Abstract
Solutions of two-dimensional unsteady self-similar problems of the unlimited shock-free compression and expansion of an ideal gas into a vacuum when the gas is at rest at the initial instant of time inside a prism and cone-shaped bodies at constant density and pressure are constructed. The flow fields are partially constructed using classes of accurate solutions of the non-linear equation for the velocity potential, and partially by numerical calculations, in particular, by the method of characteristics. The features of the formulation of the boundary-value problems for conical unsteady flows are investigated. Approximate laws of the control of the motion of compressing pistons are constructed analytically. The degrees of cumulation of energy and density are obtained and it is shown that the non-uniform compression processes described are more favourable energy-wise than the process of spherical compression for obtaining local superhigh densities of a material. The flow fronts with points of discontinuity are constructed for problems of flow into a vacuum from a cone.
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