Some models of viscous gas dynamics

In this paper, the problems containing two or more small parameters are investigated. In the analysis of such problems, a diagrammatic method is used to visualize the structure of perturbed flow regions, and to estimate the similarity parameters and mathematical models depending on the limiting transitions. The interaction between the laminar flows and transonic flows is considered in the context of the problem containing a small parameter inverse to the Reynolds number, the Mach number other than 1 and the pressure perturbation amplitude of the initiating viscous-inviscid interaction processes. The results of the flow analysis in a laminar boundary layer under the assumption of discontinuity of boundary conditions, for example, discontinuity of the surface velocity, are presented. For such problems a diagram of possible embedded perturbed flow regions is plotted. In addition, the results of studying the nonstationary processes of interaction between the flow in the boundary layer and the external supersonic flow are discussed. (paper)