A solution of the stationary flow problem of spatial bodily lifting system of a viscous incompressible fluid based on the full Navier ? Stokes equations is presented. Based on the developed apparatus of vector-tensor analysis,it is proved that the most effective method for solving a wide spectrum of boundary value problems of continuum mechanics is the method of boundary integral equations. The results of numerical implementation for determining the main cinematic and dynamic characteristics of the interaction of a viscous flow of the carrier surface are given, as well as of the study of the convergence of the computational process.
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