This paper gives a spatial mathematical formulation of the problem of internal ballistics based on the Navier – Stokes equations, taking into account the swirl of the flow due to the rotation of the projectile. The k-e model of turbulent viscosity is used. The control volume method is used for the numerical solution of systems of equations. The gas parameters at the boundaries of the control volumes are determined by the method of S. K. Godunov using a self-similar solution to the problem of the decay of an arbitrary discontinuity. The MUSCL scheme is used to increase the order of approximation of the difference method. For equations written in a cylindrical coordinate system, an orthogonal difference grid is constructed using the complex boundary element method. A comparative analysis of the results obtained with different approaches to modeling the process of an artillery shot is given. Quantitative data are presented on the influence of factors not previously taken into account on the characteristics of the process.