  Numerical simulations of planet-disk interactions are usually performed with
hydro-codes that -- because they consider only an annulus of the disk, over a
2D grid -- can not take into account the global evolution of the disk. However,
the latter governs planetary migration of type II, so that the accuracy of the
planetary evolution can be questioned.
  To develop an algorithm that models the local planet-disk interactions
together with the global viscous evolution of the disk, we surround the usual
2D grid with a 1D grid ranging over the real extension of the disk. The 1D and
2D grids are coupled at their common boundaries via ghost rings, paying
particular attention to the fluxes at the interface, especially the flux of
angular momentum carried by waves. The computation is done in the frame
centered on the center of mass to ensure angular momentum conservation.
  The global evolution of the disk and the local planet-disk interactions are
both well described and the feedback of one on the other can be studied with
this algorithm, for a negligible additional computing cost with respect to
usual algorithms.
