Abstract
The problem of a strong converging spherical (or cylindrical) shock collapsing at the centre (or axis) of symmetry is extended to take into account the inhomogeneity of a gaseous medium, the density of which is decreasing towards the centre (or axis) according to a power law. The perturbative approach used in this paper provides a global solution to the implosion problem yielding accurately the results of Guderley's similarity solution, which is valid only in the vicinity of the center/axis of implosion. The analysis yields refined values of the leading similarity parameter along with higher-order terms in Guderley's asymptotic solution near the center/axis of convergence. Computations of the flow field and shock trajectory in the region extending from the piston to the center/axis of collapse have been performed for different values of the adiabatic coefficient and the ambient density exponent.
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Madhumita, G., Sharma, V. Propagation of strong converging shock waves in a gas of variable density. Journal of Engineering Mathematics 46, 55–68 (2003). https://doi.org/10.1023/A:1022816118817
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DOI: https://doi.org/10.1023/A:1022816118817