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A numerical method for thermogasdynamic calculation of low-thrust liquid rocket engines is presented. These engines are used as end organs of the system of space attitude control for nanosatellites and small spacecraft. The method is based on the use of the TERRA software package for thermodynamic calculation and the Ansys CFX software package for gas-dynamic calculation using the Navier-Stokes equations. The results of the thermogasdynamic calculation, as well as the flow pattern of the working fluid in the chamber, are presented. The results of validating the described method are also presented. Its capabilities and limitations are analyzed. The validation procedure is based on the comparison with the results of experimental data on the Reynolds number and the momentum thickness.