## 1 Introduction  
The problems considered in the paper relate to the interdisciplinary field of physics (radiation plasma dynamics), which studies the physical and physicochemical processes of the generation of strong shock waves, explosive and cumulative phenomena, thermal broadband radiation in media of finite pressure and vacuum, as well as a complex of the phenomena accompanying the interaction of powerful electromagnetic radiation of different spectral compositions and strong shock waves with matter. Based on the study of these tasks, radiative plasma dynamic systems (RPDS) are developed to solve various problems of engineering, technology, and scientific research, among which the following can be distinguished:  
- electric discharge sources of ultraviolet (UV) radiation and shock waves;  
- development of a new generation of compact, controllable electrophysiological neutron sources;  
- optical pumping of powerful gas lasers in the visible and UV spectral ranges;  
- work related to plasma dynamics in coaxial plasma accelerators with an azimuthal magnetic field;  
- solution of the problem of controlled thermonuclear fusion;  
- solution of a number of environmental problems, such as the purification of natural and industrial (exhaust) gases from harmful impurities (hydrogen sulfide, nitrogen oxides, sulfur dioxide, hydrocarbons, etc. );  
- solution of a wide range of scientific problems (geophysical research, the creation of brightness standards, the study of the processes of interaction of powerful radiation fluxes and intense shock waves with matter, etc.). A great contribution to the study of radiative plasma dynamics was made by the studies carried out in the 1970s [1, 2, 3, 4, 5]. The completed series of theoretical and numerical studies was mainly related to plasma dynamics in coaxial plasma accelerators with an azimuthal magnetic field, which, in particular, led to the creation of a powerful quasi-stationary plasma accelerator. (A plasma flow velocity of more than 400 km/s was achieved. )Carrying out real physical experiments in the considered area of RPDS is characterized by high costs and is associated with many technological and technical difficulties. Therefore, one of the main directions in the development of RPDS at the present stage is the search for effective nonlinear computational models and using them to perform studies of radiation-plasma processes in technical devices, which is of great practical and scientific interest. Thus, it is expedient to determine the radiation and shock-wave characteristics of RPDS by calculation-theoretical methods. At the same time, from the point of view of numerical implementation, mathematical models of RPDS (electric discharge sources) have a number of specific features that must be taken into account when choosing and developing effective methods for their numerical analysis. Let us briefly discuss the most important of them. First, the plasma of the discharges under study consists, as a rule, of several regions with different chemical and physical properties, and the boundaries of these regions undergo strong deformation over time. At the same time, due to the processes of radiative heat transfer and the evaporation of the condensed medium, new portions of matter can enter the computational zone through the indicated boundaries, i.e., there are characteristic difficulties associated with the variability of the gas mass involved in the calculation. For these reasons, the use of Lagrangian coordinates seems inconvenient. When using Euler coordinates, certain problems also arise, the removal of which imposes corresponding requirements on the applied solution methods. In particular, since during the calculation the contact boundary separating plasma regions with different properties can move noticeable distances, the computational scheme of the gasdynamic stage must have a small countable diffusion in order not to \"smear\" the contact boundary zone.