With the advancements of numerical upstream method in modeling flows in different paths including the flow inside turbine blades, employing the numerical CUSP technique in Jameson’s finite volume method can simultaneously benefit from the positive features of both mentioned methods. The novelty of this paper is to improve Jameson’s method in modeling a 2D supersonic flow between the blades of a steam turbine using the CUSP method, and defining the most optimum control function mode using Levenberg-Marquardt (LM) inverse method by effect of Weighing of experimental data and by accounting for the mass conservation equation. By considering the importance of the shock regions in the blade’s surface suction side, the focus of the mentioned method is in this part which results in the significant improvement of the pressure ratio in Jameson’s finite volume method. The results of the combined method (Jameson, CUSP and LM) at the shock region of the blade’s suction surface desirably agree with the experimental data, and a decrease of numerical errors at this region is resulted. Furthermore, the results of the combined method shows that in comparison, by average, the conservation of mass condition is improved 16% at the shock region of the blade’s suction surface.

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