Preprint 2004-028

Propagation of Curved Shock Fronts using Shock Ray Theory and Comparison with Other Theories

S. Baskar and Phoolan Prasad

Abstract: Shock ray theory (SRT) has been found to be quite useful and computationally efficient in finding 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 compatibility 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 geometrical 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 finite charge, into a circular shock front. We find 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.

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S. Baskar, <>
Phoolan Prasad, <>
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<> May 28 2004.

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