Numerical modeling of the magnetosphere with data based internal magnetic field and arbitrary magnetopause

We present a new model of the magnetospheric magnetic field. Using the finite element method, ChapmanFerraro problem is solved numerically in the considered approach. The whole magnetic field is a sum of: the dipole field, the field, produced by the internal current systems (cross-tail, Birkeland, ring currents) and the field induced by the magnetopause currents. In contrast to similar earlier models, the internal magnetospheric magnetic fields are taken from Tsyganenko data-based model. The magnetosphere boundary could be arbitrary (generally non-axisymmetric). Input model parameters are the solar wind parameters, the Dst index and the dipole tilt angle. We discuss some results, obtained in three dimensional solution of the Neumann-Dirichlet problem corresponding to a closed magnetosphere