Mathematical modeling of nonequilibrium processes on chair of physical mechanics of St. Petersburg State University. Part 1. Modeling of processes in gas, fluid and solid

The article gives the review of works of employees of chair and laboratory of physical mechanics of St.Petersburg State University from the moment of its establishment in 1986 and till 2023 inclusive, that are devoted to modeling of the non-equilibrium processes in gas, fluid and solid. The basic attention is given several major results: 1) creation of model of adsorption layer for the description of locomotion of flying vehicles in near space and an upper atmosphere; 2) a theoretical and experimental substantiation of the general approach to modeling high-speed and short-duration processes in various mediums; 3) application of the specified general approach to studying of shock-induced processes in solid. The detailed substantiation of necessity of the integro-differential form of the transport equations for nonequilibrium processes is given. That is shown that time's evolution of system, to which interaction of structural elements of medium on the mesoscale leads, is described by the cybernetic methods developed by A. L. Fradkov within the limits of the Control Theory of adaptive systems with feedback. Other results are given short enough.