boundary of the 2D grid) and the outer part of the disk (ranging from the outer boundary of the 2D grid to the physical outer edge, e.g. the photo-dissociation radius at hundreds of AU) are represented with a 1D grid. The 1D grids have open outflow boundaries at the inner and outer physical edges, and exchange information with the 2D grid for the definition of realistic, time-dependent boundary conditions of the latter. The algorithm for the interfacing between the 1D and 2D grids is driven by the requirement that the angular momentum of the global system (the disk in the 2D section, plus the disk in the 1D section plus the planet-star system) is conserved. With this approach, the global viscous evolution of the disk and the local planet-disk interactions are both well described and the feedback of one on the other can be properly taken into account. Because the migration of giant planets depends on the global evolution of the disk, this code provides more realistic results than the usual algorithms, in which the evolution of the considered portion of the disk depends crucially on the adopted (arbitrary) boundary conditions. [For more information and accuracy tests we refer the 