Collective relativistic fluid dynamics is the dominant description of heavy ion reactions. 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 shear flow, vorticity and Lambda polarization for different energies. The origin 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 quickly with time in the low energy domain, and the decline curve fits well the recent results of Beam Energy Scan (BES) program launched by the STARCollaboration at the Relativistic Heavy Ion Collider (RHIC). The time evolution of polarization is also discussed.