MATHEMATICAL MODELING OF STRUCTURES FORMATION IN PROBLEMS OF PHYSICAL KINETICS WITH METHODS INTEGRATION OF COMPUTATIONAL FLUID DYNAMICS
The mathematical modeling of flows described by Liouville, Boltzmann, Smoluchowski equations and generalized systems of conservation laws are described in the paper. These balance equations (continuity) are the fundamental relationships that determine the statistical solutions of dynamical systems modeling the interaction of particles by long-range potentials and local collisions. The nonlinear dynamics of the flows described by these equations leads to the appearance of singularities for hydrodynamic parameters interpreted as the appearance of a front-type structure stable at macroscopic scales. The mechanisms of the appearance of the structures and computational aspects of their localization are considered.