Scientific school of non-equilibrium aeromechanics in Saint Petersburg State University

The review is devoted to the foundation and development of the scientific school of S. V. Vallander at the Leningrad (now St Petersburg) State University. The achievements of the scientific school in the development of the kinetic theory methods for modeling nonequilibrium flows, construction of rigorous self-consistent mathematical models of varying complexity for strong and weak deviations from equilibrium, and the use of the developed models in challenging problems of modern aerodynamics are discussed. Particular attention is paid to the study of non-equilibrium kinetics and transport processes in carbon dioxide, identification of key relaxation mechanisms of polyatomic molecules, derivation of physically based reduced hybrid models, and optimization of non-equilibrium flow numerical simulations using modern machine learning methods. Correct description of electronic excitation in the kinetics and transport processes, models of local equilibrium gas flows with multiple ionization, and features of modeling bulk viscosity in polyatomic gases are discussed.