This study takes place in the frame of a research project to better understand the flow that develops in multistage high-speed compressors. First, the paper presents the high-speed 3.5-stage compressor CREATE and the methods that are considered to increase the data reliability and the investigation capability with such realistic compressors. Second, flow simulations, achieved with three-dimensional unsteady Reynolds-averaged Navier-Stokes computations over the whole compressor spatial and temporal periodicities, are analyzed through a study of their sensitivity to some parameters such as the inlet conditions, the space and time discretization, and technological effects such as tip and hub clearances. Finally the paper focuses on the methodology used to compare the experimental and numerical results over the whole compressor periodicities. The local spatial and temporal flow structures are well estimated. The key is the advection of these structures, which interact with each other and produce a significant part of the flow fluctuations in-the downstream stages. The paper presents the zone close to the casing, where losses and blockage are induced by the interaction between the tip leakage flow and the incoming wakes. This is where the numerical simulation has to be improved, in order to accurately predict the performance.