A new finite element method for magneto-dynamical problems: Two-dimensional results

European Journal of Mechanics, B/Fluids

Volumn 22, Issue 6, 2003, Pages 555-579

  Guermond, J L ^a,c   Leorat J ^b   Nore, C ^a,d  

^a CNRS   (France)

^b UNIVERSITÉ PARIS DIDEROT   (France)

^c UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^d UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

2D magnetodynamics; Finite element method

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; MAXWELL EQUATIONS; PROBLEM SOLVING; REYNOLDS NUMBER;

2D MAGNETODYNAMICS; HYBRID DOMAIN; INSULATING REGIONS; MAGNETIC SCALAR;

MAGNETOHYDRODYNAMICS;

EID: 3042737626     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7546(03)00054-2     Document Type: Article

References (26)

1. Moffatt H.K. Magnetic Field Generation in Electrically Conducting Fluids. Cambridge Monographs Mech. Appl. Math. 1978;Cambridge University Press, Cambridge.
2. Amari T., Luciani J.F., Joly P. A preconditioned semi-implicit method for magnetohydrodynamics equation. SIAM J. Sci. Comput. 21:1999;970-986.
3. Ben Salah N., Soulaimani A., Habashi W.G. A finite element method for magnetohydrodynamics. Comput. Methods Appl. Mech. Engrg. 190:(43-44):2001;5867- 5892.
4. Gerbeau J.-F. A stabilized finite element method for the incompressible magnetohydrodynamic equations. Numer. Math. 87:(1):2000;83-111.
5. Meir A.J., Schmidt P.G. Analysis and numerical approximation of a stationary MHD flow problem with non-ideal boundary. SIAM J. Numer. Anal. 36:1999;1304-1332.
6. Dudley M.L., James R.W. Time-dependent kinematic dynamos with stationary flows. Proc. Roy. Soc. London Ser. A. 425:1989;407-429.
7. Léorat J. Numerical simulations of cylindrical dynamos: scope and method. 7th Beer-Sheva Onternatal Seminar. AIAA Progress in Astronautics and Aeronautic. 162:1994;282-292.
8. Léorat J. Linear dynamo simulations with time dependent helical flows. Magnetohydrodynamics. 31:1995;367-373.
9. Gailitis A., Lielausis O., Dement'ev S., Platacis E., Cifersons A., Gerbeth G., Gundrum T., Stefani F., Christen A., Hänel H., Will G. Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility. Phys. Rev. Lett. 84:2000;4365-4368.
10. Stieglitz R., Muller U. Experimental demonstration of a homogeneous two-scale dynamo. Phys. Fluids. 13:2001;561.
11. Stefani F., Gerbeth G., Gailitis A. Velocity profile optimization for the Riga dynamo experiment. Alemany A., Marty Ph., Thibault J.P. Transfer Phenomena in Magnetohydrodynamics and Electroconducting Flows. 1999;Kluwer Academic, Dordrecht.
12. Tilgner A. A kinematic dynamo with a small scale velocity field. Phys. Lett. A. 226:1998;75-79.
13. Bourgoin M., Marié L., Pétrélis F., Gasquet C., Guigon A., Luciani J.B., Moulin M., Namer F., Burguete J., Chiffaudel A., Daviaud F., Fauve S., Odier P., Pinton J.F. Magnetohydrodynamics measurements in the von Kármán sodium experiment. Phys. Fluids. 14:2002;3046-3058.
14. J. Burguete, L. Marié, F. Daviaud, J. Léorat, Numerical study of homogeneous dynamo based on experimental von Kármán type flows, 2002, submitted for publication.
15. 2 dynamo using a finite element method. Phys. Earth and Planetary Interiors. 128:2001;35-50.
16. Guermond J.-L., Minev P.D. Mixed finite element approximation of an MHD problem involving conducting and insulating regions: the 2D case. Model. Math. Anal. Numer. 36:(3):2002;517-536.
17. J.-L. Guermond, P.D. Minev, Mixed finite element approximation of an MHD problem involving conducting and Insulating regions: the 3D case, Numer. Methods Partial Differential Equations (2002), submitted for publication.
18. Ben Salah N., Soulaimani A., Habashi W.G., Fortin M. A conservative stabilized finite element method for magnetohydrodynamics equations. Int. J. Numer. Methods Fluids. 29:1999;535-554.
19. Bossavit A. Electromagnétisme en vue de la modélisation. Math. Appl. 14:1993;SMAI/Springer-Verlag, Paris. See also: Computational Electromagnetism, Variational Formulations, Complementary, Edge Elements. 1998;Academic Press.
20. Bossavit A. Electromagnétisme en vue de la modélisation. Math. Appl. 14:1993;SMAI/Springer-Verlag, Paris. See also: Computational Electromagnetism, Variational Formulations, Complementary, Edge Elements. 1998;Academic Press.
21. Bossavit A. Computational Electromagnetism, Variational Formulations, Complementary, Edge Elements. Electromagnetism. 2:1998;Academic Press.
22. Parker R.L. Reconnexion of lines of force in rotating spheres and cylinders. Proc. Roy. Soc. 291:(1424):1966;60-72.
23. Bullard E.C. Electromagnetic induction in a rotating sphere. Proc. Roy. Soc. A. 199:1949;413-443.
24. Weiss N.O. The expulsion of magnetic flux by eddies. Proc. Roy. Soc. 1966.
25. W.R. Smythe, Static and Dynamic Electricity, Hemisp. Pub. Corp., 1939.
26. Costabel M. A coercive bilinear form for Maxwell's equations. J. Math. Anal. Appl. 157:(2):1991;527-541.