Finite Element Numerical Modeling of Stationary Two-Dimensional Magnetosphere with Defined Boundary

A finite element numorical procedure is developed for two-dimensional modeling of stationary magnetosphere. The whole magnetic field is supposed to be a sum of given internal fields and a searched divergent-free and curl-free field of the magnetopause shielding current system. The boundary condition on the given boundary is the Neumann one on the magnetopause part of the computational region boundary and the Dirichlet condition on the segment part, closing this region at the tail. The algorithms used for automatic grid generation and grid transformation allow wide flexibility in determining the region shape and the assigned internal fields. Some numerical implementations not only demonstrate the method capabilities, In the frame of the two-dimensional approach these implementations could be considered as a tentative simulation of some typical features of magnetosphere magnetic field topology, which is intrinsically three-dimensional. The magnetopause geometry influence on the cusp inclination is shown. The impact of the northward and the flow-aligned field on dayside merging and tail asymmetry is aluminized. A two-dimensional approach to modelling the crosstail currents is proposed for the Earth type and Uranus type magnetospheres.