Scientific School of Nonequilibrium Aeromechanics at St. Petersburg State University

The review describes the creation and development of the scientific school of Sergei Vasilyevich Vallander at the Leningrad (now St. Petersburg) State University. We discuss the achievements of the scientific school in the development of methods of the kinetic theory of gases for the simulation of nonequilibrium flows, the construction of rigorous self-consistent mathematical models of varying complexity for strong and weak deviations from equilibrium, and the application of the developed models in solving modern problems of aerodynamics. Particular attention is paid to the study of nonequilibrium kinetics and transport processes in carbon dioxide, identifying the key relaxation mechanisms of polyatomic molecules, the development of physically reasonable reduced hybrid models, and the optimization of numerical simulation of flows using modern machine-learning methods. We discuss the problems of correctly accounting for electronic excitation in modeling the kinetics and transport processes, models of equilibrium gas flows with multiple ionization, and the peculiarities of simulating bulk viscosity in polyatomic gases.