The problem of weight decrease is crucial for modern gas turbine engines. Application of supersonicand transonic compressors is one of the ways of solving this problem. This allows reaching a higher pressureratio at each stage than while using subsonic compressors and thus reducing the number of stages required toproduce the desired value of pressure ratio. In compressors of this kind the flow is slowed down due to a systemof shockwaves in the supersonic part and due to the flow deflection in the diffuser channels formed by the rotorblades and guide vanes in the subsonic part. The design of new compressors and modernization of old ones isinextricably connected with the usage of computational fluid dynamics methods at the present stage of engineconstruction development. The necessity of simulating a shockwave system imposes high demands on the constructionof a computational mesh. In particular, the choice of the method of parameter passing between the domainsof rotating blades and those of fixed guide vanes is an urgent task. It is shown in the paper that the use ofdifferent methods of averaging and parameter passing between domains can make a significant difference incompressor design characteristics (for example, a three-stage low-pressure compressor). Three methods of passingparameters between the domains that are used in the software package NUMECA/Fine Turbo are analyzed.The calculated compressor characteristics are compared with the experimental data at different rotation frequenciesof the rotor. The data obtained show the adequacy of the numerical model of the work process in the compressorunder investigation. Typically, air bleeding for various needs takes place in compressors. Compressorperformance changes when the air enters it, which should be considered in the calculations. It is shown in theexample of the compressor tested that the inclusion of air bleeding results in quantitative and qualitative changesin the compressor performance. Among other things, parameters like pressure ratio and dynamic stability marginare changed, which may lead to inconsistent operation of the compressor as part of the engine. Thus, a conclusionabout the necessity of taking into account the simulation of air bleeding in the calculation of supersoniccompressors is made. The results obtained make it possible to expand the understanding of the working processof supersonic and transonic compressors and can be used later in the creation of numerical computational modelsof compressors of this type.