The Semi-Lagrangian Method for the Numerical Resolution of the Vlasov Equation

Journal of Computational Physics

Volumn 149, Issue 2, 1999, Pages 201-220

  Sonnendrücker, Eric ^a   Roche, Jean ^a   Bertrand, Pierre ^b   Ghizzo, Alain ^b  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Computational plasma physics; Semi Lagrangian method; Time splitting; Vlasov equations

Indexed keywords

DISTRIBUTION FUNCTIONS; INTEGRAL EQUATIONS; LAGRANGE MULTIPLIERS; NUMERICAL METHODS;

COMPUTATIONAL PLASMA PHYSICS; DISTRIBUTION-FUNCTIONS; FINITE NUMBER; KINETIC EQUATIONS; NUMERICAL RESOLUTION; PARTICLE IN CELL METHOD; SEMI-LAGRANGIAN METHODS; TIME EVOLUTIONS; TIME SPLITTING; TIME STEP;

VLASOV EQUATION;

EID: 0347802040     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6148     Document Type: Article

References (17)

1. 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, 431 (1990).
2. A. Ghizzo, P. Bertrand, M. L. Begue, T. W. Johnston, and M. Shoucri, A Hilbert-Vlasov code for the study of high-frequency plasma beatwave accelerator, IEEE Trans. Plasma Sci. 24, 370 (1996).
3. M. R. Feix, P. Bertrand, and A. Ghizzo, Eulerian codes for the Vlasov equation, in Series on Advances in Mathematics for Applied Sciences. Vol. 22. Kinetic Theory and Computing, edited by B. Perthame (1994), p. 45.
4. O. Coulaud, E. Sonnendrücker, E. Dillon, P. Bertrand, and A. Ghizzo, Parallelization of semi-Lagrangian Vlasov codes, J. Plasma Phys., to appear.
5. C. Z. Cheng and G. Knorr, The integration of the Vlasov equation in configuration space, J. Comput. Phys. 22, 330 (1976).
6. A. Staniforth and J. Côté, Semi-Lagrangian integration schemes for atmospheric models - A review, Mon. Weather Rev. 119 (1991).
7. R. Bermejo, Analysis of an algorithm for the Galerkin-characteristic method, Numer. Math. 60 (1991).
8. M. Falcone and R. Ferreti, Convergence analysis for a class of high-order semi-Lagrangian advection schemes, SIAM J. Numer. Anal. 35(3), 909 (1998).
9. P. K. Smolarkiewicz and J. A. Pudykiewicz, A class of semi-Lagrangian approximations for fluids, J. Atmos. Sci. 49(22), 2082 (1992).
10. P. Bartello and S. J. Thomas, The cost-effectiveness of semi-Lagrangian advection, Mon. Weather Rev. 124, 2883 (1996).
11. J. P. Boris and D. L. Book, Solution of continuity equations by the method of flux-corrected transport, in Methods of Comput. Phys. Vol. 16, edited by J. Kileen (Academic Press, New York, 1976), p. 85.
12. M. Shoucri, P. Bertrand, M. Feix, and B. Izrar, The application of shape preserving splines for the modified Korteweg-de Vries equation, Comput. Phys. Commun. 46(1), 1 (1987).
13. G. I. Marchuk, Methods of Numerical Mathematics (Springer-Verlag, New York, 1982).
14. E. Fijalkow, E. Jamin, M. Feix, P. Bertrand, A. Ghizzo, and M. Shoucri, A fully parallel 2D Vlasov code, in 14th Conference on the Numerical Simulations of Plasmas, Annapolis, 1991, Pt. 2.
15. M. Shoucri, Numerical solution of the two-dimensional Vlasov equation, IEEE Trans. Plasma Sci. PS-7(2), 69 (1979).
16. C. De Boor, A Practical Guide to Splines (Springer-Verlag, New York, 1978).
17. M. Shoucri, A two-level implicit scheme for the numerical solution of the linearized vorticity equation, Int. J. Numer. Meth. Eng. 17, 1525 (1981).