Definition of discontinuity types in computational gas dynamics

The paper proposes a technique for determining the types of discontinuities in gas dynamics problems in Euler variables. This technique makes it possible to determine the discontinuities of the solution without involving the Riemann problem, which makes it possible to solve gas dynamics problems with an arbitrary equation of state. This approach works efficiently for multidimensional problems and can be effectively used on parallel computing machines, since the type of the discontinuity is determined locally in each computational cell. This method allows to adapt the computational algorithm to regions occupied by different types of discontinuities, which provides an optimal artificial viscosity for obtaining monotonic solutions and ensuring the condition of non-diminishing entropy. This paper gives an example of a gas dynamics problem, in which different types of discontinuities are present.