Self-gravitating disks in binary systems: an SPH approach. I. Implementation of the code and reliability tests

The study of the stability of massive gaseous disks around a star in a nonisolated context is a difficult task and becomes even more complicated for disks that are hosted by binary systems. The role of self-gravity is thought to be significant when the ratio of the disk-to-star mass is non-negligible. To solve these problems, we implemented, tested, and applied our own smoothed particle hydrodynamics (SPH) algorithm. The code (named GaSPH) passed various quality tests and shows good performances, and it can therefore be reliably applied to the study of disks around stars when self-gravity needs to be accounted for. We here introduce and describe the algorithm, including some performance and stability tests. This paper is the first part of a series of studies in which self-gravitating disks in binary systems are let evolve in larger environments such as open clusters.