Propagation of curved shock fronts using shock ray theory and comparison with other theories

conservation laws, shock dynamics, blast waves, piston problems. Shock ray theory (SRT) has been found to be quite useful and computationally ecient in nding successive positions of a curved weak shock front. In this article we solve some piston problems and show that the shock ray theory with two com-patibility conditions gives shock positions, which are very close to those obtained by solving the same problems by numerical solution of Euler's equations (Euler Solutions). Comparison of the results obtained by shock ray theory and geometri-cal shock dynamics (GSD) of Whitham with Euler solution shows that the shock ray theory gives more accurate results for any piston motion. Aim of the work is not just this comparison but also in investigating the role of the nonlinearity in accelerating the process of evolution of a shock, produced by an explosion of a non-circular nite charge, into a circular shock front. We nd that the nonlinear waves propagating on the shock front appreciably accelerate this process. We also discuss a situation, for shock Mach number very close to 1, when GSD and shock ray theory may fail to give any result.