Vlasov and drift kinetic simulation methods based on the symplectic integrator

Transport Theory and Statistical Physics

Volumn 34, Issue 3-5, 2005, Pages 287-309

  Watanabe, T H ^a   Sugama, H ^a  

^a GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

Author keywords

Drift kinetic equation; Gyrokinetic equation; Simulation method; Symplectic integrator; Vlasov equation

Indexed keywords

EID: 29144501237     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411450500274550     Document Type: Conference Paper

References (31)

1. Arber, T. D., Vann, R. G. L. (2002). A critical comparison of eulerian-grid-based Vlasov solvers. J. Comput. Phys. 180:339-357.
2. Besse, N., Sonnendrücker, E. (2003). Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. J. Comput. Phys. 191:341-376.
3. Birdsall, C. K., Langdon, A. B. (1985). Plasma Physics via Computer Simulation. New York: McGraw-Hill.
4. Blanes, S., Moan, P. (2001). Splitting methods for non-autonomous Hamiltonian equations. J. Comput. Phys. 170:205-230.
5. Canuto, C., Hussaini, M. Y., Quarteroni, A., Zang, T. A. (1988). Spectral Methods in Fluid Dynamics. New York: Springer-Verlag.
6. Cheng, C. Z., Knorr, G. (1976). The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22:330-351.
7. deFrutos, J., Sanz-Serna, J. M. (1992). An easily implementable fourth-order method for the time integration of wave problems. J. Comput. Phys. 103:160-168.
8. Dubin, D. H. E., Krommes, J. A., Oberman, C., Lee, W. W. (1983). Nonlinear gyrokinetic equations. Phys. Fluids 26(12):3524-3535.
9. Fijalkow, E. (1999). A numerical solution to the Vlasov equation. Comput. Phys. Comm. 116:319-328.
10. Filbet, F., Sonnendrücker, E. (2003). Comparison of eulerian Vlasov solvers. Comput. Phys. Comm. 150:247-266.
11. Filbet, F., Sonnendrücker, E., Bertrand, P. (2001). Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172:166-187.
12. Forest, E., Ruth, R. D. (1990). Fourth-order symplectic integration. Physica D 43:105-117.
13. Ghizzo, A., Izrar, B., Bertrand, P., Fijalkow, E., Feix, M. R., Shoucri, M. (1988). Stability of Bernstein-Green-Kruskal plasma equilibria. Numerical experiments over a long time. Phys. Fluids 31(1):72-82.
14. Ghizzo, A., Bertrand, P., Shoucri, M., Fijalkow, E., Feix, M. R. (1993). An eulerian code for the study of the drift-kinetic Vlasov equation. J. Comput. Phys. 108:105-121.
15. Izar, B., Ghizzo, A., Bertrand, P., Fijalkow, E., Feix, M. R. (1989). Integration of Vlasov equation by a fast fourier eulerian code. Comput. Phys. Comm. 52:375-382.
16. Klimas, A. J., Farrell, W. M. (1994). A splitting algorithm for Vlasov simulation with filamentation filtration. J. Comput. Phys. 110:150-163.
17. Lifshitz, E. M., Pitaevskii, L. P. (1981). Physical Kinetics. New York: Pergamon Press.
18. Manfredi, G., Shoucri, M., Feix, M. R., Bertrand, P., Fijalkow, E., Ghizzo, A. (1995). The numerical integration of the Vlasov equation possessing an invariant. J. Comput. Phys. 121:298-313.
19. Manfredi, G., Shoucri, M., Dendy, R. O., Ghizzo, A., Bertrand, P. (1996). Vlasov gyrokinetic simulations of ion-temperature-gradient driven instabilities. Phys. Plasmas 3(1):202-217.
20. Mangeney, A., Califano, F., Cavazzoni, C., Travnicek, P. (2002). A numerical scheme for the integration of the Vlasov-Maxwell system of equations. J. Comput. Phys. 179:495-538.
21. Nakamura, T., Yabe, T. (1999). Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space. Comput. Phys. Comm. 120:122-154.
22. Sanz-Serna, J. M. (1992). Symplectic Runge-Kutta and related methods: Recent Results. Physica D 60:293-302.
23. Shoucri, M. (2001). Numerical simulation of plasma edge turbulence due to E × B flow velocity shear. Czech. J. Phys. 51:1139-1151.
24. Shoucri, M., Knorr, G. (1976). Linear instabilities in the quasistatic guiding-center plasmas. Plasma Phys. 18:187-204.
25. Shoucri, M., Gagné, R. (1978). A Multistep technique for the numerical solution of a two-dimensional Vlasov equation. J. Comput. Phys. 27:315-322.
26. Sonnendrücker, E., Roche, J., Bertrand, P., Ghizzo, A. (1999). The semi-Lagrangian method for the numerical resolution of the Vlasov equation. J. Comput. Phys. 149:201-220.
27. Staniforth, A., Côté, J. (1991). Semi-Lagrangian integration schemes for atmospheric models - A review. Mon. Weather Rev. 119:2206-2223.
28. Watanabe, T.-H., Sugama, H. (2002). Kinetic simulation of a quasisteady state in collisionless ion temperature gradient driven turbulence. Phys. Plasmas 9:3659-3662.
29. Watanabe, T.-H., Sugama, H., Sato, T. (2000). Nondissipative kinetic simulation and analytical solution of three-mode equations of the ion temperature gradient instability. Phys. Plasmas 7(3):984-990.
30. Watanabe, T.-H., Sugama, H., Sato, T. (2001). A nondissipative simulation method for the drift kinetic equation. J. Phys. Soc. Jpn 70(12):3565-3576.
31. Yoshida, H. (1990). Construction of higher order symplectic integrators. Phys. Lett. 150:262-268.