Two-Dimensional Gas-Dynamic Modeling of the Interaction of a Shock Wave with Beds of Granular Media

A two-dimensional numerical parametric study is made of the interaction of a shock wave with a system of cylinders modeling a bed of a granular medium. The mathematical model is based on the Euler equations. The integration of the defining system of equations in a multiply connected domain is taken using an original computational algorithm of the Cartesian grid method. Computational experiments are carried out with various values for bed permeability and length, the diameter of the cylinder, and channel width. The formulation of the problem imitates natural experiments. The results of all the computational experiments in terms of overpressure behind the reflected and transmitted waves are generalized using a dimensionless criterion. The calculated results are compared with the data from the natural experiments.