Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit

SIAM Journal on Numerical Analysis

Volumn 46, Issue 3, 2008, Pages 1298-1322

  Degond, Pierre ^a   Liu, Jian Guo ^b   Vignal, Marie Hélène ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b Bldg 142   (United States)

Author keywords

Burgers Poisson; Debye length; Electron plasma; Klein Gordon; Period; Sheath problem; Stiffness

Indexed keywords

BURGERS-POISSON; DEBYE LENGTH; ELECTRON PLASMA; KLEIN-GORDON; PERIOD; SHEATH PROBLEM;

LINEARIZATION; PLASMA STABILITY; POISSON DISTRIBUTION; POISSON EQUATION; STABILITY; SYSTEM STABILITY;

ASYMPTOTIC ANALYSIS;

EID: 55349136613     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/070690584     Document Type: Article

References (32)

1. F. F. CHEN, Introduction to Plasma Physics and Controlled Fusion, 2nd ed., Plenum, New York, 1984.
2. H.-H. CHOE, N. S. YOON, S. S. KIM, AND D.-I. CHOI, A new unconditionally stable algorithm for steady-state fluid simulation of high density plasma discharge, J. Comput. Phys., 170 (2001), pp. 550-561.
3. B. I. COHEN, A. B. LANGDON, AND A. FRIEDMAN, Implicit time integration for plasma simulation, J. Comput. Phys., 46 (1982), pp. 15-53.
4. PH. COLELLA, M. R. DORR, AND D. D. WAKE, A conservative finite difference method for the numerical solution of plasma fluid equations, J. Comput. Phys., 149 (1999), pp. 168-193.
5. M. G. CRANDALL AND A. MAJDA, Monotone difference approximations for scalar conservation laws, Math. Comp., 34 (1980), pp. 1-21.
6. P. CRISPEL, P. DEGOND, C. PARZANI, AND M.-H. VIGNAL, Trois formulations d'un modèle de plasma guasi-neutre avec courant non-nul, C. R. Acad. Sci. Paris Sér. I Math., 338 (2004), pp. 327-332.
7. P. CRISPEL, P. DEGOND, AND M.-H. VIGNAL, An asymptotically stable discretization for the Euler-Poisson system in the quasineutral limit, C. R. Acad. Sci. Paris Sér. I Math., 341 (2005), pp. 323-328.
8. P. CRISPEL, P. DEGOND, AND M.-H. VIGNAL, Quasi-neutral fluid models for current carrying plasmas, J. Comput. Phys., 205 (2005), pp. 408-438.
9. P. CRISPEL, P. DEGOND, AND M.-H. VIGNAL, An asymptotically preserving scheme for the two-fluid Euler-Poisson model in the quasi-neutral limit, J. Comput. Phys., 223 (2007), pp. 208-234.
10. 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 Sér. I Math., 343 (2006), pp. 613-618.
11. P. DEGOND, C. PARZANI, AND M.-H. VIGNAL, Un modèle d'expansion de plasma dans le vide, C. R. Acad. Sci. Paris Sér. I Math., 335 (2002), pp. 399-404.
12. P. DEGOND, C. PARZANI, AND M.-H. VIGNAL, A one-dimensional model of plasma expansion, Math. Comput. Modelling, 38 (2003), pp. 1093-1099.
13. P. DEGOND, C. PARZANI, AND M.-H. VIGNAL, Plasma expansion in vacuum: Modeling the breakdown of quasineutrality, Multiscale Model. Simul., 2 (2003), pp. 158-178.
14. P. DEGOND, C. PARZANI, AND M.-H. VIGNAL, On plasma expansion in vacuum, in Free Boundary Problems: Theory and Applications, P. Colli, C. Verdi, and A. Visintin, eds., Internat. Ser. Numer. Math. 147, Birkhäuser Verlag, Basel, 2004, pp. 103-112.
15. G. DIPESO, D. W. HEWETT, AND G. F. SIMONSON, Extension of the streamlined Darwin model to quasineutral plasmas, J. Comput. Phys., 111 (1994), pp. 237-247.
16. S. FABRE, Stability analysis of the Euler-Poisson equations, J. Comput. Phys., 101 (1992), pp. 445-461.
17. K. FELLNER, AND C. SCHMEISER, Burgers-Poisson: A nonlinear dispersive model equation, SIAM J. Appl. Math., 64 (2004), pp. 1509-1525.
18. R. N. FRANKLIN AND J. R. OCKENDON, Asymptotic matching of plasma and sheath in an active low pressure discharge, J. Plasma Physics, 4 (1970), pp. 371-385.
19. A. FRIEDMAN, Implicit multiscale PIC and related topics, in Workshop on Multiscale Processes in Fusion Plasmas, Institute for Pure and Applied Mathematics, UCLA, Los Angeles, CA, 2005, http://www.ipam.ucla.edu/ publications/fus2005/fus2005.5425.pdf.
20. S. Y. HA AND M. SLEMROD, Global existence of plasma ion sheaths and their dynamics, Comm. Math. Phys., 238 (2003), pp. 149-186.
21. N. A. KRALL AND A. W. TRIVELPIECE, Principles of Plasma Physics, San Francisco Press, San Fransico, CA, 1986.
22. N. N. KUZNECOV AND S. A. VOLOSIN, On monotone difference approximations for a first-order quasi-linear equation, Soviet Math. Dokl., 17 (1976), pp. 1203-1206.
23. A. B. LANGDON, B. I. COHEN, AND A. FRIEDMAN, Direct implicit large time-step particle simulation of plasmas, J. Comput. Phys., 51 (1983), pp. 107-138.
24. G. LAPENTA, F. IINOYA, AND J. U. BRACKBILL, P article-in-cell simulations of glow discharges in complex geometries, IEEE Trans. Plasma Sci., 23 (1995), pp. 769-779.
25. P. A. MARKOWICH, C. RINGHOFER, AND C. SCHMEISER, Semiconductor Equations, Springer, Wien, 1990.
26. R. J. MASON, Implicit moment particle simulation of plasmas, J. Comput. Phys., 41 (1981), pp. 233-244.
27. R. J. MASON, Implicit moment PIC-hybrid simulation of collisional plasmas, J. Comput. Phys., 51 (1983), pp. 484-501.
28. R. SCHNEIDER AND C.-D. MUNZ, The approximation of two-fluid plasma flow with explicit upwind schemes, Internat. J. Numer. Model., 8 (2005), pp. 399-416.
29. U. SHUMLAK AND J. LOVERICH, Approximate Riemann solver for the two-fluid plasma model, J. Comput. Phys., 187 (2003), pp. 620-638.
30. V. VAKHNENKO AND J. PARKES, A novel nonlinear evolution equation integrable by the inverse scattering method, Proceedings of the Institute of Mathematics of NAS of Ukraine, 43 (2002), pp. 384-391.
31. P. L. G. VENTZEK, T. J. SOMMERER, R. J. HOEKSTRA, AND M. J. KUSHNER, Two-dimensional hybrid model of inductively coupled plasma sources for etching, Appl. Phys. Lett., 63 (1993), pp. 605-607.
32. P. L. G. VENTZEK, R. J. HOEKSTRA, AND M. J. KUSHNER, Two-dimensional modeling of high plasma density inductively coupled sources for materials processing, J. Vac. Sci. Technol. B, 12 (1994), pp. 461-477.