Shocks in Vertically Oscillated Granular Layers

TL;DR

This paper investigates shock formation in vertically oscillated granular layers through simulations and continuum modeling, revealing the shock's dynamics, shape, and dependence on inelasticity.

Contribution

It combines molecular dynamics and continuum equations to analyze shock behavior in granular layers, highlighting the effects of inelasticity and validating the models against each other.

Findings

Shock propagates upward in a quarter cycle

Shock velocity increases with decreasing inelasticity

Continuum and molecular dynamics results agree well

Abstract

We study shock formation in vertically oscillated granular layers, using both molecular dynamics simulations and numerical solutions of continuum equations to Navier-Stokes order. A flat layer of grains is thrown up from an oscillating plate during each oscillation cycle and collides with the plate later in the cycle. The collisions produce layer compaction near the plate and a high temperature shock front that rapidly propagates upward through the layer. The shock is highly time-dependent, propagating through the layer in only a quarter of the cycle. We compare numerical solutions of the continuum equations to molecular dynamics simulations that assume binary, instantaneous collisions between frictionless hard spheres. The two simulations yield results for the shock position, shape, and speed that agree well. An investigation of the effect of inelasticity shows that the shock velocity increases continuously with decreasing inelasticity; the elastic limit is not singular.