Abstract: The nonlinear evolution of stimulated Brillouin scattering (SBS) in inhomogeneous flowing plasmas is self-consistently investigated by the Vlasov-Maxwell simulations. In the physical regime where ion trapping is dominant, simulations show that the evolution of SBS includes a linear convective stage and a nonlinear stage. In the linear stage, the reflectivity is in good agreement with the theoretical prediction from the Rosenbluth gain. In the nonlinear stage, the reflectivity shows a continuous increase and becomes much larger than the theoretical value. And the auto-resonant growing of ion acoustic wave (IAW) shows a nature of absolute instability, which can be explained as the compensation of the negative kinetic frequency shift from trapped ions and the detuning due to the flow velocity gradient. Methods using the incoherence in the pump waves to mitigate the enhanced SBS are proposed. The saturation of SBS by the decay to solitary turbulence of the IAW is demonstrated in the fluid dominant regime. The formation of solitary structures is due to the generation of harmonics of IAW.