With a Yang-Mills flux-tube initial state and a high resolution (3+1)D Particle-in-Cell Relativistic (PICR) hydrodynamics simulation, we calculate the $\Lambda$ polarization for different energies. The origination of polarization in high energy collisions is discussed, and we find linear impact parameter dependence of the global $\Lambda$ polarization. Furthermore, the global $\Lambda$ polarization in our model decreases very fast in the low energy domain, and the decline curve fits well the recent results of Beam Energy Scan (BES) program launched by the STAR collaboration at the Relativistic Heavy Ion Collider (RHIC). The time evolution of polarization is also discussed.
