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The hybrid multiscale simulation technology. An introduction with application to astrophysical and laboratory plasmas. (English) Zbl 1015.76001

Scientific Computation. Berlin: Springer. xviii, 403 p. (2002).
The book is concerned with a modern approach of exploring the behaviour of plasmas, having in mind a rather large class of characteristic problems. Under “plasma” can be meant material of stellar interior and atmosphere, solar winds and magnetospheres, and laboratory or industrial realizations. Thie book is divided in two parts. Part 1 mainly presents different hybrid models and the corresponding numerical model and algorithms. Part 2 treats applications of hybrid code simulations to space astrophysical and laboratory plasmas.
In part 1, seven chapters describe the classification of plasmas and Vlasov equation, the hybrid simulation method, combined approaches used to study plasma models (including charge-exchange and photo-ionization processes), and finally the analysis of numerical schemes for updating particle velocities and positions. The particle and field-weighting techniques are described, and conservation laws for general hybrid codes are considered. The analysis of numerical schemes for time integration is given for electromagnetic field equations and electron pressure equation, and some deeper considerations are presented. The author also discusses possible numerical algorithms for multiscale simulations, including general computational loops which turned out to be useful in recent hybrid simulations. The material is presented for different types of boundary conditions.
Part 2 describes simulations of collisionless shock wave structures and particle dynamics at shock fronts; in particular, pick up ions and their effect on transition layers are investigated. The author also discusses the dynamics of tangential discontinuities and their stability, wave generation in transition layers, diffusion processes and Kelvin-Helmholtz instability. A chapter is devoted to the simulation of magnetic field reconnection inside neutral current sheets. The simulation results are also given for the generation of low-frequency electromagnetic waves by beams. Finally, the global simulation of interaction of solar wind with comets, nonmagnetic planets and other astrophysical objects is reviewed. Besides, a detailed discussion is given on the formation of inductive magnetospheres, bow shock waves and magnetic barriers of nonmagnetic planets.
An appendix presents Maxwell’s equations and electron pressure equation in Cartesian, cylindrical and spherical coordinates, and gives the main formulas for solving one-dimensional difference equations. The book also offers training problems; some of them are used to derive the necessary formulas, but others are real problems the solutions of which are given at the end of the book. The list of references contains almost six hundred items.

MSC:

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
78A35 Motion of charged particles
76Mxx Basic methods in fluid mechanics

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