GSD models for blast propagation]{Two-dimensional geometrical shock dynamics for blast wave propagation and post-shock flow effects

Geometrical shock dynamics (GSD) is a numerical model capable of efficiently predicting the position, shape and strength of a shock wave. Compared to the traditional Euler method that solves the inviscid Euler equations, GSD is a reduced-order model derived from the method of characteristics which results in a more computationally efficient approach since it only considers the motion of the shock front instead of the entire flow field. Here, a study of post-shock flow effects in two dimensions has been performed. These post-shock flow effects become increasingly important when modeling blast wave propagation over extended times or distances, i.e. a shock front that decays in speed and that has decaying properties behind it. A comparison between the first-order complete, and fully complete GSD models (point-source GSD and a model that combines PGSD and the shock-shock approximate theory for cylindrical shock reflection off a straight surface, called PGSDSS) reveals the importance of preserving an intact post-shock flow term, which is truncated by the original GSD model, in predicting blast motion. Lagrangian simulations were performed for the case of interaction between two cylindrical blast waves and results were compared to prior experimental work. Results showed an agreement in attenuation of the maximum pressure at the Mach stem, but an overestimation of the Mach stem growth at its early stage by PGSD was observed.