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This comprehensive text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis laid on the magnetohydrodynamics of liquid metals, and on a prototypical industrial application. Aimed at research mathematicians, engineers, and physicists, as well as those working in industry, and starting from a good understanding of the physics at play, the approach is a highly mathematical one, based on the rigorous analysis of theequations at hand, and a solid numerical analysis to found the simulations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally, wheneverpossible, on real industrial cases.
This comprehensive text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis laid on the magnetohydrodynamics of liquid metals, and on a prototypical industrial application. Aimed at research mathematicians, engineers, and physicists, as well as those working in industry, and starting from a good understanding of the physics at play, the approach is a highly mathematical one, based on the rigorous analysis of the equations at hand, and a solid numerical analysis to found the simulations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally, whenever possible, on real industrial cases.
Liquid metal MHO is within the scope of two series of international conferences. One is the International Congress on "MHD Power Generation", held every four years, which includes technical and economical aspects as well as scientific questions. The other if the Beer-Sheva Seminar on "MHO Flows and Turbulence", held every three years in Israel. In addition to these well established meetings, an IUTAM Symposium was previously organized in Cambridge (UK) in 1982 on "Metallurgical Applications of MHD" by the late Arthur Shercliff. It was focussed on a very specific subject developing radiply from the middle of the 1970's. The magnetic field was generally AC, including frequencies high enough for the skin-depth to be much smaller than the typical length scale of the liquide pool. And the development of new technologies, or the improvement of existing ones, was the main justification of most of the researches presented and discussed. Only two participants from Eastern countries attended this Symposium. By the middle of the 1980's we felt that on this very same topic ideas had reached much more maturity than in 1982. We also realized that a line of research on MHD flows related to fusion reactors (tokamaks) was developing significantly, with particular emphasis on flows at large interaction parameter.
Magnetic fields are routinely used in industry to heat, pump, stir and levitate liquid metals. There is the terrestrial magnetic field that is maintained by fluid motion in the earth's core, the solar magnetic field, which generates sunspots and solar flares, and the galactic field that influences the formation of stars. This introductory text on magnetohydrodynamics (MHD) (the study of the interaction of magnetic fields and conducting fluids) is intended to serve as an introductory text for advanced undergraduates and graduate students in physics, applied mathematics and engineering. The material in the text is heavily weighted toward incompressible flows and to terrestrial (as distinct from astrophysical) applications. The final sections of the text, which outline the latest advances in the metallurgical applications of MHD, make the book of interest to professional researchers in applied mathematics, engineering and metallurgy.
New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals. The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.