Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...247..707n&link_type=abstract
Astrophysical Journal, Part 1, vol. 247, July 15, 1981, p. 707-733.
Astronomy and Astrophysics
Astrophysics
23
Magnetohydrodynamics, Method Of Characteristics, Solar Atmosphere, Solar Magnetic Field, Stellar Evolution, Three Dimensional Flow, Boundary Conditions, Difference Equations, Eigenvalues, Energy Dissipation, Nonlinear Equations, Plasma-Electromagnetic Interaction, Self Consistent Fields, Solar Flares
Scientific paper
The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.
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