Technique for Determining the Types of Discontinuities in the Calculations of Gas Flows

This paper presents a technique for determining the types of discontinuities in the numerical solution of various problems of gas dynamics. The relevance of the topic is determined by the fact that in complex gas-dynamic formulations, the correct definition of the regions occupied by rarefaction waves (RWs), contact discontinuities, and shock waves (SWs) is required. The choice of the scheme for the numerical solution of the problem depends on the correct definition of such regions. In this paper, we present a technique that makes it possible to determine in a unified way the boundaries of regions containing discontinuities and waves of various types. To do this, in terms of the required gas-dynamic functions, inequalities are derived that single out such regions. This information is used when modifying known or constructing new difference schemes in order to increase their stability and/or monotonicity. For example, the resulting inequalities allow us to single out numerical schemes whose solutions satisfy the requirement of a nondecreasing entropy. The main consideration is given in the one-dimensional case. The technique is generalized to the multidimensional case. Examples are given of applying the technique to solving a number of well-known test problems in gas dynamics.