Department of Computational Mathematics

Collaboration with Space Research Institute of the Austrian academy of Sciences.

1. Magnetohydrodynamic (MHD) models of the solar wind flow around planets (Earth, Venus, Jupiter, Saturn), and magnetic clouds.
2. A dissipative nonsteady MHD model is elaborated for reconnection of magnetic field lines in cases of nonhomogeneous plasma resistivity.
3. Mathematical modelling is performed for the slow magnetosonic and Alfven waves propagating along the narrowing and curved magnetic flux tubes which are typical ones for the magnetospheres of planets.
4. MHD instabilities are studied for thin magnetic layers characterized by a finite curvature radius.

With regard to the solar wind flow around planets and magnetic clouds, the enhanced magnetic field regions were studied which were called «magnetic barrier». The magnetic barrier is a thin layer adjacent to the sunward side of the magnetospheric boundary which contains an enhanced magnetic field originating from the interplanetary magnetic field. This layer accumulates magnetic energy which is generated by the solar wind flow because of magnetic field stretching in front of the magnetosphere (magnetic field line draping). It may thus act as a reservoir for magnetic field reconnection. The magnetic barrier is characterized by a decreased plasma pressure which becomes much less than the magnetic pressure. The thickness of the magnetic barrier is inversely proportional to the Alfv'en-Mach number squared. A scale of the magnetic energy variation in front of the magnetosphere is of the same order as the magnetic barrier thickness. The magnetic field plays a dominant role near by the magnetospheric boundary where the magnetic forces strongly affect the plasma flow pattern. This influence of the magnetic field results in the formation of the stagnation line flow pattern at the dayside magnetospheric boundary, different from the stagnation point flow which is typical of hydrodynamic flow past a blunt object.

The magnetic barrier forms the background for the analysis of dissipative processes, magnetic field line reconnection, and instabilities at the magnetospheric boundary.

Further developments of the solar wind flow models deal with the anisotropy of plasma pressure in a magnetized plasma In the case of anisotropy, the plasma pressure is a tensor with different parallel and perpendicular components relative to the magnetic field. The ratio of the perpendicular and parallel pressures is an unknown parameter and an additional relation is required in order to close the anisotropic MHD system of equations. Variety of the closure relations have been analyzed and the results have been compared with space probe observations.