Isentropic self-similar gas compression

Self-similar isentropic compression of perfect gas is studied in 1D spherical and cylindrical symmetry for two cases: (1) compression of homogeneous gas by means of smooth compression wave (e.g. with the help of convergent piston) and (2) steady velocity convergence of gas shell with self-similar initial profile of gas. Main attention is paid to flows with two-stage limited compression of matter by smooth isentropic convergent wave and shock wave reflected from the center of symmetry with jump of entropy. Being isentropic the solutions present the most efficient way to dynamically compress the gas, which can be used in various experimental program on inertial confinement fusion and similar. The presented solutions can be useful to test numerical codes designed to simulate the problem with so strong sharpening of flows.