Abstract
Computational Magnetohydrodynamics (CMHD) is the science of numerically solving the coupled set of equations of fluid dynamics and electrodynamics occasionally supplemented by mathematical models for phase transitions including solidification, melting, evaporation and condensation.
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References
Mai S. (Ed.) 1994: Proceedings of the First International Congress on Electromagnetic Processing of Materials, Nagoya 25–28 October 1994.
Mai, S. (Ed.), 2000: Proceedings of the 3`d International Symposium on Electromagnetic Processing of Materials, April 3–6, 2000, Nagoya, Japan; The Iron and Steel Institute of Japan.
Binns K.J.; P.J. Lawrenson; C.W. Trowbridge 1992: The Analytical and Numerical Solution of Electric and Magnetic Fields, John Wiley and Sons Ltd.
Biskamp, D., 1993: Nonlinear Magnetohydrodynamics, Cambridge University Press.
Biskamp, D.; W. C. Müller, 1999: Decay laws for three-dimensional MHD turbulence, Phys. Rev. Lett., vol. 83 (11), pp. 2195–2198.
Crawford C.H., G.E. Karniadakis 1997: Reynolds stress analysis of EMHD-controlled wall turbulence. Phys. Fluids vol. 9, 788.
Davidson P.A., RI. Lindsay 1998: Stability of interfacial waves in aluminium reduction cells, J. Fluid Mech, vol. 362, pp. 273–296.
Davis, S. H., 1990: Hydrodynamic interactions in directional solidification J. Fluid Mech, vol. 212, pp. 241–262.
Davis, S. H.; H. E. Ripped; U. Müller; M. G. Worster (Eds.), 1992: Interactive Dynamics of Convection and Solidification, NATO ASI Series, vol. 219, Kluwer Academie Publishers, Dordrecht.
Egry, I.; Szekely J., 1991: The measurement of thermophysical properties in microgravity using electromagnetic levitation, Adv. Space Res., vol. 11 (7), pp. 263–266.
Felten F., Y. Fautrelle, Y. Du Terrail, O. Metais 1999: Numerical modeling of electromagnetically driven flows using LES methods, in: Fluid Flow Phenomena in Metals Processing, Eds. N. El-Kaddah, D.G.C. Robertson, S.T. Johansen, V.R. Voller, The Minerals, Metals and Materials Society, pp. 571–579.
Friedrich J., Y.-S. Lee, B. Fischer, C. Kupfer, G. Müller 1999: Experimental and numerical study of Rayleigh-Benard convection affected by a rotating magnetic field, Phys. Fluids vol. 11, 853.
Galperin B., S.A. Orszag (Eds.) 1993: Large Eddy Simulation of Complex Engineering and Geophysical Flows, Cambridge University Press.
Gamier M. (Ed.) 1997: Proceedings of the 2nd International Congress on Electromagnetic Processing of Materials, Paris 27–29 May 1997.
Glatzmeier, G.; P. H. Roberts, 1995: Nature, vol. 377, pp. 203.
Hossain M. 1994: Reduction in the dimensionality of turbulence due to a strong rotation, Phys. Fluids, vol. 6, pp. 1077–1080.
Incropera, F. P.; D. P. DeWitt, 1996: Fundamentals of Heat and Mass Transfer, John Wiley and Sons. New York.
Jackson, J. D, 1962: Classical Electrodynamics, John Wiley and Sons, New York.
Kaiser, T.; K. W. Benz, 1998: Taylor vortex instabilities induced by a rotating magnetic field: A numerical approach. Phys. Fluids, vol. 10, 1104.
Kolesnikov Y.B., A.B. Tsinober 1974: Izv. Akad. Nauk SSSR - Mech Zhid I Gaza, vol 4, 146.
Landau, L. D.; E. M. Lifshitz, 1987: Fluid Mechanics, Course of Theoretical Physics, vol. 6, Pergamon Press.
Mahesh, K.; Moin, P., 1998: DNS: A tool in turbulence research, Annu. Rev. Fluid Mech. vol. 30, pp. 539–578.
Martin-Witkowski, L. M.; Ph. Marty, 1998: Effect of a rotating magnetic field of arbitrary frequency on a liquid metal column. Eur. I. Mech. B/Fluids, vol. 17, 239.
Meir, A. J.; P. G. Schmidt, 1994: A velocity–current formulation for stationary MHD flow, Appl. Math. Comp., vol. 65, pp. 95–109.
Moffatt H.K. 1967: On the suppression of turbulence by a uniform magnetic field, J. Fluid Mech, vol. 28, pp. 571–592.
Muizhnieks A.R., A.T. Yakovich 1988: Numerical study of closed axisymmetric MHD rotation in an axial magnetic field with mechanical interaction of azimuthal and meridional flows, Magnetohydrodynamics, vol. 24, pp. 50–55.
Oughton, S.; E. R. Priest; W. H. Matthaeus, 1994: The influence of a mean magnetic field on three-dimensional MHD turbulence, J. Fluid Mech., vol. 280, pp. 95–117.
Rosensweig, R E., 1985: Ferrohydrodynamics, Cambridge University Press.
Scardovelli, R.; S. Zaleski, 1999: Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech., vol. 31, pp. 567–603.
Schumann U. 1976: Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field, J. Fluid Mech, vol. 74, pp. 31–58.
Tacke K.H.; K. Schwerdtfeger 1979: Stirring velocities in continuously cast round billets as induced by rotating electromagnetic fields, Stahl und Eisen, vol. 99, pp. 7–12.
Vlasyuk V.K.; V.I. Sharamkin 1987: Effect of vertical magnetic field on heat and mass transfer in a parabolic liquid metal bath, Magnetohydrodynamics, vol. 23, pp. 211–216.
Widlund O., S. Zahrai, F. Bark 1998: Development of a Reynolds stress closure for modeling of homogeneous MHD turbulence, Phys. Fluids, vol. 10, 1987.
Wilcox D.O 1998: Turbulence modeling for CFD, DCW Industries.
Zikanov, O.; A. Thess, 1999: Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number, J. Fluid Mech., vol. 358, pp. 299–333.
Zikanov O., D. Ziegler, P.A. Davidson, A. Thess 2000: Metall Trans. (in press).
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Thess, A., Schulze, D. (2002). Computational Magnetohydrodynamics Part I — Fundamentals. In: Davidson, P.A., Thess, A. (eds) Magnetohydrodynamics. International Centre for Mechanical Sciences, vol 418. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2546-5_4
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DOI: https://doi.org/10.1007/978-3-7091-2546-5_4
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