Based upon the results of a literature review, a set of physical parameters suitable for quantitative comparison in experimental and numerical studies is determined. The review showed the feasibility of modeling the process of the outflow of an immersed jet of inert gas into the surrounding space and the evolution of a free shear layer formed by hot and cold gases to analyze the process of convective and diffusion transport of various types of particles. In the model formulation we consider the problem of solid destruction by a melt of the same substance, as well as by a nitrogen stream at high temperature. The test simulation of the problems of two-phase interaction of a immersed jet of molten liquid and hot gas, on the whole, qualitatively showed the reproduction of the main characteristics of the flow: The generation of large-scale vortices around the jet in the induction zone, the oscillations of the jet when it collides with an obstacle, and the shape of the cavity formed. © Published under licence by IOP Publishing Ltd.