A drift-kinetic Semi-Lagrangian 4D code for ion turbulence simulation

Journal of Computational Physics

Volumn 217, Issue 2, 2006, Pages 395-423

  Grandgirard, V ^a   Brunetti, M ^b   Bertrand, P ^c   Besse, N ^d   Garbet, X ^a   Ghendrih, P ^a   Manfredi, G ^c   Sarazin, Y ^a   Sauter, O ^b   Sonnendrucker E ^d   Vaclavik, J ^b   Villard, L ^b  

^a IRFM   (France)

^b EPFL   (Switzerland)

^c INSTITUT JEAN LAMOUR   (France)

^d UNIVERSITÉ LOUIS PASTEUR   (France)

Author keywords

Conservation laws; Drift kinetic; Ion temperature gradient; Leap frog; Semi Lagrangian; Time splitting

Indexed keywords

CODES (SYMBOLS); INTEGRAL EQUATIONS; KINETIC ENERGY; KINETICS; LAGRANGE MULTIPLIERS; THERMAL GRADIENTS; TURBULENCE;

CONSERVATION LAW; DRIFT KINETICS; GYROKINETICS; ION TEMPERATURE GRADIENT; LARMOR RADII; LEAP-FROG; NON-LINEAR REGIMES; SEMI-LAGRANGIAN; TIME SPLITTING; TURBULENCE SIMULATION;

IONS;

EID: 33748429358     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.01.023     Document Type: Article

References (43)

