Abstract: This work studied numerically the transient themal blooming and the transition to the“steady-state”in iso-bar approximation for laser atmosphere propagation,using a transient 4D thermal blooming code,in comparison with the results computed by an isobar approximation 4D thermal blooming code. At a bout 4t_H（t_H is fluid dynamic time scale）,the results co mputed by the transient code were close to that comp uted by the isobar 4D code. In addition,this work also carried 0ut the phase compenstion ation computation. When the intensity was a few kW/cm²,the thermal distortion in the transient regime could be real-timely compensated by the ideal adaptive optical method.