  We present a multiscale simulation algorithm for amorphous materials, which
we illustrate and validate in a canonical case of dense granular flow. Our
algorithm is based on the recently proposed Spot Model, where particles in a
dense random packing undergo chain-like collective displacements in response to
diffusing "spots" of influence, carrying a slight excess of interstitial free
volume. We reconstruct the microscopic dynamics of particles from the "coarse
grained" dynamics of spots by introducing a localized particle relaxation step
after each spot-induced block displacement, simply to enforce packing
constraints with a (fairly arbitrary) soft-core repulsion. To test the model,
we study to what extent it can describe the dynamics of up to 135,000
frictional, viscoelastic spheres in granular drainage simulated by the
discrete-element method (DEM). With only five fitting parameters (the radius,
volume, diffusivity, drift velocity, and injection rate of spots), we find that
the spot simulations are able to largely reproduce not only the mean flow and
diffusion, but also some subtle statistics of the flowing packings, such as
spatial velocity correlations and many-body structural correlations. The spot
simulations run over 100 times faster than DEM and demonstrate the possibility
of multiscale modeling for amorphous materials, whenever a suitable model can
be devised for the coarse-grained spot dynamics.
