Abstract. The methods of increasing the efficiency of the numerical solution of non-stationary problems of gas dynamics for a multicomponent mixture and acceleration the processes of detection of stationary solutions by the establishment method are discussed. Here is considered the relevant algorithms and are shown evaluations of increasing the effectiveness of numerical solutions.Despite the impressive progress in the capabilities of computer technology for many practical applications, there is not least for the important value of the effectiveness of the algorithms. They should reflect as accurately as possible the physical reality and to have the minimum for the one time step for calculate. In this case, these techniques can be widely used in the preliminary evaluation of selectable technical structures or techniques that require multivariate numerical studies. The same time, the economical use of a single calculation requires on-line tracking technology processes. This is especially true for different streams of high-energy working body of the flow path. The high gas velocity causes intensive heat exchange the working fluid of with different structural elements of power aggregate, which ultimately determines the basic parameters of the transient and stationary modes, and thermodynamic properties and viscosity of a multicomponent gas mixture for specifying dynamics of the process.The system of equations expressing the basic conservation laws are often written in the integral form that is independent of the coordinate system with respect to the control volume V, bounded by a closed surface, partially or wholly permeable to gas surface A and impermeable S, at which have the heat and mass transfer between gases flow and structural elements: