Theoretical analysis of fully conservative difference schemes with adaptive viscosity

For the equations of gas dynamics in Eulerian variables, a family of two-layer in time completely conservative difference schemes with space-profiled time weights is constructed. Considerable attention is paid to the methods of constructing regularized flows of mass, momentum, and internal energy that do not violate the properties of complete conservatism of difference schemes of this class, to the analysis of their amplitudes and the possibility of their use on non-uniform grids. Effective preservation of the balance of internal energy in this type of divergent difference schemes is ensured by the absence of constantly operating sources of difference origin that produce "computational" entropy (including those based on singular features of the solution). The developed schemes can be easily generalized in order to calculate high-temperature flows in media that are nonequilibrium in temperature (for example, in a plasma with a difference in the temperatures of the electronic and ionic components), when, with the set of variables necessary for describing the flow, it is not enough to equalize the total energy balance.