Mathematical modeling of instabilities in the interaction of wave processes with the contact discontinuities between gases of different densities

Abstract

Works performed in the field of mathematical modeling of the process of mixing of gases of different densities on the interface between them under the action of transmitted and reflected shock waves and compression and rarefaction waves are reviewed. A mathematical model of two-velocity, two-temperature gases, which has been derived from the basic principles, is proposed for this modeling. A number of examples on the interaction of the above wave processes with the interfaces in helium–xenon and helium–argon mixtures are given; the appearing Richtmyer–Meshkov instability and the distinctive features of the wave dynamics of flow of a mixture are described. The performed comparison of the time dependence of the mixing-zone breadth and other dependences has shown that the description of the phenomenon within the framework of the proposed approach is satisfactory.