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Two-dimensional flow around a semi-circular profile at the zero angle of attack and at Re = 50000 on the self-oscillatory period is extensively studied by the URANS method involving the standard semi-empirical SST turbulence models, the SST turbulence model with the correction for streamline curvature modified within the Rodi-Leschziner-Isaev and Smirnov-Menter approaches, as well as involving Hanjalic's four-parameter eddy viscosity elliptic relaxation model and its analog - eddy viscosity elliptic blending model proposed in the present work. This has been done with the use of different-structure grids (multiblock with structured overlapping and unstructured composite). Different numerical approximation methods realized in six codes (VP2/3, SigmaFlow, Fluent, CFX, OpenFOAM, and StarCCM+) are used. An underestimation (up to 30%) of time-averaged integral aerodynamic loads is revealed by means of the standard near-wall SST model. This is explained by the high vortex viscosity production in the profile wake. Wind tunnel tests show that the location of cutoff washers on the semi-circular profile provides a quasi-two-dimensional flow around it and allows applying measurement data to verify two-dimensional turbulent flow. The best agreement of experimental results and numerical predictions when comparing the Strouhal number and time-averaged surface pressure coefficient distributions is achieved using both the modified SST model with the correction for streamline curvature and the modified eddy viscosity elliptic blending model. When the SST model with the correction for streamline curvature, modified within the Rodi-Leschziner-Isaev, Smirnov-Menter and Durbin approaches, is used, all the above codes yield close predictions of a vertical aerodynamic load on the oscillation period.