1. Dimits A.M., et al. Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7 3 (2000) 969-983
2. Hammett G.W., and Perkins F.W. Fluid models for Landau damping with application to the ion-temperature-gradient instability. Phys. Rev. Lett. 64 (1990) 3019-3022
3. M.A. Beer, Gyrofluid Models of Turbulent Transport in Tokamaks, Ph.D. Thesis, Princeton University, 1995.
4. Waltz R.E., Staebler G.M., Dorland W., et al. A gyro-Landau-fluid transport model. Phys. Plasmas 4 (1997) 2482-2496
5. Lee W.W. Gyrokinetic approach in particle simulation. Phys. Fluids 26 2 (1983) 556
6. Kim C.C., and Parker S.E. Massively Parallel three dimensional Toroidal gyrokinetic Flux-Tube turbulence Simulations. J. Comput. Phys. 161 2 (2000) 589-604
7. Lin Z., Hahm T.S., Lee W.W., Tang W.M., and White R.B. Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows. Phys. Plasmas 7 5 (2000) 1857-1862
8. T.M. Tran, K. Appert, M. Fivaz, G. Jost, J. Vaclavik, L. Villard, Global gyrokinetic simulation of Ion-Temperature-Gradient driven instabilities, Th. Fusion Plasmas, in: Proceedings of the International Workshop, Varenna, 1998, Ed. Compositori, Bologna, 1999, pp. 45-49.
9. A. Bottino, T.M. Tran, O. Sauter, J. Vaclavik, L. Villard, Linear gyrokinetic simulations using particles for small perpendicular wavelength perturbations, Th. Fusion Plasmas, in: Proceedings of the International Workshop, Varenna, 2000, Ed. Compositori, Bologna, 2001, pp. 327-332.
10. Idomura Y., Tokuda S., and Kishimoto Y. Global gyrokinetic simulation of ion temperature gradient driven turbulence in plasmas using a canonical Maxwellian distribution. Nucl. Fusion 43 (2003) 234-243
11. Sugama H., Watanabe T.H., and Horton W. Comparison between kinetic and fluid simulations of slab ion temperature gradient driven turbulence. Phys. Plasmas 10 3 (2003) 726-736
12. Birdsall C.K., and Langdon A.B. Plasma Physics via Computer Simulation (1985), McGraw-Hill, New York
13. Hatzky R., Tran T.M., Könies A., et al. Energy conservation in a nonlinear gyrokinetic Particle-In-Cell code for ion-temperature-gradient-driven modes in theta-pinch geometry. Phys. Plasmas 9 3 (2002) 898-912
14. Allfrey S.J., and Hatzky R. A revised delta f algorithm for nonlinear PIC simulations. Comp. Phys. Commun. 154 2 (2003) 98-104
15. Villard L., Allfrey S.J., Bottino A., Brunetti M., Falchetto G.L., Grandgirard V., Hatzky R., Nührenberg J., Peeters A.G., Sauter O., Sorge S., and Vaclavik J. Full radius linear and non-linear gyrokinetic simulations for Tokamaks and Stellerators: zonal flows, applied E × B flows, trapped electrons and finite beta. Nucl. Fusion 1 (2004) 172-180
16. Pohn E., Shoucri M., and Kamelander G. Eulerian Vlasov codes. Comp. Phys. Commun. 166 2 (2005) 81-93
17. Ghizzo A., Bertrand P., Fijalkow E., Feix M.R., and Shoucri M. An Eulerian code for the study of drift-kinetic Vlasov equation. J. Comput. Phys. 108 1 (1993) 105-121
18. Manfredi G., Shoucri M., Dendy R.O., Ghizzo A., and Bertrand P. Vlasov gyrokinetic simulations of ion-temperature-gradient driven instabilities. Phys. Plasmas 3 1 (1996) 202-217
19. Dorland W., Jenko F., Kotschenreuther M., and Rogers B.N. Electron temperature gradient turbulence. Phys. Rev. Lett. 85 (2000) 5579-5582
20. Jenko F., Dorland W., Kotschenreuther M., and Rogers B.N. Massively parallel Vlasov simulation of electromagnetic drift-wave turbulence. Comp. Phys. Commun. 125 (2000) 196-209
21. Shoucri M. Numerical simulation of plasma edge turbulence due to E × B flow velocity shear. Czech. J. Phys. 51 10 (2001) 1139-1151
22. Candy J., and Waltz R.E. An Eulerian gyrokinetic-Maxwell solver. J. Comput. Phys. 186 2 (2003) 545-581
23. Fijalkow E. A numerical solution of the Vlasov equation. Comp. Phys. Commun. 116 (1999) 319-328
24. Filbet F., Sonnendrücker E., and Bertrand P. Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172 (2001) 166-187
25. Cheng C.Z., and Knorr G. The integration of the Vlasov equation in configuration spaces. J. Comput. Phys. 22 (1976) 330-351
26. Sonnendrücker E., and Roche J. The semi-Lagrangian method for the numerical resolution of Vlasov equation. J. Comput. Phys. 149 (1999) 201-220
27. Depret G., Garbet X., Bertrand P., and Ghizzo A. Trapped-ion driven turbulence in tokamak plasmas. Plasma Phys. Control. Fusion 42 (2000) 949-971
28. Brunetti M., Grandgirard V., Bertrand P., Sauter O., Vaclavik J., and Villard L. Fine-scale structures and negative density regions: comparison of numericals methods for solving advection equation. Transport Theory Stat. Phys. 34 3-5 (2005) 261-274
29. F. Jenko, W. Dorland, B. Scott, Strinzi, in: Proceedings of the 20th International School of Plasma Physics on the Theory of Fusion Plasmas, Simulation and Theory of Electromagnetic ETG Turbulence, Varenna, 2002, pp. 147-152.
30. Sarazin Y., Grandgirard V., Fleurence E., Garbet X., Ghendrih Ph., Bertrand P., and Depret G. Kinetic features of interchange turbulence. Plasma Phys. Control. Fusion 47 (2005) 1817-1839
31. Press W.H., Teukolsky A., Vetterling W.T., and Flannery B.P. Numerical Recipes in Fortran. second ed. (1992), Cambridge University Press, Cambridge pp. 43-50
32. Boisvert R.F. Algorithms for special tridiagonal systems. SIAM J. Sci. Stat. Comput. 12 2 (1991) 423-442
33. Marchuk G.I. Method of Numerical Mathematics (1982), Springer-Verlag, New York
34. Strang G. On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 506-517
35. DeBoor C. A practical guide to splines. Applied Mathematical Sciences vol. 27 (2001), Springer-Verlag, New York
36. Fried B.D., and Conte S.D. The Plasma Dispersion Function (1961), Academic Press, New York
37. Davies B. Locating the zeros of an analytic function. J. Comput. Phys. 66 (1986) 36-49
38. Brunner S., and Vaclavik J. Global approach to the spectral problem of microinstabilities in a cylindrical plasma using a gyrokinetic model. Phys. Plasmas 5 2 (1998) 365-375
39. Bourdelle C., Garbet X., Hoang G.T., Ongena J., and Budny R.V. Stability analysis of improved confinement discharges: internal barriers in Tore Supra and radiative improved mode in Textor. Nucl. Fusion 42 (2002) 892-902
40. Fivaz M., Brunner S., De Ridder G., et al. Finite element approach to global gyrokinetic Particle-In-Cell simulations using magnetic coordinates. Comp. Phys. Commun. 111 (1998) 27-47
41. V. Grandgirard, P. Bertrand, G. Depret, X. Garbet, A. Ghizzo, G. Manfredi, O. Sauter, T.M. Tran, J. Vaclavick, L. Villard, A semi-Lagrangian method for the resolution of a drift-kinetic equation applied to ITG studies, in: 28th EPS Conference on Controlled Fusion and Plasma Physics - Funchal, Madeira, Portugal, 2001.
42. Brunetti M., Grandgirard V., Sauter O., Vaclavik J., and Villard L. A semi-Lagrangian code for nonlinear global simulations of electrostatic drift-kinetic ITG modes. Comp. Phys. Commun. 163 (2004) 1-21
43. Watanabe T.H., and Sugama H. Kinetic simulation of a quasisteady state in collisionless ion temperature gradient driven turbulence. Phys. Plasmas 9 9 (2002) 3659-3662