Numerical solution of supersonic aerodynamics problems using modern end-to-end counting schemes

The report is devoted to the application of modern end-to-end counting schemes to solving problems arising in supersonic aerodynamics and some other sections of continuum mechanics and electrodynamics.
After a brief overview of the computational algorithms and the developed calculation codes, the results of numerical solution of specific problems are presented. The article describes the studies of shock wave interactions, including the problem of the transition from regular to Mach reflection, dating back to the works of E. Mach and J. von Neumann, and shock wave configurations arising from the three-dimensional interaction of compaction surges. It is shown that transition hysteresis is a typical feature of flows involving interacting gas-dynamic discontinuities.
The results of direct numerical modeling of the development of disturbances and the transition to turbulence in free and wall supersonic flows: boundary and viscous shock layers, mixing layers and jets are presented.
The features of numerical simulation of rarefied flows using continuum and molecular kinetic approaches, the use of model kinetic equations for their description, and the solution of the Boltzmann equation by direct statistical modeling are discussed.
Issues related to the modeling of detonation waves, two-dimensional degenerating turbulence, and a new formulation of Maxwell's equations for numerical simulation of electromagnetic radiation propagation in vacuum and continuous media are also considered.