Dynamical evolution plays a key role in shaping the current properties of star clusters and star cluster systems. Globular Clusters (GCs), very old and massive star clusters, are ideal objects to explore many aspects of stellar dynamics and to investigate the dynamical and evolutionary mechanisms of their host galaxy. Almost every surveyed galaxy of sufficiently large mass has an associated group of GCs, i.e. a Globular Cluster System (GCS). The GCSs evolve due to various mechanisms, among which dynamical friction and tidal interaction with the galactic field are the most important. Due to these mechanisms GCs decay to the galactic center and there they merge and contribute to the formation/accretion of a luminous and compact central Nuclear Star Cluster (NSC). This is known as the « merger model » for the formation of NSCs, observed at the center of many galaxies and also in the Milky Way (MW) center. In this seminar I will initially present a new high performance code, NBSymple. NBSymple is an efficient N-body integrator implemented on a hybrid CPU+GPU platform, exploiting a double-parallelization on CPUs and on the hosted Graphic Processing Units (GPUs). I will also describe the results obtained exploring the merger model for the Galactic NSC formation, using high precision self consistent simulations. The decay and following merging of clusters in the central zone of the Galaxy (where a SMBH is located) and its following evolution due to two-body relaxation generates a NSC that actually resembles the one observed at the center of the MW. By mean of numerical simulations carried on with NBSymple, I investigated more in detail the dynamical evolution of GCs in the MW potential with particular attention to the formation of clumpy structures in the tidal tails that arise around the orbiting cluster. Although various hypotheses have been proposed, the formation process of these clumps is not yet clearly understood. Studying and comparing such simulations with observational data we could gain to a deeper knowledge of the shape Galactic potential and, more generally, of the Galactic dynamics.