An Asymptotically Stable Semi-Lagrangian scheme in the Quasi-neutral Limit

Journal of Scientific Computing

Volumn 41, Issue 3, 2009, Pages 341-365

  Belaouar, R ^a   Crouseilles, N ^b   Degond, P ^c   Sonnendrucker E ^b  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b UNIVERSITÉ DE STRASBOURG   (France)

^c INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Asymptotic preserving scheme; Quasi neutral limit; Semi Lagrangian method; Vlasov equation

Indexed keywords

A-STABILITY; ASYMPTOTIC PRESERVING SCHEMES; ASYMPTOTICALLY STABLE; DEBYE LENGTH; EXPLICIT SCHEME; NUMERICAL COSTS; NUMERICAL SCHEME; NUMERICAL SIMULATION; PHASE SPACES; PLASMA FREQUENCIES; PLASMA PERIOD; QUASI-NEUTRAL LIMIT; SEMI-LAGRANGIAN METHODS; SEMI-LAGRANGIAN SCHEME; TIME STEP; VLASOV EQUATION; VLASOV-POISSON; VLASOV-POISSON EQUATIONS;

ASYMPTOTIC ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; COSMOLOGY; EQUATIONS OF MOTION; PHASE SPACE METHODS; PLASMA WAVES; POISSON DISTRIBUTION; POISSON EQUATION; SIMULATORS; STRUCTURES (BUILT OBJECTS);

LAGRANGE MULTIPLIERS;

EID: 72249091036     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-009-9302-4     Document Type: Article

References (28)

1. Birdsall, C.K., Langdon, A.B.: Plasma Physics via Computer Simulation. IOP Publishing, Bristol (1991)
2. Y. Brenier 2000 Convergence of the Vlasov-Poisson system to the incompressible Euler equations Commun. Part. Differ. Equ. 25 737 754 0970.35110 10.1080/03605300008821529 1748352
3. B.I. Cohen A.B. Langdon A. Friedman 1982 Implicit time integration for plasma simulations J. Comput. Phys. 46 15 0495.76105 10.1016/0021-9991(82)90002- X 665802
4. P. Crispel P. Degond M.-H. Vignal 2005 An asymptotically stable discretization for the Euler-Poisson system in the quasineutral limit C.R. Acad. Sci. Paris, Ser. I 341 341 346 2166148
5. P. Crispel P. Degond M.-H. Vignal 2007 An asymptotically preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit J. Comput. Phys. 203 208 234 10.1016/j.jcp.2006.09.004 2314389
6. N. Crouseilles F. Filbet 2004 Numerical approximation of collisional plasma by high order methods J. Comput. Phys. 201 2 546 572 1076.76053 10.1016/j.jcp.2004.06.007 2100514 (Pubitemid 39518796)
7. N. Crouseilles G. Latu E. Sonnendrücker 2007 Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation Int. J. Appl. Math. Comput. Sci. 17 3 101 115
8. P. Degond C. Parzani M.-H. Vignal 2003 Plasma expansion in vacuum: modeling the breakdown of quasineutrality SIAM Multiscale Model. Simul. 2 158 10.1137/030600333 2044960
9. P. Degond F. Deluzet L. Navoret 2006 An asymptotically stable Particle-In-cell (PIC) scheme for collisionless plasma simulations near quasineutrality C.R. Acad. Sci. Paris, Ser. I 343 613 618 1105.65095 2269874
10. P. Degond J.G. Liu M.-H. Vignal 2008 Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit SIAM J. Numer. Anal. 46 1298 1322 05567317 10.1137/070690584 2390995
11. Delcroix, J.-L., Bers, A.: Physique des Plasmas, vols. 1, 2. Inter Editions/Editions du CNRS, Paris (1994)
12. Duclous, R., Dubroca, B., Filbet, F.: Analysis of a high order finite volume scheme for the Vlasov-Poisson system. http://hal.archives-ouvertes.fr/ hal-00287630/fr
13. S. Fabre 1992 Stability analysis of the Euler-Poisson equations J. Comput. Phys. 101 445 0758.65077 10.1016/0021-9991(92)90020-Y 1174635
14. F. Filbet E. Sonnendrücker 2003 Comparison of Eulerian Vlasov solvers Comput. Phys. Commun. 151 247 266 10.1016/S0010-4655(02)00694-X
15. F. Filbet E. Sonnendrücker P. Bertrand 2001 Conservative numerical schemes for the Vlasov equation J. Comput. Phys. 172 166 187 0998.65138 10.1006/jcph.2001.6818 1852326 (Pubitemid 33098528)
16. Fried, B.D., Comte, S.D.: The Plasma Dispersion Function. Academic Press, New York (1961)
17. S.Y. Ha M. Slemrod 2003 Global existence of plasma ion sheaths and their dynamics Commun. Math. Phys. 238 149 1055.35085 1989673
18. Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations. Series in Computational Mathematics, vol. 31. Springer, Berlin (2002)
19. D.W. Hewett C.W. Nielson 1987 A multidimensional quasineutral plasma simulation model J. Comput. Phys. 72 121 0636.76126 10.1016/0021-9991(87)90075-1
20. Hockney, R.W., Eastwood, J.W.: Computer Simulation Using Particles. IOP Publishing, Bristol (1998)
21. A.B. Langdon B.I. Cohen A. Friedman 1983 Direct implicit large time-step particle simulation of plasmas J. Comput. Phys. 51 107 0572.76123 10.1016/0021-9991(83)90083-9 713943
22. A. Mankofsky R.N. Sudan J. Denavit 1983 Hybrid simulation of ion beams in background plasma J. Comput. Phys. 51 484 10.1016/0021-9991(83)90165-1
23. R.J. Masson 1981 Implicit moment particle simulations of plasmas J. Comput. Phys. 41 233 10.1016/0021-9991(81)90094-2 626610
24. R.J. Masson 1983 Implicit moment PIC-hybrid simulation of collisional plasmas J. Comput. Phys. 51 484 10.1016/0021-9991(83)90165-1
25. T. Nakamura T. Yabe 1999 Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space Comput. Phys. Commun. 120 122 154 1001.82003 10.1016/S0010-4655(99)00247-7
26. P.W. Rambo 1995 Finite-grid instability in quasineutral hybrid simulations J. Comput. Phys. 118 152 0824.76056 10.1006/jcph.1995.1086
27. M. Shoucri 1979 Nonlinear evolution of the bump-on-tail instability Phys. Fluids 22 2038 2039 10.1063/1.862470
28. E. Sonnendrücker J. Roche P. Bertrand A. Ghizzo 1999 The semi-Lagrangian method for the numerical resolution of the Vlasov equations J. Comput. Phys. 149 201 220 0934.76073 10.1006/jcph.1998.6148 1672731