We present non-linear self-consistent global simulations of the SOL plasma dynamics using the Global Braginskii Solver (GBS) code. The code solves on the drift-reduced Braginkii equations, with cold ions. Studied originally for the simulation of the Simple Magnetized Torus (SMT) experiment TORPEX (CRPP, Lausanne), the GBS code has been recently upgraded to describe the SOL turbulence with the introduction of the variable curvature along the magnetic field lines, the magnetic shear, and the electromagnetic effects. The code peculiarity lies in the capability of evolving self-consistently equilibrium and fluctuations as a results of the interplay among the sources, the turbulent transport and the plasma losses at the limiter plates. The non-linear simulations have been interpreted by means of linear analysis of the fluid equations modeling the system. This points out the presence of two main instabilities driving turbulence: the Drift Wave and the Resistive Balloning instabilities. The dependence of the instabilities growth rate and of their properties on the physical parameters of the system, for example the typical length of variation of the plasma density, the safety factor and the magnetic shear have been explained and we identify the regions where each instability dominates.