On a two-layer completely conservative difference scheme of gas dynamics in Eulerian variables with adaptive regularization of solution

For the equations of gas dynamics in Eulerian variables, a family of two-layer completely conservative difference schemes with temporal weights profiled on space has been constructed. The effective conservation of an internal energy in this type of divergent difference schemes is ensured by the absence of constantly operating sources of difference origin in the internal energy equation that produce “computational” entropy (including on singular features of the solution). Great attention is paid to the methods of constructing regularizing mass, momentum and internal energy fluxes that do not violate the properties of complete conservatism of difference schemes of this class, to the analysis of their amplitude and to the admissibility of adaptive use on variable structure grids, including on implicit layers in time. The developed type of difference schemes can be used to calculate multitemperature processes (electron and ion temperatures), where for the available number of unknowns, a single balance equation for the total energy of the medium is not enough.