Features of non-stationary self-similar, supersonic axisymmetric and two-dimensional conic flows of ideal (non-viscous and non-heat-conducting) gas with shock waves (SW) are described. Self-similar one-dimensional non-stationary problems are considered in the assumption of change of adiabatic exponent on SW, coming («reflected») from the centre or an axis of symmetry (further ? symmetry centre SC) or from a plane. Problems of the collapse of an empty spherical cavity, of reflection of strong SW from SC and a simpler problem with self-similarity exponent unity are considered. In the assumption of adiabatic exponent growth self-similar solutions of the two first problems are rejected because of entropy reduction from the moment of SW reflection. In the assumption of adiabatic exponent reduction the solution of these problems for the same reason become unsuitable only after the lapse of finite time. Until the reduction of adiabatic exponent has reached some threshold, the structure of the self-similar solution does not undergo qualitative changes. Beyond the specified threshold, the self-similar solution is possible, when cylindrical or spherical piston extends under the special law from the moment of the reflection from SC. In the absence of the piston the flow behind the reflected wave is no more self-similar. In stagnating flat flows, modes with SW adjunction to a centered rarefaction wave from different sides are possible. In supersonic streams going to a symmetry axis weak SW strengthening and their irregular reflection from the axis is studied. In the approach of nonlinear acoustics, in contradiction with results of Euler equations, numerical integration strengthening of weak SW does not depend on and Mach number of the flow. A nonlinear theory is constructed which lacks this deficiency. It is shown for conic flows arising for supersonic flows over angular configurations of crossing semi-planes, that both rarefaction and compression flows can continuously adjoin to the conically supersonic uniform flow on a Mach cone. The erroneous statement about the impossibility of the second became the basis for the introduction of the so-called «hanging» discontinuities.
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