On the basis of the Euler equations, the interaction of a shock wave in a combustible gas with an elliptical bubble of an inert gas of increased density is numerically simulated within a plane two-dimensional formulation. The finite-volume Godunov-type method of the second order of approximation is applied. Gas combustion is modeled using the Korobeinikov-Levin two-stage kinetics. Various values of the Mach number of the incident wave and the elongation of the inert bubble are considered, and the refraction and focusing of the incident shock are described. Qualitatively different regimes of gas detonation initiation have been found, including direct initiation by a strong wave, ignition upon reflection of an average-intensity wave from the gas interface, and upon focusing of secondary shock waves at lower shock Mach numbers. The dependence of the ignition mode on the shock intensity and the shape of the bubble is determined.

Based on the numerical solution of the Euler equations, the problem of the interaction of a shock wave with an ellipsoidal gas bubble of increased density adjacent to a solid wall is studied. The process of refraction and focusing of the shock wave is described - the formation and reflection of transverse shock waves from the axis of symmetry and from the wall. It is found that, depending on the shape of the bubble, qualitatively different flow regimes take place, in which the focusing of the wave on the axis of symmetry occurs before or after the beginning of the reflection of the wave transmitted through the bubble from the wall. The grid convergence of various measures of impulse shock impact on the wall is studied and their dependence on the bubble shape is determined. The highest pressure impulse is achieved for slightly flattened bubbles, when the transverse waves are focused near the center of the wall immediately after the plane transmitted wave is reflected from it.