  A new class of integro-partial differential equation models is derived for
the prediction of granular flow dynamics. These models are obtained using a
novel limiting averaging method (inspired by techniques employed in the
derivation of infinite-dimensional dynamical systems models) on the Newtonian
equations of motion of a many-particle system incorporating widely used
inelastic particle-particle force formulas. By using Taylor series expansions,
these models can be approximated by a system of partial differential equations
of the Navier-Stokes type. The exact or approximate governing equations
obtained are far from simple, but they are less complicated than most of the
continuum models now being used to predict particle flow behavior. Solutions of
the new models for granular flows down inclined planes and in vibrating beds
are compared with known experimental and analytical results and good agreement
is obtained.
