Numerical simulation of cylindrically converging shock waves

The converging shock wave is assumed to be generated by an instantaneous energy release on a rigid cylindrical wall. The fluid flow caused by its propagation is numerically simulated. The behavior of the solution in the focusing stage is closely investigated and compared with the selfsimilar solution. Results include new details of the transition of the solution from the nonselfsimilar region to the selfsimilar region. Numerical methods such as the random choice method, the method of characteristics, and the second-order accurate finite difference method with artificial viscosities are adopted. The results are also compared with those of the method of integral relations. They all agreed well with one another except for the focusing stage. The random choice method and the method of characteristics produce nearly identical results in the focusing stage, suggesting the mutual credibility of the two methods. Artificial viscosities involved in the finite difference scheme smear out the shock front as it approaches the axis. The comparison with the selfsimilar solution is then difficult.