sauter, E. Sonnendrücker, J. Vaclavik and L. Villard, A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation. J. Comput. Phys.217 (2006) 395–423.  
  20. R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics – ETH-Zurich. Birkhauser-Verlag, Basel, Switzerland (1990).  
  21. 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).  
  22. 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).  
  23. M.J. Mandell, V.A. Davies, D.L. Cooke, A.T. Wheelock and C.J. Roth, Nascap-2k spacecraft charging code overview. IEEE Trans. Plasma Sci.34 (2006) 2084–2093.  
  24. 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).  
  25. J.-F. Roussel, Spacecraft plasma environment and contamination simulation code: description and first tests. J. Spacecr. Rockets35 (1998) 205–211.  
  26. 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).  
  27. 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).  
  28. M. Shoucri and G. Knorr, Numerical integration of the Vlasov equation. J. Comput. Phys.14 (1974) 84–92.  
  29. 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).  
  30. E. Sonnendrücker, J. Roche, P. Bertrand and A. Ghizzo, The semi-lagrangian method for the numerical resolution of the Vlasov equation. J. Comput. Phys.149 (1999) 201–220.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.