## 5. The numerical procedureIn the two outer regions of the sharp interface model, i.e. the two
semi-infinite homogeneous regions, the solutions for
and Since we are primarily interested in localized surface type eigenmodes, with evanescent amplitudes in both homogeneous regions to the left and the right of the interface, the related oscillation frequencies should lie in the intervals : and The analytical evanescent solution of (7) valid for is simply where and where and Thus the procedure for solving the eigenvalue problem for the MHD
surface modes on the sharp interface is a shooting method from
to . Starting at
with the evanescent analytical solution for the
homogeneous region to the left of the interface, we numerically
integrate the ideal MHD Eqs. (7). If a resonance is encountered
during the calculations, then the dissipative solutions (11) or (13)
are applied continuously between the endpoints
of the corresponding dissipative layer. After having passed through
the dissipative layer the computations return to the ideal
Eqs. (7) until the final point is reached.
Application of the continuity condition for and
© European Southern Observatory (ESO) 1998 Online publication: March 23, 1998 |