SELF-CONSISTENT ISOLATION OF DISCONTINUITIES IN CONTINUOUS CALCULATIONS OF GAS-DYNAMIC FLOWS

New algorithms for the self-consistent isolation of discontinuities when constructing numerical solutions of one-dimensional and axisymmetric problems of gas dynamics are presented. Self-consistent isolation is taken to mean the use of special adjustable grids which, over the course of time, automatically capture and then track accurately specific discontinuities that arise in gas-dynamic flow. An essential feature of the approach is that when discontinuities are isolated in this way the difference scheme remains continuous. The algorithms combine the advantages and simplicity of the methods of the continuous calculation of flows (ENO-methods in this paper) with the accuracy of the calculation of discontinuities by methods in which they are isolated specially. The effectiveness of the approach is illustrated by examples of the calculation of one-dimensional and axisymmetric problems.