2020 , Volume 25, № 4, p.4-19

The aim of this study is to construct a solution to the problem of the decay of a special discontinuity in physical space, i.e., two-dimensional isentropic flows of polytropic gas, arising after the instantaneous destruction of an impenetrable wall that separates an inhomogeneous resting gas from a vacuum. The study takes into account the effect of gravity.Research Methods. A variable, which governs the evolution of the self-similar singularity from the initial interface is introduced into the system of equations of gas dynamics. For the resulting system, the Cauchy problem is posed with prescribed values on the sound characteristic. The solution to this problem is constructed in the form of power series. The coefficients of the series are determined by solving algebraic and ordinary differential equations. Further, to prove the convergence of this series, an initial-boundary-value problem is posed in a special functional space. The solution to this initial-boundary value problem is constructed in the form of its convergent power series and the equivalence of solutions for the first and second initial-boundary value problems is proved.Solutions of the problem for the decay of a special discontinuity are constructed in the form of convergent power series. The equivalence of solutions in the physical and special functional space is proved.Conclusions. The solution constructed in physical space determines the initial conditions for the difference scheme for the numerical simulation of the given characteristic Cauchy problem, while the one, built in a special functional space, allows setting boundary conditions for this scheme