The characteristic Cauchy problem of standard form for~describing the outflow of a polytropic gas into vacuum from an obligue wall

E. I. Pon'kin

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 322-338

Résumé

The initial-boundary value problem for the system of equations of gas dynamics, the solution of which describes the expansion of a polytropic gas into vacuum from an oblique wall in the space of self-similar variables $x/t$, $y/t$ in the general inconsistent case, is reduced to the characteristic Cauchy problem of standard form in the space of new independent variables $\vartheta$, $\zeta$. Equation $\vartheta=0$ defines the characteristic surface through which the double wave adjoins the well-known solution known as the centered Riemann wave. Equation $\zeta=0$ means that an oblique wall is chosen for the new coordinate axis, on which the impermeability condition is satisfied. For this new initial-boundary value problem, in contrast to the well-known solution of a similar problem obtained by S. P. Bautin and S. L. Deryabin in the space of special variables, the theorem of existence and uniqueness for the solution of the system of equations of gas dynamics in the space of physical self-similar variables in the form of a convergent infinite series was proved. An algorithm is described to build the series coefficients.

Détail

Keywords: characteristic Cauchy problem of standard form, analogue of Kovalevskaya's theorem, characteristic surface
Mots-clés : oblique wall, series coefficient construction algorithm.