[Show abstract][Hide abstract] ABSTRACT: A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.
Full-text · Article · Jul 1987 · Astronomy and Astrophysics
[Show abstract][Hide abstract] ABSTRACT: We examine the responses of the magnetic field and the atmospheric plasma to locally converging or diverging mass motions near the photo spheric magnetic neutral line, using a self-consistent, two-dimensional, nonplanar, time-dependent MHD model. This is an exploratory study using an MHD model, where we emphasize the self-consistency of the model, in contrast to using ad hoc realistic assumptions. The numerical results imply the following physical consequences in the solar atmosphere: (1) the development of a general atmospheric circulation with maximum motion occurring along the neutral line in the case of convergence, (2) a rapid rise of field lines and the development of a slow circulation with upward plasma-flow motion along the neutral line in the case of divergence. (3) During these converging and diverging motions, the generated MHD fast modes of rarefaction and compression waves result in a significant cooling and heating of the corona. In addition, a wide range of parameters (i.e., speed of motion and various plasma beta0 0) were examined. We show that the deformation of the magnetic field is strongly dependent on these parameters. Some of the numerical results may be associated with various observed solar phenomena, e.g., the submerging and emerging of magnetic flux and formation of low-lying loops.
Full-text · Article · Aug 1986 · The Astrophysical Journal
[Show abstract][Hide abstract] ABSTRACT: A full-implicit-continuous-Eulerian (FICE) scheme is developed for solving multidimensional transient magnetohydrodynamic (MHD) flow problems. The resulting difference equations are solved through a single-loop iteration in which the time-advanced pressure equation is solved by using the line-by-line iteration method (Patankar, “Numerical Heat Flow,” Hemisphere, Washington, D.C., 1980). In order to keep the boundary conditions self-consistent, a new formulation of boundary conditions is developed for this two-dimensional initial boundary value magnetohydrodynamic (MHD) flow problem. The merit of this new formulation is that improved consistency and accuracy on both physical and computational boundary values are obtained when compared to earlier methods. The stipulation of the boundary conditions is based on the projected characteristic method. The boundaries in a numerical computation may be classified into the following two categories: (i) Physical boundaries, on which the number of dependent variables are to be arbitrarily specified, would be limited to the number of incoming characteristics that are projected in the n - t plane, where n is the unit normal of the boundary in question and t is time. The rest of the variables (if any) should satisfy the compatibility equations along the outgoing projected characteristics in the n - t plane. (ii) Computational boundaries, on which a related set of compatibility equations should also be satisfied. In addition, a new nonreflecting boundary condition is introduced by taking all the spatial derivative terms of dependent variables to be zero in the characteristic equations along the incoming projected characteristics in the n - t plane. A numerical example for an astrophysical fluid is given to illustrate the present algorithm and boundary conditions. In addition, the comparison between the results of using the present nonreflecting boundary condition and the two conventional ones (i.e., equivalue and linear extrapolations) is made. It shows that the nonreflecting boundary condition formulated in this paper gives much smaller (almost null) reflection after the disturbance has reached the boundary and, therefore, can provide more accurate numerical results.
No preview · Article · Jul 1984 · Journal of Computational Physics
[Show abstract][Hide abstract] ABSTRACT: A self-consistent MHD model of shearing magnetic loops is used to investigate magnetic energy buildup in active region AR 2372 (Boulder number), in the period of April 5-7, 1980. The magnetic field and sunspot motions in this region, derived using observational data obtained by the Marshall Space Flight Center Solar Observatory, suggest the initial boundary conditions for the model. It is found that the plasma parameters (i.e., density, temperature, and plasma flow velocity) do not change appreciably during the process of energy buildup as the magnetic loops are sheared. Thus, almost all of the added energy is stored in the magnetic field. Furthermore, it is shown that dynamical processes are not important during a slow buildup (i.e., for a shearing velocity less than 1 km/s). Finally, it is concluded that the amount of magnetic energy stored and the location of this stored magnetic energy depend on the initial magnetic field (whether potential or sheared) and the magnitude of the shearing motion.
[Show abstract][Hide abstract] ABSTRACT: Observations indicate that various dynamic solar phenomena lead to enhanced emission of electromagnetic waves from radio to X-ray wavelengths which can be traced to magnetic activity in the photospheric level. A number of previous investigations have ignored the dynamic responses in the solar atmosphere. On the other hand, Nakagawa et al. (1978, 1981) have studied the atmospheric responses in the frame of MHD in the supersonic super-Alfvenic region. Studies of the slowly varying dynamic response (subsonic) have been unsuccessful because of the requirements of high accuracy in the numerical scheme in which a rigorous mathematical treatment of the boundary conditions is necessary. Recently, a numerical MHD model was constructed by using the full implicit continuous eulerian method. The present investigation makes use of a method which is written in a more convenient numerical code. A two-dimensional, time-dependent, nonplanar MHD model is used to investigate the induced mass and wave motions in the lower solar atmosphere due to the shear motion of flux tubes.
Full-text · Article · Apr 1983 · The Astrophysical Journal
[Show abstract][Hide abstract] ABSTRACT: A new ideal magnetohydrodynamic (MHD) model is used to examine the dynamical response of the upper solar atmosphere to the injection of cold mass from the photosphere, a surge perturbation. Theoretical results show that mass ejections from the photosphere will form loop structures with internally-moving plasma blobs, which is due to the mass injections from both legs in active regions leading to a reflection of waves at the top of the loop. The mass-loaded loop will remain as long as ejection continues, and will excite MHD waves propagating outward to the upper atmosphere, which may trigger a class of coronal disturbances.
No preview · Article · May 1982 · Astrophysics and Space Science