Two-Layer Completely Conservative Difference Scheme of Gas Dynamics in Eulerian Variables with Adaptive Regularization of Solution

摘要

For the equations of gas dynamics in Euler variables, a family of two-layer in time completely conservative difference schemes profiled on the space with time weights is constructed. The effective conservation of 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, producing "computational" entropy (including singularities of the solution). Considerable attention in this work is paid to the methods of constructing regularizing mass, momentum and internal energy flows that do not violate the properties of complete conservatism of difference schemes of this class, to the analysis of their amplitude and admissibility of adaptive use on variable structure grids in space and on implicit layers in time. The developed type of difference schemes can be used to calculate multi-temperature processes (electron and ion temperatures), where for the available number of variables, a single balance equation for the total energy of the medium is not enough.