Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables

For the equations of gas dynamics in Eulerian variables, a family of two-layer time-fully conservative difference schemes (FCDS) with space-profiled time weights is investigated. Nodal schemes and a class of divergent adaptive viscosities for FCDS with space-time profiled weights connected with variable masses of moving nodal particles of the medium are developed. Considerable attention is paid to the methods of constructing regularized flows of mass, momentum and internal energy that preserve the properties of fully conservative difference schemes of this class, to the analysis of their stability and to the possibility of their use on uneven grids. The effective preservation of the internal energy balance in this class of divergent difference schemes is ensured by the absence of constantly operating sources of difference origin that produce "computational’’ entropy (including entropy production on the singular features of the solution). Developed schemes may be used in modelling of high-temperature flows in temperature-disequilibrium media, for example, if it is necessary to take into account the electron-ion relaxation of temperature in a short-living plasma under conditions of intense energy input.