Numerical simulation of imploding shock waves

TL;DRAbstract

A numerical study was made of imploding shock waves. The objective of the present paper is to clarify the propagation and instability of the converging cylindrical and elliptical shock waves. In order to make the simulation, a second order explicit MacCormack type finite difference method was employed to solve the unsteady compressible Euler equations. At first, a one-dimensional simulation was preformed for converging cylindrical shock waves. The results were found to be in good agreement with the Chester, Chisnell and whitham relation. Also, the numerical results were in good agreement with other published 1-D numerical simulations (e.g. method of characteristic). A two-dimensional simulation was also developed for initially perturbed implosions. The governing fluid dynamics equations have been solved in polar coordinates. The 2-D scheme is an extension to the 1-D case, using the operator splitting, where the multi-dimensional solution is evolved from a factored sequence of one dimen

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