Technique for determining the types of fault in calculations of gas flows

The 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, a correct definition of the areas occupied by rarefaction waves, contact discontinuities and shock waves is required. The choice of one or another 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 one to single out numerical schemes whose solutions satisfy the requirement of 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.