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Efficient finite volume schemes for magnetohydrodynamic simulations in solar physics. Incl. CD-ROM. (English) Zbl 1030.76002

Freiburg i. Br.: Univ. Freiburg, Fakultät für Mathematik und Physik (Diss.), viii, 394 p. (2003).
This is a doctor’s thesis which discusses physical problems of solar physics (solar corona, coronal heating, solar wind, sunspots) and refers to convection zones, magnetic flux tubes and solar photosphere. The main aim, however, is to develop and implement numerical methods in two and three dimensions which allow realistic simulations and particularly, the tracking of rising and exploding magnetic flux tubes. From physical point of view this means to perform simulations in two regions of the Sun, the solar convection zone and photosphere. This imposes quite different requirements. In the convection zone, there are localized structures in a physically unbounded domain, which requires local grid adaptation and artificial boundaries for a finite computational domain. In the photosphere, the author deals with shocks and takes into account the partial ionization of plasma, and, finally, considers the nonlocal transport of radiation. Both regions are modelled by compressible magnetohydrodynamics, but, as regards the equation of state, special attention must be paid to radiative source terms in fundamental equations. A mathematical study is performed to assure the confidence in the calculations and to verify their correctness. The results are summarized in fifteen points, with comparatively long statements, concretizing the computational aspects of the work.

MSC:

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
85-08 Computational methods for problems pertaining to astronomy and astrophysics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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