Post-shock flow effect in geometrical shock dynamics model

Focusing of shock waves can generate extreme thermodynamic conditions, such as high pressure and temperature, at the focal region. Among all numerical approaches to simulate the propagation of shock waves, geometrical shock dynamics (GSD) is an appealing model to predict the shock motion. Compared to the traditional Euler method, such simplified model is much more computationally efficient especially for converging shock waves. Assuming uniform initial state behind the shock, GSD has shown its success in evaluating the effect of geometry change upon the shock, but the ignorance of the interaction between the shock front and non-uniform flow immediately behind it (post-shock flow effect) leads to a significant loss of accuracy when blast waves are considered, where an initial decay of all major flow properties is presented just behind the blast front. Such post-shock flow effect can be expressed as infinite number of coupled non-linear differential equations, and the influence of the order of completeness of such closed system on accuracy is studied in this work. Several comparisons are also performed with a similar approach that takes into account the post-shock flow effect by coupling the post-shock flow conditions obtained from existing data into the 0^th-order GSD solution.