Аннотация:The results of the theoretical solution of aerodynamic problems based on direct numericalsimulation by integrating the Navier – Stokes equations without involving additional modelsand empirical constants are shown. Modern approaches to the theoretical study of high-speedflows are determined. The advantages, problems, development trends and scientific directionsof research on various approaches are revealed. The advantages and disadvantages of the directnumerical simulation are analyzed. The velocity vectors of laminar and transient flows ina rectangular channel with a sudden expansion at the inlet are presented in different planes. Theconvergence of the method is studied when the computational domain is quantized in space. Itis discovered that fast relaminarization is characteristic of transitional flows. A mathematicalmodel for calculating bottom drag is presented. The numerical results are compared with thedata of physical experiments and the results of other methods. It is shown that the results ofsimulation based on DNS are not inferior in accuracy to RANS and LES results. The resultsof a parametric study of a transonic flow around a profile are presented. The high-speed buffetonset is investigated. The distribution surfaces of the velocity pulsation energy generation areshown. The frequency of self-oscillations is determined on the basis of spectral analysis.