Capturing shock waves in inelastic granular gases

Shock waves in granular gases generated by hitting an obstacle at rest are treated by means of a shock capturing scheme that approximates the Euler equations of granular gas dynamics with an equation of state (EOS), introduced by Goldshtein and Shapiro [J. Fluid Mech. 282 (1995) 75–114], that takes into account the inelastic collisions of granules. We include a sink term in the energy balance to account for dissipation of the granular motion by collisional inelasticity, proposed by Haff [J. Fluid Mech. 134 (1983) 401–430], and the gravity field added as source terms. We have computed the approximate solution to a one-dimensional granular gas falling on a plate under the acceleration of gravity until the close-packed limit.