The converging shock wave from a spherical or cylindrical piston

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Abstract
A spherical or cylindrical cavity containing quiescent gas begins to contract at high constant radial speed, driving an axisymmetric shock wave inward to collapse at the centre. We analyse the flow field by expanding the solution in powers of time, and calculate 40 terms by delegating the arithmetic to a computer. Analysis of the series for the radius of the shock wave confirms Guderley's local self-similar solution for the focusing, including recent refined values for his similarity exponent, and yields higher terms in his local expansion. In the range of adiabatic exponent where the Guderley solution has been shown not to be unique we find, in accord with a conjecture of Gel'fand, that the smallest admissible similarity exponent is realized.