Normal shock propagation in a granular funnel

We examined the propagation of a normal shock formed in a quasi-two dimensional funnel. We compare results from experiment and MD simulations to a Hugoniot-Rankine type approximation of the inelastic continuum equations. Both MD and experimental results show behavior similar to the simplified equations, but inelastic collisions cause evolution of the shock unaccounted for in this simple approximation. We find the flow parameters behind the shock and the shock speed as a function of inelasticity compare well with an asymptotic solution of a set of inelastic equations proposed by Goldshtein, et al [1-2].\newline \newline [1] A. Goldshtein et al. \textit{JFM} \textbf{287}, 349 (1995). \newline [2] V. Kamenetsky et al$.$ \textit{Phys of Fluids} \textbf{12}, 3036 (2000):