High order eulerian schemes for fluid modelling of streamer dynamics

Advances and Applications in Fluid Mechanics

Volumn 8, Issue 1, 2010, Pages 1-31

  Ducasse, O ^a   Eichwald, O ^a   Yousfi, M ^a  

^a UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Convergence of numerical methods; Fluid transport equations; High order eulerian finite difference schemes; Streamer dynamics modelling; Validation and test of numerical methods

Indexed keywords

EID: 79551694210     PISSN: 09734686     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. H.-H. Kim, Nonthermal plasma processing for air-pollution control: a historical review, current issues, and future prospects, Plasma Process. Polym. 1 (2004), 91-110.
2. E. Marotta, A. Callea, X. Ren, M. Rea and C. Paradisi, A mechanistic study of pulsed corona processing of hydrocarbons in air at ambient temperature and pressure, Int. J. Plasma Environ. Sci. Technol. 1(1) (2007), 39-45.
3. S. M. Starikovskaia, Plasma assisted ignition and combustion, J. Phys. D: Appl. Phys.39 (2006), R265-R299.
4. E. Moreau, Airflow control by non-thermal plasma actuators, J. Phys. D: Appl. Phys.40 (2007), 605-636.
5. M. Laroussi, Nonthermal decontamination of biological media by atmosphericpressure plasmas: review, analysis and prospects, IEEE Trans. Plasma. Sci. 30(4) (2002), 1409-1415.
6. G. Fridman, G. Friedman, A. Gutsol, A. B. Shekhter, V. N. Vasilets and A. Fridman, Applied plasma medicine, Plasma Process. Polym. 5 (2008), 503-533.
7. U. Ebert and D. Sentman, Streamers, sprites, leaders, lightning: from micro- to macroscales, J. Phys. D: Appl. Phys. 41 (2008), 230301, pp. 7.
8. Eichwald, O. Ducasse, D. Dubois, A. Abahazem, N. Merbahi, M. Benhenni and M. Yousfi, Experimental analysis and modelling of positive streamer in air: towards an estimation of O and N radical production, J. Phys. D: Appl. Phys. 41(23) (2008), 234002.
9. O. Eichwald, O. Ducasse, N. Merbahi, M. Yousfi and D. Dubois, Effect of order fluid models on flue gas streamer dynamics, J. Phys. D: Appl. Phys. 39(1) (2006), 99-107.
10. Li, W. J. M. Brok, U. Ebert and J. J. A. M. van der Mullen, Deviations from the local field approximation in negative streamer heads, J. Appl. Phys. 101(12) (2007), 123305.
11. O. Ducasse, L. Papageorghiou, O. Eichwald, N. Spyrou and M. Yousfi, Critical analysis on two-dimensional point-to-plane streamer simulations using the finite element and finite volume methods, IEEE Trans. Plasma Sci. 35(5) (2007), 1287-1300.
12. Soria-Hoyo, F. Pontiga and A. Castellanos, Two dimensional numerical simulation of gas discharges: comparison between particle-in-cell and FCT techniques, J. Phys. D: Appl. Phys. 41 (2008), 205206.
13. J. P. Boris, FCT modules for solving generalized continuity equations, NRL Memorandum Report 3237, Plasma Physics Division, 1976.
14. S. T. Zalesak, Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys. 31(3) (1979), 335-362.
15. C. D. Munz, On the dissipation of high resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 77(1) (1988), 18-39.
16. P. L. Roe and M. J. Baines, Algorithms for advection and shock problems, Proceedings of the 4th GAMM Conference on Numerical Methods in Fluid Mechanics, H. Viviand, ed., Vol. 5, Vieweg: Braunschweig, Wiesbaden, 1982, p. 281.
17. P. Colella and P. R. Woodward, The piecewise parabolic method (PPM) for gasdynamical simulations, J. Comput. Phys. 54 (1984), 174-201.
18. P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys. 54(1) (1984), 115-173.
19. R. Morrow, Numerical solution of hyperbolic equations for electron drift in strongly non-uniform electric fields, J. Comput. Phys. 43 (1981), 1-15.
20. J. P. Boris and D. L. Book, Flux-corrected transport: I. SHASTA, a fluid transport algorithm that works, J. Comput. Phys. 11 (1973), 38-69.
21. Liska and B. Wendroff, Comparison of several difference schemes on 1D and 2D test problems for the Euler equations, SIAM J. Sci. Comput. 25(3) (2003), 995-1017. (electronic).
22. J. A. Greenough and W. J. Rider, A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov, J. Comput. Phys. 196(1) (2004), 259-281.
23. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in FORTRAN, The Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge, 1992.
24. D. L. Book, J. P. Boris and K. Hain, Flux-corrected transport II: generalizations of the method, J. Comput. Phys. 18 (1975), 248-283.
25. J. P. Boris and D. L. Book, Flux-corrected transport III: minimal-error FCT algorithms, J. Comput. Phys. 20 (1976), 397-431.
26. J. P. Boris and D. L. Book, Solution of continuity equations by the method of flux corrected transport, Methods in Computational Physics, Vol. 16, Academic Press, New York, 1976, pp. 85-129.
27. Flux-Corrected Transport, Principles, Algorithms and Applications, D. Kuzmin, R. Löhner and S. Turek, eds., Scientific Computation, Springer-Verlag, Berlin, 2005.
28. A. F. Shchepetkin and J. C. McWilliams, Quasi-monotone advection achemes based on explicit locally adaptive dissipation, Monthly Weather Review 126 (1998), 1541-1580.
29. B. van Leer, Towards the ultimate conservative difference scheme V, a second order sequel to Godunov's methods, J. Comput. Phys. 32 (1979), 101-136.
30. A. J. Davies, Numerical solutions of continuity equations and plasma growth, Workshop Plasmas Chauds et Modélisation des Décharges, CIRM, Luminy, 1992, pp. 45-53.
31. A. J. Davies and W. Niessen, The Solution of the Continuity Equations in Ionization and Plasma Growth, Plasma Press, New York, 1990, pp. 197-217.
32. M. Yousfi, A. Poinsignon and A. Hamani, Finite element method for conservation equations in electrical gas discharge areas, J. Comput. Phys. 113(2) (1994), 268-278.