The transient performances of impeller machinery under typical mutational working conditions play an important role in the area of engineering and have attracted extensive attention. In order to fully understand transient behaviors of impeller machinery under mutational working conditions, it is very necessary to confirm an efficient and reliable solving method. In this paper, the dynamic mesh method and the sliding mesh method are respectively used to be solved the inner transient flow of a 2D centrifugal pump model during abrupt start-up period. The Renormalization-group (RNG) k-e turbulence model in eddy viscosity models is chosen to close the Reynolds-average equation and to complete the turbulence calculation. Moreover, the SIMPLE algorithm is also adapted to accomplish the coupling calculation between velocity and pressure. The study shows that in theory, the most appropriate method to solve transient flow is the dynamic mesh method, but it has the shortage of low mesh quality during mesh reconstruction. The sliding mesh method with high mesh quality is an ideal solving method under mutational working conditions. In general, both of the methods would reflect the basic characteristics of inner flow, while the sliding mesh method has higher solution precision.